Digital waves in economics

Ledenyov, Dimitri O. and Ledenyov, Viktor O. (2015): Digital waves in economics.

Abstract

The recent discovery of the Ledenyov digital waves in the economies of scale and scope led to an origination of considerable scientific interest in the modeling of new types of the discrete-time digital signals generators for the business cycles generation in the macroeconomics. Article aims: 1) to model the discrete-time digital signals generators for the business cycles generation in the macroeconomics, 2) to demonstrate the technical differences between the new model of the discrete-time digital signals generator and the existing models of the continuous-time (continuous wave) signals generators in the macroeconomics; 3) to accurately analyze the spectrum of discrete-time digital signals in the economies of scale and scope, 4) to improve the Ledenyov discrete time digital signals theory to precisely characterize the discrete time digital signals in the macroeconomics, 5) to better develop the complex software program to forecast the business cycles, going from the spectral analysis of the discrete time digital signals and the continuous time signals in the nonlinear dynamic economic system over the selected time period. The developed MicroSA software program intends: 1) to perform the spectrum analysis of the discrete-time digital signals and the continuous-time signals in the macroeconomics; 2) to make the computer modeling and to forecast the business cycles, going from the spectral analysis of the discrete time signals and the continuous time signals in the macroeconomics. The MicroSA can be used by a) the central banks with the purpose to make the strategic decisions on the monetary policies, financial stability policies, and b) the commercial/investment banks with the aim to make the business decisions on the minimum capital allocation, countercyclical capital buffer creation, and capital investments.

• Item Type: MPRA Paper
• Language: English
• Keywords: discrete-time digital waves, discrete-time digital signals generators, spectrum analysis of discrete-time digital signals, amplitude of discrete-time digital signal, frequency of discrete-time digital signal, wavelength of discrete-time digital signal, period of discrete-time digital signal, phase of discrete-time digital signal, mixing of discrete-time digital signals, harmonics of discrete-time digital signal, nonlinearities of discrete-time digital signal, Juglar fixed investment cycle, Kitchin inventory cycle, Kondratieff long wave cycle, Kuznets infrastructural investment cycle, econophysics, econometrics, nonlinear dynamic economic system, economy of scale and scope, macroeconomics.
• Subjects: E - Macroeconomics and Monetary Economics > E0 - General; E - Macroeconomics and Monetary Economics > E0 - General > E00 - General; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E10 - General; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E17 - Forecasting and Simulation: Models and Applications; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E20 - General; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E22 - Investment ; Capital ; Intangible Capital ; Capacity; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E27 - Forecasting and Simulation: Models and Applications; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E30 - General; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E37 - Forecasting and Simulation: Models and Applications; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E40 - General; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E44 - Financial Markets and the Macroeconomy; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E47 - Forecasting and Simulation: Models and Applications; E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E50 - General; E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E58 - Central Banks and Their Policies; F - International Economics > F0 - General; F - International Economics > F4 - Macroeconomic Aspects of International Trade and Finance > F40 - General; F - International Economics > F4 - Macroeconomic Aspects of International Trade and Finance > F41 - Open Economy Macroeconomics; F - International Economics > F4 - Macroeconomic Aspects of International Trade and Finance > F44 - International Business Cycles; F - International Economics > F4 - Macroeconomic Aspects of International Trade and Finance > F47 - Forecasting and Simulation: Models and Applications; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O31 - Innovation and Invention: Processes and Incentives; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O33 - Technological Change: Choices and Consequences ; Diffusion Processes; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O35 - Social Innovation

References

Economics Science, Finance Science, Economic History Science:

1. Joseph Penso de la Vega 1668, 1996 Confusión de Confusiones re-published by John Wiley and Sons Inc USA.

2. Mortimer Th 1765 Every man his own broker 4th edition London UK.

3. Smith A 1776, 2008 An inquiry into the nature and causes of the wealth of nations W Strahan and T Cadell London UK, A Selected Edition edited by Kathryn Sutherland Oxford Paperbacks Oxford UK.

4. Menger C 1871 Principles of Economics (Grundsätze der Volkswirtschaftslehre) Ludwig von Mises Institute Auburn Alabama USA http://www.mises.org/etexts/menger/Mengerprinciples.pdf .

5. Bagehot W 1873, 1897 Lombard Street: A description of the money market Charles Scribner's Sons New York USA.

6. von Böhm-Bawerk E 1884, 1889, 1921 Capital and interest: History and critique of interest theories, positive theory of capital, further essays on capital and interest Austria; 1890 Macmillan and Co Smart W A (translator) London UK http://files.libertyfund.org/files/284/0188_Bk.pdf .

7. Hirsch M 1896 Economic principles: A manual of political economy The Russkin Press Pty Ltd 123 Latrobe Street Melbourne Australia.

8. Bachelier L 1900 Theorie de la speculation Annales de l’Ecole Normale Superieure Paris France vol 17 pp 21 – 86.

9. Schumpeter J A 1906 Über die mathematische methode der theoretischen ökonomie ZfVSV Austria.

10. Schumpeter J A 1933 The common sense of econometrics Econometrica.

11. Schumpeter J A 1911; 1939, 1961 Theorie der wirtschaftlichen entwicklung; The theory of economic development: An inquiry into profits, capital, credit, interest and the business cycle Redvers Opie (translator) OUP New York USA.

12. Schumpeter J A 1939 Business cycle McGraw-Hill New York USA.

13. Schumpeter J A 1947 The creative response in economic history Journal of Economic History vol 7 pp 149 – 159.

14. Slutsky E E 1910 Theory of marginal utility M Sc Thesis Vernadsky National Library Kiev Ukraine.

15. Slutsky Е Е 1915 Sulla teoria sel bilancio del consumatore Giornale degli economisti e rivista di statistica 51 no 1 pp 1 – 26 Italy.

16. Slutsky E E 1923 On calculation of state revenue from emission of paper money Local Economy 2 pp 39 – 62 Kiev Ukraine.

17. von Mises L 1912 The theory of money and credit Ludwig von Mises Institute Auburn Alabama USA http://mises.org/books/Theory_Money_Credit/Contents.aspx .

18. Hayek F A 1931, 1935, 2008 Prices and production 1st edition Routledge and Sons London UK, 2nd edition Routledge and Kegan Paul London UK, 2008 edition Ludwig von Mises Institute Auburn Alabama USA.

19. Hayek F A 1948, 1980 Individualism and economic order London School of Economics and Political Science London UK, University of Chicago Press Chicago USA.

20. Keynes J M 1936 The general theory of employment, interest and money Macmillan Cambridge University Press Cambridge UK.

21. Keynes J M 1998 The collected writings of John Maynard Keynes Cambridge University Press Cambridge UK ISBN 978-0-521-30766-6.

22. Ellis H, Metzler L (editors) 1949 Readings in the theory of international trade Blakiston Philadelphia USA.

23. Friedman M (editor) 1953 Essays in positive economics Chicago University Press Chicago USA.

24. Baumol W 1957 Speculation, profitability, and stability Review of Economics and Statistics 39 pp 263 – 271.

25. Debreu G 1959 Theory of value Cowles Foundation Monograph vol 17 John Wiley & Sons Inc New York USA.

26. Minsky H P 1974 The modeling of financial instability: An introduction Modeling and Simulation Proceedings of the Fifth Annual Pittsburgh Conference 5.

27. Minsky H P May 1992 The financial instability hypothesis Working Paper no 74: 6–8 http://www.levy.org/pubs/wp74.pdf .

28. Minsky H P 2015 Minsky archive The Levy Economics Institute of Bard College Blithewood Bard College Annandale-on-Hudson New York USA http://www.bard.edu/library/archive/minsky/ .

29. Krugman P, Wells R 2005 Economics Worth Publishers 1st edition ISBN-10: 1572591501 ISBN-13: 978-1572591509 pp 1 – 1200.

30. Stiglitz J E 2005 Principles of macroeconomics W W Norton 4th edition ISBN-10: 0393926249 ISBN-13: 978-0393926248 pp 1 – 526.

31. Stiglitz J E 2015 The great divide Public Lecture on 19.05.2015 London School of Economics and Political Science London UK http://media.rawvoice.com/lse_publiclecturesandevents/richmedia.lse.ac.uk/publiclecturesandevents/20150519_1830_greatDivide.mp4 .

32. Dodd N 2014 The social life of money Princeton University Press NJ USA ISBN: 9780691141428 pp 1 – 456.

Juglar Economic Cycle:

33. Juglar C 1862 Des crises commerciales et de leur retour périodique en France en Angleterre et aux États-Unis Guillaumin Paris France.

34. Schumpeter J A 1939 Business cycle McGraw-Hill New York USA.

35. Grinin L E, Korotayev A V, Malkov S Y 2010 A mathematical model of Juglar cycles and the current global crisis in History & Mathematics Grinin L, Korotayev A, Tausch A (editors) URSS Moscow Russian Federation.

Kondratiev Economic Cycle:

36. Kondratieff N D 1922 The world economy and its trends during and after war Regional branch of state publishing house Vologda Russian Federation.

37. Kondratieff N D 1925 The big cycles of conjuncture The problems of conjuncture 1 (1) pp 28 – 79.

38. Kondratieff N D 1926 Die langen wellen der konjunktur Archiv fuer Sozialwissenschaft und Sozialpolitik 56 (3) pp 573 – 609.

39. Kondratieff N D 1928 The big cycles of conjuncture Institute of Economics RANION Moscow Russian Federation.

40. Kondratieff N D, Stolper W F 1935 The long waves in economic life Review of Economics and Statistics The MIT Press 17 (6) pp 105 – 115 doi:10.2307/1928486 JSTOR 1928486.

41. Kondratieff N D 1984 The Long wave cycle Richardson & Snyder New York USA.

42. Kondratieff N D 2002 The big cycles of conjuncture and theory of forecast Economics Moscow Russian Federation.

43. Garvy G 1943 Kondratieff's theory of long cycles Review of Economic Statistics 25 (4) pp 203 – 220.

44. Silberling N J 1943 The dynamics of business: An analysis of trends, cycles, and time relationships in American economic activity since 1700 and their bearing upon governmental and business policy McGraw-Hill New York USA.

45. Rostow W W 1975 Kondratieff, Schumpeter and Kuznets: Trend periods revisited Journal of Economic History 25 (4) pp 719 – 753.

46. Forrester J W 1978 Innovation and the economic long wave MIT System Dynamics Group Working Paper Massachusetts Institute of Technology Cambridge USA.

47. Forrester J W 1981 The Kondratieff cycle and changing economic conditions MIT System Dynamics Group Working Paper Massachusetts Institute of Technology Cambridge USA.

48. Forrester J W 1985 Economic conditions ahead: Understanding the Kondratieff wave Futurist 19 (3) pp 16 – 20.

49. Kuczynski Th 1978 Spectral analysis and cluster analysis as mathematical methods for the periodization of historical processes: Kondratieff cycles – Appearance or reality? Proceedings of the Seventh International Economic History Congress vol 2 International Economic History Congress Edinburgh UK pp 79–86.

50. Kuczynski Th 1982 Leads and lags in an escalation model of capitalist development: Kondratieff cycles reconsidered Proceedings of the Eighth International Economic History Congress vol B3 International Economic History Congress Budapest Hungary pp 27.

51. Barr K 1979 Long waves: A selective annotated bibliography Review 2 (4) pp 675 – 718.

52. Van Duijn J J 1979 The long wave in economic life De Economist 125 (4) pp 544 – 576.

53. Van Duijn J J 1981 Fluctuations in innovations over time Futures 13(4) pp 264 – 275.

54. Van Duijn J J 1983 The long wave in economic life Allen and Unwin Boston MA USA.

55. Eklund K 1980 Long waves in the development of capitalism? Kyklos 33 (3) pp 383 – 419.

56. Mandel E 1980 Long waves of capitalist development Cambridge University Press Cambridge UK.

57. Van der Zwan A 1980 On the assessment of the Kondratieff cycle and related issues in Prospects of Economic Growth Kuipers S K, Lanjouw G J (editors) North-Holland Oxford UK pp 183 – 222.

58. Tinbergen J 1981 Kondratiev cycles and so-called long waves: The early research Futures 13 (4) pp 258 – 263.

59. Van Ewijk C 1982 A spectral analysis of the Kondratieff cycle Kyklos 35 (3) pp 468 – 499.

60. Cleary M N, Hobbs G D 1983 The fifty year cycle: A look at the empirical evidence in Long Waves in the World Economy Freeman Chr (editor) Butterworth London UK pp 164 – 182.

61. Glismann H H, Rodemer H, Wolter W 1983 Long waves in economic development: Causes and empirical evidence in Long Waves in the World Economy Freeman Chr (editor) Butterworth London UK pp 135 – 163.

62. Bieshaar H, Kleinknecht A 1984 Kondratieff long waves in aggregate output? An econometric test Konjunkturpolitik 30 (5) pp 279 – 303.

63. Wallerstein I 1984 Economic cycles and socialist policies Futures 16 (6) pp 579 – 585.

64. Zarnowitz V 1985 Recent work on business cycles in historical perspective: Review of theories and evidence Journal of Economic Literature 23 (2) pp 523 – 580.

65. Summers L H 1986 Some skeptical observations on real business cycle theory Federal Reserve Bank of Minneapolis Quarterly Review 10 pp 23 – 27.

66. Freeman C 1987 Technical innovation, diffusion, and long cycles of economic development in The long-wave debate Vasko T (editor) Springer Berlin Germany pp 295–309.

67. Freeman C, Louçã F 2001 As time goes by: From the industrial revolutions to the information revolution Oxford University Press Oxford UK.

68. Goldstein J 1988 Long cycles: Prosperity and war in the modern age Yale University Press New Haven CT USA.

69. Solomou S 1989 Phases of economic growth, 1850–1973: Kondratieff waves and Kuznets swings Cambridge University Press Cambridge UK.

70. Berry B J L 1991 Long wave rhythms in economic development and political behavior Johns Hopkins University Press Baltimore MD USA.

71. Metz R 1992 Re-examination of long waves in aggregate production series New Findings in Long Wave Research Kleinknecht A, Mandel E, Wallerstein I (editors) St. Martin’s New York USA pp 80 – 119.

72. Metz R 1998 Langfristige wachstumsschwankungen – Trends, zyklen, strukturbrüche oder zufall Kondratieffs Zyklen der Wirtschaft. An der Schwelle neuer Vollbeschäftigung? Thomas H, Nefiodow L A, Herford (editors) pp 283 – 307.

73. Metz R 2006 Empirical evidence and causation of Kondratieff cycles Kondratieff Waves, Warfare and World Security Devezas T C (editor) IOS Press Amsterdam The Netherlands pp 91 – 99.

74. Tylecote A 1992 The long wave in the world economy Routledge London UK.

75. Cooley Th (editor) 1995 Frontiers of business cycle research Princeton University Press USA ISBN 0-691-04323-X.

76. Modelski G, Thompson W R 1996 Leading sectors and world politics: The co-evolution of global politics and economics University of South Carolina Press Columbia SC USA.

77. Modelski G 2001 What causes K-waves? Technological Forecasting and Social Change 68 pp 75 – 80.

78. Modelski G 2006 Global political evolution, long cycles, and K-waves Kondratieff Waves, Warfare and World Security Devezas T C (editor) IOS Press Amsterdam The Netherlands pp 293 – 302.

79. Perez C 2002 Technological revolutions and financial capital – The dynamics of bubbles and golden ages Edward Elgar Cheltenhem UK.

80. Rennstich J K 2002 The new economy, the leadership long cycle and the nineteenth K-wave Review of International Political Economy 9 pp 150 – 182.

81. Rumyantseva S Yu 2003 Long waves in economics: Multifactor analysis St. Petersburg University Publishing House St. Petersburg Russian Federation.

82. Diebolt C, Doliger C 2006 Economic cycles under test: A spectral analysis in Kondratieff Waves, Warfare and World Security Devezas T C (editor) IOS Press Amsterdam The Netherlands pp 39 – 47.

83. Linstone H A 2006 The information and molecular ages: Will K-waves persist? Kondratieff Waves, Warfare and World Security edited by Devezas T C IOS Press Amsterdam The Netherlands pp 260 – 269.

84. Thompson W 2007 The Kondratieff wave as global social process in World System History, Encyclopedia of Life Support Systems Modelski G (editor) EOLSS Publishers Oxford UK http://www.eolss.net.

85. Papenhausen Ch 2008 Causal mechanisms of long waves Futures 40 pp 788 – 794.

86. Korotayev A V, Tsirel S V 2010 A spectral analysis of world GDP dynamics: Kondratieff waves, Kuznets swings, Juglar and Kitchin cycles in global economic development, and the 2008–2009 economic crisis Structure and Dynamics vol 4 issue 1 pp 1 – 55 http://www.escholarship.org/uc/item/9jv108xp .

87. Wikipedia 2015a Kondratieff Wikipedia USA www.wikipedia.org.

Kitchin Economic Cycle:

88. Kitchin J 1923 Cycles and trends in economic factors Review of Economics and Statistics The MIT Press 5 (1) pp 10 – 16 doi:10.2307/1927031 JSTOR 1927031.

Kuznets Economic Cycle:

89. Kuznets S 1924 Economic system of Dr. Schumpeter M. Sc. Thesis under Prof. Wesley Clair Mitchell Columbia University NY USA.

90. Kuznets S 1930 Secular movements in production and prices Ph. D. Thesis under Prof. Wesley Clair Mitchell Columbia University NY USA.

91. Kuznets S 1930 Secular movements in production and prices. Their nature and their bearing upon cyclical fluctuations Houghton Mifflin Boston USA.

92. Kuznets S 1937 National income and capital formation, 1919 – 1935.

93. Kuznets S 1941 National income and its composition, 1919 – 1938.

94. Kuznets S March 1955 Economic growth and income inequality American Economic Review 45 pp 1 – 28.

95. Kuznets S 1963 Quantitative aspects of the economic growth of nations, VIII: The distribution of income by size Economic Development and Cultural Change 11 pp 1 – 92.

96. Kuznets S 1966 Modern economic growth: Rate, structure, and spread.

97. Kuznets S 1968 Toward a theory of economic growth, with reflections on the economic growth of modern nations.

98. Kuznets S 1971 Economic growth of nations: Total output and production structure.

99. Kuznets S 1973a Population, capital and growth.

100. Kuznets S 1973b Modern economic growth: Findings and reflections American Economic Review 63 pp 247 – 58.

101. Abramovitz M 1961 The nature and significance of Kuznets cycles Economic Development and Cultural Change 9 (3) pp 225 – 248.

102. Abramovitz M March 1986 Simon Kuznets 91901 – 1985) The Journal of Economic History vol 46 no 1 pp 241 – 246.

103. Lundberg E 1971 Simon Kuznets contributions to economics The Swedish Journal of Economics 73 (4) pp 444 – 459 DOI:10.2307/3439225, JSTOR 3439225.

104. Hozelitz B F January 1983 Bibliography of Simon Kuznets Economic Development and Cultural Change vol 31 no 2 pp 433 – 454.

105. Ben-Porath Y April 1988 Simon Kuznets in person and in writing Economic Development and Cultural Change vol 36 no 3 pp 435 – 447.

106. Street J H June 1988 The contribution of Simon S. Kuznets to institutionalist development theory Journal Economic Issues vol 22 no 2 pp 499 – 509.

107. Kapuria-Foreman V, Perlman M November 1995 An economic historian’s economist: Remembering Simon Kuznets The Economic Journal 105 pp 1524 – 1547.

108. Fogel R W 2000 Simon S. Kuznets: April 30, 1901 – July 9, 1985 NBER Working Paper no W7787 NBER USA.

109. Fogel R W, Fogel E M, Guglielmo M, Grotte N 2013 Political arithmetic: Simon Kuznets and the empirical tradition in economics University of Chicago Press Chicago USA ISBN 0-226-25661-8.

110. Syed M K, Mohammad M J 2004 Revisiting Kuznets hypothesis: An analysis with time series and panel data Bangladesh Development Studies 30 (3-4) pp 89 – 112.

111. Diebolt C, Doliger C 2008 New international evidence on the cyclical behaviour of output: Kuznets swings reconsidered. Quality & quantity. International Journal of Methodology 42 (6) pp 719 – 737.

112. Wikipedia 2015b Simon Kuznets Economist Wikipedia USA www.wikipedia.org.

Accurate Characterization of Properties of Economic Cycles:

113. George H 1881, 2009 Progress and poverty Kegan Paul USA; reissued by Cambridge University Press Cambridge UK ISBN 978-1-108-00361-2.

114. Schumpeter J A 1939 Business cycle McGraw-Hill New York USA.

115. Burns A F, Mitchell W C 1946 Measuring business cycles National Bureau of Economic Research New York USA.

116. Dupriez L H 1947 Des mouvements economiques generaux vol 2 pt 3 Institut de Recherches Economiques et Sociales de 1'Universite de Louvain Belgium.

117. Samuelson P A 1947 Foundations of economic analysis Harvard University Press Cambridge MA USA.

118. Hicks J R 1950 A contribution to the theory of the trade cycle Oxford University Press Oxford UK.

119. Goodwin R M 1951 The nonlinear accelerator and persistence of business cycles Econometrica 19 no 1 pp 1 – 17.

120. Inada K, Uzawa H 1972 Economical development and fluctuations Iwanami Tokyo Japan.

121. Bernanke B S 1979 Long-term commitments, dynamic optimization, and the business cycle Ph. D. Thesis Department of Economics Massachusetts Institute of Technology USA.

122. Marchetti C 1980 Society as a learning system: Discovery, invention, and innovations cycles revisited Technological Forecast and Social Change 18 pp 257 – 282.

123. Kleinknecht A 1981 Innovation, accumulation, and crisis: Waves in economic development? Review 4 (4) pp 683 – 711.

124. Dickson D 1983 Technology and cycles of boom and bust Science 219 (4587) pp 933 – 936.

125. Hodrick R J, Prescott E C 1997 Postwar U.S. business cycles: An empirical investigation Journal of Money, Credit, and Banking vol 29 no 1 pp 1 – 16.

126. Anderson H M, Ramsey J B 1999 Economic Research Reports PR # 99-01 New York University NY USA.

127. Baxter M, King R G 1999 Measuring business cycles: Approximate band-pass filters for economic time series Review of Economics and Statistics 81 (4) pp 575 – 593.

128. Kim Ch-J, Nelson Ch 1999 Has the U.S. economy become more stable? A Bayesian approach based on a Markov-switching model of the business cycle Review of Economics and Statistics.

129. McConnell M, Pérez-Quirós G 2000 Output fluctuations in the United States: What has changed since the early 1980s? American Economic Review.

130. Devezas T C, Corredine J T 2001 The biological determinants of long-wave behavior in socioeconomic growth and development Technological Forecasting & Social Change 68 pp 1 – 57.

131. Devezas T C, Corredine J T 2002 The nonlinear dynamics of technoeconomic systems. An informational interpretation Technological Forecasting & Social Change 69 pp 317 – 357.

132. Devezas T C (editor) 2006 Kondratieff Waves, Warfare and World Security IOS Press Amsterdam The Netherlands.

133. Arnord L 2002 Business cycle theory Oxford University Press Oxford UK 2002.

134. Stock J, Watson M 2002 Has the business cycle changed and why? NBER Macroeconomics Annual NBER USA.

135. Helfat C E, Peteraf M A 2003 The dynamic resource-based view: Capability life cycles Strategic Management Journal 24 (10) pp 997 – 1010.

136. Selover D D, Jensen R V, Kroll J 2003 Studies in Nonlinear Dynamics & Econometrics 7 p 1.

137. Sussmuth B 2003 Business cycles in the contemporary World Springer Berlin Heidelberg Germany.

138. Hirooka M 2006 Innovation dynamism and economic growth: A nonlinear perspective Edward Elgar Cheltenham UK Northampton MA USA.

139. Kleinknecht A, Van der Panne G 2006 Who was right? Kuznets in 1930 or Schumpeter in 1939? in Kondratieff Waves, Warfare and World Security Devezas T C (editor) IOS Press Amsterdam The Netherlands pp 118 – 127.

140. Iyetomi H, Aoyama H, Ikeda Y, Souma W, Fujiwara Y 2008 Econophysics Kyoritsu Shuppan Tokyo Japan.

141. Iyetomi H, Nakayama Y, Yoshikawa H, Aoyama H, Fujiwara Y, Ikeda Y, Souma W 2011 What causes business cycles? Analysis of the Japanese industrial production data Journal of the Japanese and International Economies 25 (3) pp 246 – 272.

142. Iyetomi H, Aoyama H, Fujiwara Y, Sato A-H (editors) 2012 Econophysics 2011 - The Hitchhiker's guide to the economy Proceedings of the YITP Workshop on Econophysics Japan Progress of Theoretical Physics Supplement no 194.

143. Jourdon Ph 2008 La monnaie unique Europeenne et son lien au developpement economique et social coordonne: une analyse cliometrique Thèse Universite Montpellier France.

144. Taniguchi M, Bando M, Nakayama A 2008 Business cycle and conserved quantity in economics Journal of the Physical Society of Japan vol 77 no 11.

145. Drehmann M, Borio C, Tsatsaronis K 2011 Anchoring countercyclical capital buffers: The role of credit aggregates International Journal of Central Banking vol 7 no 4 pp 189 – 240.

146. Ikeda Y, Aoyama H, Fujiwara Y, Iyetomi H, Ogimoto K, Souma W, Yoshikawa H 2012 Coupled oscillator model of the business cycle with fluctuating goods markets Proceedings of the YITP Workshop on Econophysics Japan Progress of Theoretical Physics Supplement no 194 pp 111 – 121. arXiv:1110.6679v1 .

147. Ikeda Y, Aoyama H, Yoshikawa H 2013a Synchronization and the coupled oscillator model in international business cycles RIETI Discussion Paper October 13-E-089 The Research Institute of Economy, Trade and Industry Japan http://www.rieti.go.jp/en/ .

148. Ikeda Y, Aoyama H, Yoshikawa H 2013b Direct evidence for synchronization in international business cycles Financial Networks and Systemic Risk.

149. Ikeda Y 2013 Direct evidence for synchronization in Japanese business cycles Evolutionary and Institutional Economic Review 10 (2) pp 1 – 13 arXiv:1305.2263v1 .

150. Swiss National Bank 2012 Swiss National Bank financial stability report 2012 http://www.snb.ch/en/mmr/reference/stabrep_2012/source/stabrep_2012.en.pdf .

151. Swiss National Bank 2013 Countercyclical capital buffer: Proposal of the Swiss National Bank and decision of the Federal Council http://www.snb.ch/en/mmr/reference/pre_20130213/source/pre_20130213.en.pdf .

152. Uechi L, Akutsu T 2012 Conservation laws and symmetries in competitive systems Progress of Theoretical Physics Supplement no 194 pp 210 – 222.

153. Central Banking Newsdesk 2013 Swiss board member supports counter-cyclical capital buffer http://www.centralbanking.com/central-banking/speech/2203857/swiss-board-member-supportscountercyclical-capital-buffer .

154. Union Bank of Switzerland 2013 UBS outlook Switzerland http://www.ubs.com/global/en/wealth_management/wealth_management_research/ubs_outlook_ch.html .

155. Da Costa (2015) Weak first-quarter growth due to seasonal issues after all, SF Fed says The Wall Street Journal New York USA.

156. Federal Reserve Bank of St Louis 2015 US Federal Reserve Economic Data (FRED) Federal Reserve Bank of St Louis http://research.stlouisfed.org/fred

157. Wikipedia 2015c Business cycle Wikipedia California USA www.wikipedia.org.

Disruptive Innovation in Terms of Economics Science:

158. Schumpeter J A 1911; 1939, 1961 Theorie der wirtschaftlichen entwicklung; The theory of economic development: An inquiry into profits, capital, credit, interest and the business cycle Redvers Opie (translator) OUP New York USA.

159. Schumpeter J A 1939 Business cycle McGraw-Hill New York USA.

160. Schumpeter J A 1947 The creative response in economic history Journal of Economic History vol 7 pp 149 – 159.

161. Solow R H August 1957 Technical change and the aggregate production function Review of Economics and Statistics 39 pp 214 – 231.

162. Christensen C M June 16, 1977 Fatal attraction: The dangers of too much technology Computerworld Leadership Series pp 3 – 11.

163. Christensen C M Fall 1992a Exploring the limits of the technology S-curve, Part 1: Component Technologies Production and Operations Management 1 pp 334 – 357.

164. Christensen C M Fall 1992b Exploring the limits of the technology S-curve, Part 2: Architectural technologies Production and Operations Management 1 pp 358 – 366.

165. Bower J L, Christensen C M January February 1995 Disruptive technologies: Catching the wave Harvard Business Review 73 no 1 pp 43 – 53.

166. Bower J L, Christensen C M 1997 Disruptive technologies: Catching the wave in Seeing differently: Insights on innovation Brown J S (editor) Harvard Business School Press Boston MA USA.

167. Christensen C M 1997 The innovator's dilemma: When new technologies cause great firms to fail Harvard Business School Press Boston MA USA.

168. Christensen C M, Armstrong E G Spring 1998 Disruptive technologies: A credible threat to leading programs in continuing medical education? Journal of Continuing Education in the Health Professions 69 no 80 pp 69 – 80.

169. Christensen C M 1998 The evolution of innovation in Technology management handbook Dorf R (editor) CRC Press Boca Raton FL USA.

170. Christensen C M December 1998 Disruptive technologies: Catching the wave TN Harvard Business School Teaching Note 699 - 125.

171. Christensen C M, Cape E G December 1998 Disruptive technology a heartbeat away: Ecton, Inc Harvard Business School Case 699 - 018.

172. Christensen C M April 1999a Value networks and the impetus to change: Managing innovation: Overview teaching note for module 1 Harvard Business School Teaching Note 699 - 163.

173. Christensen C M April 1999b Finding new markets for new and disruptive technologies: Managing innovation, overview teaching note for module 2 Harvard Business School Teaching Note 699 - 164.

174. Christensen C M April 1999c Teradyne: The Aurora project & Teradyne: Corporate management of disruptive change, TN Harvard Business School Teaching Note 399 - 087.

175. Christensen C M, Dann J June 1999 Processes of strategy definition and implementation, The Harvard Business School Background Note 399 - 179.

176. Bower J L, Christensen C M 1999 Disruptive technologies: Catching the wave Ch 29 in The entrepreneurial venture 2nd edition Sahlman W A, Stevenson H H, Roberts M J, Bhide A V pp 506 – 520 Harvard Business School Press Boston MA USA.

177. Christensen C M 1999a Innovation and the general manager Irwin McGraw-Hill Homewood IL USA.

178. Christensen C M 1999b Impact of disruptive technologies in telecommunications in Bringing PC economies to the telecommunications industry PulsePoint Communications.

179. Christensen C M, Tedlow R S January February 2000 Patterns of disruption in retailing Harvard Business Review 78 no 1 pp 42 – 45.

180. Christensen C M, Donovan T March 2000 Disruptive technology a heartbeat away: Ecton, Inc TN Harvard Business School Teaching Note 600 - 129.

181. Christensen C M, Overdorf M March April 2000 Meeting the challenge of disruptive change Harvard Business Review 78 no 2 pp 66 – 76.

182. Christensen C M, Bohmer R M J, Kenagy J September October 2000 Will disruptive innovations cure health care? Harvard Business Review 78 no 5 pp 102 – 117.

183. Christensen C M, Craig Th, Hart S March April 2001 The great disruption Foreign Affairs 80 no 2.

184. Christensen C M Summer 2001 Assessing your organization's innovation capabilities Leader to Leader no 21 pp 27 – 37.

185. Christensen C M, Milunovich S March 2002 Technology strategy: The theory and application of the Christensen model Merrill Lynch Report Series.

186. Bass M J, Christensen C M April 2002 The future of the microprocessor business IEEE Spectrum 39 no 4.

187. Anthony S D, Roth E A, Christensen C M April 2002 The policymaker's dilemma: The impact of government intervention on innovation in the telecommunications industry Harvard Business School Working Paper no 02 - 075.

188. Kenagy J, Christensen C M May 2002 Disruptive innovation: A new diagnosis for health care's 'Financial flu' Healthcare Financial Management pp 62 – 66.

189. Christensen C M, Johnson M W, Rigby D K Spring 2002 Foundations for growth: How to identify and build disruptive new businesses MIT Sloan Management Review 43 no 3.

190. Kenagy J W, Christensen C M 2002 Disruptive innovation - New diagnosis and treatment for the systemic maladies of healthcare World Markets Series Business Briefing Global Healthcare 2002 pp 14 – 17.

191. Christensen C M June 2002 The rules of innovation Technology Review.

192. Hart S L, Christensen C M Fall 2002 The great leap: Driving innovation from the base of the global pyramid MIT Sloan Management Review 44 no 1 pp 51 – 56.

193. Christensen C M, Verlinden M, Westerman G November 2002 Disruption, disintegration, and the dissipation of differentiability Industrial and Corporate Change 11 no 5 pp 955 – 993.

194. Christensen C M 2003 The opportunity and threat of disruptive technologies Harvard Business School Publishing Class Lecture HBSP Product Number 1482C Boston MA USA.

195. Shah Ch D, Brennan T A, Christensen C M April 2003 Interventional radiology: Disrupting invasive medicine.

196. Christensen C M March April 2003 Beyond the innovator's dilemma Strategy & Innovation 1 no 1.

197. Christensen C M, Raynor M E 2003 The innovator's solution: Creating and sustaining successful growth Harvard Business School Press Boston MA USA.

198. Burgelman R A, Christensen C M, Wheelwright S C 2003 Strategic management of technology and innovation 4th edition McGraw-Hill Irwin USA.

199. Christensen C M, Anthony S D January February 2004 Cheaper, faster, easier: Disruption in the service sector Strategy & Innovation 2 no 1.

200. Christensen C M, Anthony S D, Roth E A 2004 Seeing what's next: Using the theories of innovation to predict industry change Harvard Business School Press Boston MA USA.

201. Christensen C M January 2006 The ongoing process of building a theory of disruption Journal of Product Innovation Management 23 pp 39 – 55.

202. Christensen C M, Baumann H, Ruggles R, Sadtler Th M December 2006 Disruptive innovation for social change Harvard Business Review 84 no 12.

203. Christensen C M, Horn M B, Johnson C W 2008 Disrupting class: How disruptive innovation will change the way the World learns McGraw-Hill USA.

204. Christensen C M, Grossman J H, Hwang J 2009 The innovator's prescription: A disruptive solution for health care McGraw-Hill USA.

205. Dyer J H, Gregersen H B, Christensen C M December 2009 The innovator's DNA Harvard Business Review 87 no 12.

206. Christensen C M, Donovan T May 2010 Disruptive IPOs? WR Hambrecht & Co Harvard Business School Case 610-065.

207. Dyer J H, Gregersen H B, Christensen C M 2011 The innovator's DNA: Mastering the five skills of disruptive innovators Harvard Business Press Boston MA USA.

208. Christensen C M, Talukdar Sh, Alton R, Horn M B Spring 2011 Picking green tech's winners and losers Stanford Social Innovation Review USA.

209. Christensen C M, Wang D, van Bever D October 2013 Consulting on the cusp of disruption Harvard Business Review 91 no 10 pp 106 – 114.

210. Bhattacharya S, Ritter J R 1983 Innovation and communication: Signaling with partial disclosure Review of Economic Studies 50 pp 331 – 346.

211. Scherer F M 1984 Innovation and growth: Schumpeterian perspectives MIT Press Cambridge MA USA. Probability Theory, Statistics Theory, Spectrum Analysis Theory, Brownian Movement Theory, Diffusion Theory, Chaos Theory, Information Communication Theory in Econometrics and Econophysics Sciences:

212. Huygens 1657 De ratiociniis in aleae ludo (On calculations in games of chance).

213. Bernoulli J 171 3 Ars conjectandi (The art of guessing).

214. Bernoulli D 1738, 1954 Specimen theoria novae de mensura sortis Commentarii Academiae Scientiarium Imperialis Petropolitanae Petropoli vol 5 pp 175 – 192; Exposition of a new theory on the measurements of risk Sommer L (translator) Econometrica vol 22 pp 23 – 36.

215. De Moivre 1730 Miscellanea analytica supplementum (The analytic method).

216. Fourier J-B J 1807-1822, 1878, 2009 Théorie Analytique de la Chaleur Firmin Didot, Cambridge University Press ISBN 978-1-108-00178-6, ISBN 978-1-108-00180-9.

217. Fourier J-B J 1824 Mémoires de l'Académie Royale des Sciences de l'Institut de France VII pp 570 – 604 http://www.academie-sciences.fr/activite/archive/dossiers/Fourier/Fourier_pdf/Mem1827_p569_604.pdf .

218. De Laplace 1812 Théorie analytique des probabilities Paris France.

219. Bunyakovsky V Ya 1825 Rotary motion in a resistant medium of a set of plates of constant thickness and defined contour around an axis inclined with respect to the horizon Ph D Thesis no 1 under Prof. Augustin - Louis Cauchy supervision École Polytechnique Paris France.

220. Bunyakovsky V Ya 1825 Determination of the radius-vector in elliptical motion of planets Ph D Thesis no 2 under Prof. Augustin - Louis Cauchy supervision École Polytechnique Paris France.

221. Bunyakovsky V Ya 1825 Heat propagation in solids Ph D Thesis no 3 under Prof. Augustin - Louis Cauchy supervision École Polytechnique Paris France.

222. Bunyakovsky V Ya 1846 Foundations of the mathematical theory of probability St. Petersburg Russian Federation.

223. Connor J J, Robertson E F (July) 2000 Viktor Yakovlevich Bunyakovsky (December 16, 1804 - December 12, 1889) School of Mathematics and Statistics University of St Andrews Scotland UK http://www-history.mcs.st-andrews.ac.uk/Biographies/Bunyakovsky.html .

224. V Ya Bunyakovsky International Conference (August 20 - 21) 2004 Private communications with conference participants on V Ya Bunyakovsky’s mathematical theory of probability and its applications in econophysics and econometrics during a tour to Town of Bar Vinnytsia Region Ukraine V Ya Bunyakovsky International Conference Institute of Mathematics of National Academy of Sciences of Ukraine (NASU) Kyiv Ukraine www.imath.kiev.ua/~syta/bunyak .

225. Chebyshev P L 1846 An experience in the elementary analysis of the probability theory Crelle’s Journal fur die Reine und Angewandte Mathematik.

226. Chebyshev P L 1867 Des valuers moyennes Journal de Math’ematics Pures et Appliqu’ees vol 12 pp 177 – 184.

227. Chebyshev P L 1891 Sur deux theoremes relatifs aux probabilities Acta Mathematica vol 14.

228. Chebyshev P L 1936 Theory of probability: Lectures given in 1879 and 1880 Lyapunov A N (lecture notes writer) Krylov A N (editor) Moscow - St Petersburg Russian Federation.

229. Markov A A 1890 On one problem by D I Mendeleev Zapiski Imperatorskoi Akademii Nauk SPb 62 pp 1 – 24.

230. Markov A A 1899 Application des functions continues au calcul des probabilit´es Kazan Bulletin 9 (2) pp 29 – 34 Russian Federation.

231. Markov A A 1900, 1912, 1913 Calculation of probabilities St Petersburg Russian Federation; Wahrscheinlichkeits-Rechnung Teubner Leipzig-Berlin Germany; 3rd edition St Petersburg Russian Federation.

232. Markov A A 1906 Extension of law of big numbers on variables, depending from each other Izvestiya Fiziko-Matematicheskogo Obschestva pri Kazanskom Universitete 2nd series vol 15 (94) pp 135 – 156 Russian Federation.

233. Markov A A 1907, 1910 Research on fine case of depending trials Izvestiya Akademii Nauk SPb 6th series vol 1 (93) pp 61 – 80; Recherches sur un cas remarquable d’epreuves dependantes Acta Mathematica 33 pp 87 – 104 Stockholm Sweden.

234. Markov A A 1908, 1912, 1971 Extension of limit theorems of calculation of probabilities to sum of variables, connected in chain Zapiski Akademii Nauk po Fiziko-Matematicheskomu Otdeleniyu 8th series vol 25 (3); Ausdehnung der Satze uber die Grenzwerte in der Wahrscheinlichkeitsrechnung auf eine Summe verketteter Grossen Liebmann H (translator) in Wahrscheinlichkeitsrechnung Markov A A (author) pp 272 – 298 Teubner B G Leipzig Germany; Extension of the limit theorems of probability theory to a sum of variables connected in a chain Petelin S (translator) in Dynamic probabilities systems Howard R A (editor) vol 1 pp 552 – 576 John Wiley and Sons Inc New York USA.

235. Markov A A 1910 Research on common case of trials, connected in chain Zapiski Akademii Nauk po Fiziko-Matematicheskomu Otdeleniyu 8th series vol 25 (93) Russian Federation.

236. Markov A A 1911 On one case of trials, connected in complex chain Izvestiya Akademii Nauk SPb 6th series vol 5 (93) pp 171 – 186 Russian Federation.

237. Markov A A 1912 On trials of connected in chain unobserved events Izvestiya Akademii Nauk SPb 6th series vol 6 (98) pp 551 – 572 Russian Federation.

238. Markov A A 1913 Example of statistical research on text of “Eugene Onegin”, illustrating interconnection of trials in chain Izvestiya Akademii Nauk SPb 6th series vol 7 (93) pp 153 – 162 Russian Federation.

239. Fisher I 1892 Mathematical investigations in the theory of value and prices Transactions of the Connecticut Academy 9 pp 1 – 124.

240. Einstein A 1905 On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat Annalen der Physik 17 pp 549 – 560.

241. Einstein A 1956 Investigation on the theory of the Brownian motion Furth R (editor) Dover New York USA.

242. Einstein A, Smolukhovsky M 1936 Brownian movement: Collection of research papers ONTI Moscow Russian Federation.

243. Slutsky E E 1910 Theory of marginal utility M Sc Thesis Vernadsky National Library Kiev Ukraine.

244. Slutsky Е Е 1912 Theory of correlation and elements of study about distribution curves Kiev Commerce Institute Bulletin 16 pp 1 – 208 Kiev Ukraine.

245. Slutsky Е Е 1913 On the criterion of goodness of fit of the regression lines and the best method of fitting them to the data Journal Royal Statistics Society vol 77 part I pp 8 – 84.

246. Slutsky Е Е 1914 Sir William Petty: Short overview of his economic visions with attachment of his several important research works Kiev Commerce Institute Bulletin 18 pp 5 – 48 Kiev Ukraine.

247. Slutsky Е Е 1915 Sulla teoria sel bilancio del consumatore Giornale degli economisti e rivista di statistica 51 no 1 pp 1 – 26 Italy.

248. Slutsky Е Е 1922a Statistics and mathematics. Review of Kaufman Statistics Bulletin 3 – 4 pp 104 – 120.

249. Slutsky E E 1922b To the question of logical foundations of probability calculation Statistics Bulletin 9 - 12 pp 13 – 21.

250. Slutsky E E 1923a On the some patterns of correlation connection and the systematic error of correlation coefficient Statistics Bulletin 1 – 3 pp 31 – 50.

251. Slutsky E E 1923b On a new coefficient of mean density of population Statistics Bulletin 4 – 6 pp 5 – 19.

252. Slutsky E E 1923c On calculation of state revenue from emission of paper money Local Economy 2 pp 39 – 62 Kiev Ukraine.

253. Slutsky E E 1925a On the law of large numbers Statistics Bulletin 7 – 9 pp 1 – 55.

254. Slutsky E E 1925b Ueber stochastische Asymptoten und Grenzwerte Metron Padova Italy vol 5 no 3 pp 3 – 89.

255. Slutzhi E E 1926 Ein Beitrag zur Formal-praxeologischen Grundlegung der Oekonomik Ann de la classe des sci soc-econ Akad Oukrainienne des Sciences Kiev Ukraine vol 4 pp 3 – 12.

256. Slutsky E E 1927a The summation of random causes as sources of cyclic processes Problems of Conjuncture (Voprosy Kon’yunktury) vol 3 issue 1 pp 34 – 64 Moscow Russian Federation.

257. Slutzhi Е Е 1927b Zur Kritik des Bohm-Bawerkschen Wertbegriffs und seiner Lehre von der Messbarkeit des Wertes Schmollers Jb 51 (4) pp 37 – 52.

258. Slutsky E E 1929 Sur l’erreur quadratique mogenne du coefficient de correlation dans le cas des suites des epreuves non independantes Comptes rendus 189 pp 612 – 614.

259. Slutsky E E 1935 To the extrapolation problem in connection with forecast problem Geophysics Journal 5 (3) pp 263 – 277.

260. Slutsky E E 1937a Quelche propositione relative alla teoria delle funzioni aleatorie Giornale dell Istituto Italiano degli Attuari 8 no 2 pp 3 – 19.

261. Slutsky E E 1937b The summation of random causes as the source of cyclical processes Econometrica 5 pp 105 – 146.

262. Slutsky E E 1942, 1999 Autobiography of December 3, 1942 Economics School 5 pp 18 – 21.

263. Slutsky E E 1960 Selected research works (Izbrannye trudy) Academy of Sciences of USSR Moscow Russian Federation.

264. Bowley A L 1924 The mathematical groundwork of economic Clarendon Press Oxford UK.

265. Kolmogorov A N 1937 Markov chains with countable many states Bulletin Moscow University 1.

266. Kolmogorov A N 1938 On analytic methods in probability theory in Selected works of Kolmogorov A N vol 2 Probability theory and mathematical statistics Shiryaev A N (editor) Springer Germany.

267. Kolmogorov A N 1947 The contribution of Russian science to the development of probability theory Uchenye Zapiski Moskovskogo Universiteta no 91.

268. Kolmogorov A N 1956 Probability theory in Mathematics: Its contents, methods, and meaning Academy of Sciences USSR vol 2.

269. Kolmogorov A N 1956 Foundations of the theory of probability Chelsea New York USA.

270. Kolmogorov A N 1985 Mathematics and mechanics Selected works vol 1 Nauka Publishing House Moscow Russian Federation.

271. Kolmogorov A N 1986 Probability theory and mathematical statistics Selected works vol 2 Nauka Publishing House Moscow Russian Federation.

272. Allen R G D 1938 Mathematical analysis for economists Macmillan London UK.

273. Cramer H 1940 On the theory of stationary random processes Ann Math vol 41 pp 215 – 230.

274. Cramer H 1946 Mathematical methods of statistics Princeton University Press USA.

275. Cramer H, Leadbetter M 1967 Stationary and related stochastic processes. Sample function properties and their applications John Wiley and Sons Inc NY USA.

276. Bemshtein S N 1946 Theory of probability 4th edition Gostehizdat Moscow Russian Federation.

277. Bogolyubov N N 1946 Dynamic problems in statistic physics.

278. Neyman J, Scott E L 1948 Consistent estimates based on partially consistent observations Econometrica 16 pp 1 – 32.

279. Shannon C E 1948 A mathematical theory of communication Bell System Technical Journal 27 pp 379 – 423 and pp 623 – 656.

280. Terletsky Ya P 1950 Dynamic and statistic laws of physics Publishing House of Moscow State University Russian Federation pp 1 – 96.

281. Hannan E J 1960 Time series analysis Methuen London.

282. Hannan E J 1970 Multiple time series John Wiley and Sons Inc New York USA.

283. Mandelbrot B B 1960 The Pareto-Levy law and the distribution of income International Economic Review no 1.

284. Mandelbrot B B 1963a The stable Paretian income distribution when the apparent exponent is near two International Economic Review no 4.

285. Mandelbrot B B 1963b The variation of certain speculative prices Journal of Business vol 36 pp 394 – 419.

286. Mandelbrot B B 1965 Une classe de processus stochastiques homothetiques a soi: Application a la loi climatologique de H. E. Hurst Comptes Rendus de l'Academie des Sciences vol 240 pp 3274 – 3277 Paris France.

287. Mandelbrot B B 1967a The variation of some other speculative prices Joural of Business vol 40 pp 393 – 413.

288. Mandelbrot B B (April) 1967b Some noises with 1/f spectrum: A bridge between direct current and white noise IEEE Transactions on Information Theory USA.

289. Mandelbrot B B, Taylor H M 1967 On the distribution of stock price difference Operations Research vol 15 no 6 pp 1057 – 1062.

290. Mandelbrot B B, van Ness J W 1968 Fractional Brownian motions, fractional noises and applications SIAM Review vol 10 no 4 pp 422 – 437.

291. Mandelbrot B B 1969 Robustness of the rescaled range R/S in the measurement of non-cyclic long-run statistical dependence Water Resources Research vol 5 no 5 pp 967 – 988.

292. Mandelbrot B B, Wallis J R 1969 Computer experiments with fractional Gaussian noises I, II, III Water Resources Research vol 5 pp 228 – 267.

293. Mandelbrot B B 1971 When can price be arbitrated efficiently? A limit of the validity of the random walk and martingale models Review of Economics and Statistic vol 53 pp 225 – 236.

294. Mandelbrot B B 1972 Statistical methodology for non-periodic cycles: From the covariance to R/S analysis Annals of Economic and Social Measurement vol 1 no 3 pp 259 – 290.

295. Mandelbrot B B 1975a Les objects fractals Flammarion Paris France.

296. Mandelbrot B B 1975b Limit theorems on the self-normalized range for weakly and strongly dependent process Zeitschrift Wahrscheinlichkeitsttheorie und Verwandte Gebiete vol 31 pp 271 – 285.

297. Mandelbrot B B 1977 Fractals: Form, chance and dimension W H Freeman San Francisco USA.

298. Mandelbrot B B 1982 The fractal geometry of nature W H Freeman San Francisco USA.

299. Mandelbrot B B 1997 Fractals and scaling in finance Springer New York USA.

300. Gnedenko B V, Khinchin A Ya 1961 An elementary introduction to the theory of probability Freeman San Francisco USA.

301. Gnedenko B V 1988 The theory of probability Mir Moscow Russian Federation.

302. Shiryaev A N 1961 The problem of the most rapid detection of a disturbance in a stationary process Soviet Mathematical Doklady 2 pp 795 – 799.

303. Shiryaev A N 1963 On optimal methods in quickest detection problems Theory of Probability and its Applications 8 (1) pp 22 – 46.

304. Shiryaev A N 1964 On Markov sufficient statistics in non-additive Bayes problems of sequential analysis Theory of Probability and its Applications 9 (4) pp 670 – 686.

305. Shiryaev A N 1965 Some exact formulas in a ’disorder’ problem Theory of Probability and its Applications 10 pp 348 – 354.

306. Grigelionis B I, Shiryaev A N 1966 On Stefan’s problem and optimal stopping rules for Markov processes Theory of Probability and its Applications 11 pp 541 – 558.

307. Shiryaev A N 1967 Two problems of sequential analysis Cybernetics 3 pp 63 – 69.

308. Liptser R S, Shiryaev A N 1977 Statistics of random processes Springer-Verlag New York USA.

309. Shiryaev A N 1972 Random processes Moscow State University Press Russian Federation.

310. Shiryaev A N 1973, 1974 Probability, statistics, random processes Moscow State University Press vols 1, 2 Russian Federation.

311. Shiryaev A N 1978, 2008b Optimal stopping rules 1st edition, 3rd edition Springer ISSN 0172-4568 Library of Congress Control Number: 2007934268 Berlin Germany pp 1 – 217.

312. Shiryaev A N 1988 Probability Springer-Verlag Berlin Heidelberg Germany.

313. Shiryaev A N 1995 Probability 2nd edition Springer - Verlag ISBN 0-387-94549-0 New York USA pp 1 – 621.

314. Shiryaev A N 1998a Foundations of stochastic financial mathematics vol 1 Fazis Scientific and Publishing House Moscow Russian Federation ISBN 5-7036-0044-8 pp 1 – 492.

315. Shiryaev A N 1998b Foundations of stochastic financial mathematics vol 2 Fazis Scientific and Publishing House Moscow Russian Federation ISBN 5-7036-0044-8 pp 493 – 1017.

316. Shiryaev A N 1999 Essentials of stochastic finance: Facts, models, theory Advanced Series on Statistical Science & Applied Probability vol 3 World Scientific Publishing Co Pte Ltd Kruzhilin N (translator) ISBN 981-02-3605-0 Singapore pp 1 – 834.

317. Shiryaev A N, Spokoiny V G 2000 Statistical experiments and decisions: Asymptotic theory World Scientific Publishing Co Pte Ltd ISBN 9810241011 Singapore pp 1 – 283.

318. Graversen S E, Peskir G, Shiryaev A N 2001 Stopping Brownian motion without anticipation as close as possible to its ultimate maximum Theory of Probability and its Applications 45 pp 125 – 136 MR1810977 http://www.ams.org/mathscinetgetitem?mr=1810977 .

319. Kallsen J, Shiryaev A N 2001 Time change representation of stochastic integrals Theory of Probability and its Applications 46 pp 579 – 585 MR1978671 http://www.ams.org/mathscinet-getitem?mr=1978671 .

320. Kallsen J, Shiryaev A N 2002 The cumulant process and Esscher’s change of measure Finance Stoch 6 pp 397 – 428 MR1932378 http://www.ams.org/mathscinetgetitem?mr=1932378 .

321. Shiryaev A N 2002 Quickest detection problems in the technical analysis of the financial data Proceedings Mathematical Finance Bachelier Congress Paris France (2000) Springer Germany pp 487 – 521 MR1960576 http://www.ams.org/mathscinet-getitem?mr=1960576 .

322. Jacod J, Shiryaev A N 2003 Limit theorems for stochastic processes 2nd edition Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 288 Springer Berlin Germany MR1943877 http://www.ams.org/mathscinetgetitem?mr=1943877 .

323. Shiryaev A N 2004 Kolmogorov and modern mathematics International Conference at Mathematical Institute named after V A Steklov June 16-21, 2003 Russian Academy of Sciences Moscow Russian Federation ISBN 5-98419-003-6 pp 1 – 195.

324. Shiryaev A N, Grossinho M R, Oliveira P E, Esquível M L (editors) 2006 Stochastic finance Springer Germany ISBN-10:0-387-28262-9 pp 1 – 364.

325. Peskir G, Shiryaev A N 2006 Optimal stopping and free-boundary problems Lectures in Mathematics ETH Zürich Birkhäuser Switzerland MR2256030 http://www.ams.org/mathscinet-getitem?mr=2256030 .

326. Feinberg E A, Shiryaev A N 2006 Quickest detection of drift change for Brownian motion in generalized Bayesian and mini-max settings Statistics & Decisions 24 (4) pp 445 – 470.

327. Kabanov Yu, Lipster R, Stoyanov J 2006 The Shiryaev festschrift: From stochastic calculus to mathematical finance Springer Germany pp 1 – 668.

328. du Toit J, Peskir G, Shiryaev A N 2007 Predicting the last zero of Brownian motion with drift Cornell University NY USA pp 1 – 17 http://arxiv.org/abs/0712.3415v1.

329. Shiryaev A N 2008a Generalized Bayesian nonlinear quickest detection problems: on Markov family of sucient statistics Mathematical Control Theory and Finance Proceedings of the Workshop of April 10–14 2007 Lisbon Portugal Sarychev A et al (editors) Springer Berlin Germany pp 377 – 386.

330. Eberlein E, Papapantoleon A, Shiryaev A N 2008 On the duality principle in option pricing: Semimartingale setting Finance Stoch 12 pp 265 – 292 http://www.ams.org/mathscinet-getitem?mr=2390191 .

331. Shiryaev A N, Novikov A A 2009 On a stochastic version of the trading rule "Buy and hold" Statistics & Decisions 26 (4) pp 289 – 302.

332. Eberlein E, Papapantoleon A, Shiryaev A N 2009 Esscher transform and the duality principle for multidimensional semimartingales The Annals of Applied Probability vol 19 no 5 pp 1944 – 1971 http://dx.doi.org/10.1214/09-AAP600 http://arxiv.org/abs/0809.0301v5 .

333. Shiryaev A N, Zryumov P Y 2009 On the linear and nonlinear generalized Bayesian disorder problem (discrete time case) optimality and risk – modern trends in mathematical finance The Kabanov Festschrift Delbaen F et al (editors) Springer Berlin Germany pp 227 – 235.

334. Gapeev P V, Shiryaev A N 2010 Bayesian quickest detection problems for some diffusion processes Cornell University NY USA pp 1 – 25 http://arxiv.org/abs/1010.3430v2 .

335. Karatzas I, Shiryaev A N, Shkolnikov M 2011 The one-sided Tanaka equation with drift Cornell University NY USA http://arxiv.org/abs/1108.4069v1 .

336. Shiryaev A N, Zhitlukhin M V 2012 Optimal stopping problems for a Brownian motion with a disorder on a finite interval Cornell University NY USA pp 1 – 10 http://arxiv.org/abs/1212.3709v1 .

337. Zhitlukhin M V, Shiryaev A N 2012 Bayesian disorder detection problems on filtered probability spaces Theory of Probability and Its Applications 57 (3) pp 453 – 470.

338. Feinberg E A, Mandava M, Shiryaev A N 2013 On solutions of Kolmogorov’s equations for nonhomogeneous jump Markov processes Cornell University NY USA pp 1 – 15 http://arxiv.org/abs/1301.6998v3 .

339. Abramowitz M, Stegun I A (editors) 1964 Handbook of mathematical functions National Bureau of Standards Applied Mathematics Series vol 55 USA.

340. Kubilius J 1964 Probabilistic methods in the theory of numbers American Mathematical Society Providence USA.

341. Akhiezer N I, Glazman I M 1966 Theory of linear operators in Hilbert space Nauka Moscow Russian Federation.

342. Lamperti J 1966 Probability Benjamin New York USA.

343. Kai-Lai Chung 1967 Markov chains with stationary transition probabilities Springer-Verlag New York USA.

344. Skorohod A V 1967 Random processes with independent increments Nauka Moscow Russian Federation.

345. Gikhman I I, Skorohod A V 1968 Stochastic differential equations Naukova Dumka Kiev Ukraine.

346. Gikhman I I, Skorohod A V 1969 Introduction to the theory of random processes 1st edition Saunders Philadelphia USA.

347. Gikhman I I, Skorohod A V 1974-1979 Theory of stochastic processes vols 1, 2, 3 Springer-Verlag New York-Berlin USA-Germany.

348. Breiman L 1968 Probability Addison-Wesley Reading MA USA.

349. Feller W 1968 An introduction to probability theory and its applications vols 1, 2 3rd edition John Wiley and Sons Inc New York USA.

350. Brush S G 1968, 1977 A history of random processes: 1. Brownian movement in Study history statistics and probability Kendall M G, Plackett R L (editors) 2 pp 347 – 382 London UK.

351. Glesjer H 1969 A new test for heteroskedasticity Journal of the American Statistical Association 64 pp 316 – 323.

352. Ash R B 1970 Basic probability theory John Wiley and Sons Inc New York USA.

353. Ash R B 1972 Real analysis and probability Academic Press New York USA.

354. Ash R B, Gardner M F 1975 Topics in stochastic processes Academic Press New York USA.

355. Box G E P, Jenkins G M 1970 Time series analysis: Forecasting and control Holden Day San Francisco California USA.

356. Renyi A 1970 Probability theory North-Holland Publishing Company Amsterdam The Netherlands.

357. Isihara A 1971 Statistical physics Academic Press New York USA.

358. Brent R P 1973 Algorithms for minimization without derivatives Englewood Cliffs USA.

359. Rubin D B 1974 Estimating causal effects of treatments in randomized and nonrandomized studies Journal of Educational Psychology 55 (5) pp 688 – 701.

360. Borovkov A A 1976 Wahrscheinlichkeitstheorie: Eine EinjUhrung 1st edition Birkhiuser Basel-Stuttgart Switzerland-Germany.

361. Grangel C W J, Newbold P 1977 Forecasting economic time series Academic Press New York USA.

362. Grangel C W J, Teräsvirta T 1993 Modeling nonlinear economic relationships Oxford University Press Oxford New York UK USA.

363. Pugachev V S 1979 Theory of probability and mathematical statistics 1st edition Nauka Moscow Russian Federation, 2nd edition Fizmatlit Moscow Russian Federation ISBN 5–92210254–0 pp 1 – 496.

364. Ross S M 1980 Introduction to probability models Academic Press New York USA.

365. Karlin S, Taylor H M 1981 A second course in stochastic processes Academic Press New York USA.

366. Venttsel A D 1981 A course in the theory of stochastic processes McGraw-Hill New York USA.

367. Maddala G S 1983 Limited-dependent and qualitative variables in econometrics Cambridge University Press Cambridge UK.

368. Yaglom A M, Yaglom I M 1983 Probability and information Reidel Dordrecht.

369. Heckman J, Singer B 1984a A method for minimizing the impact of distributional assumptions in econometric models for duration data Econometrica 52 pp 271 – 320.

370. Heckman J, Singer B 1984b Econometric duration analysis Journal of Econometrics 24 pp 63 – 132.

371. Pagan A 1984 Econometric issues in the analysis of regressions with generated regressors International Economic Review 25 pp 221 – 247.

372. Van Horne J C 1984 Financial market rates and flows Prentice Hall Englewood Cliffs NJ USA.

373. Murphy K M, Topel R H October 1985 Estimation and inference in two-step econometric models Journal of Business and Economic Statistics 3 pp 370 – 379.

374. Neter J, Wasserman W, Kutner M H 1985 Applied linear statistical models 2nd edition Irwin Homewood USA.

375. Powell J L 1986 Censored regression quantiles Journal of Econometrics 32 (1) pp 143 – 155.

376. Taylor S 1986 Modeling financial time series John Willey and Sons Inc New York USA.

377. Tong H 1986 Nonlinear time series Oxford University Press Oxford UK.

378. Tornqvist L, Vartia P, Vartia Y February 1985 How should relative change be measured? American Statistician 39 pp 43 – 46.

379. Sharkovsky A N, Maistrenko Yu L, Romanenko E Yu 1986 Differential equations and their applications Naukova Dumka Kiev Ukraine pp 1 – 280.

380. Newey W, West K 1987 A simple positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix Econometrica 55 pp 703 – 708.

381. Luukkonen R, Saikkonen P, Terasvirta T 1988 Testing linearity against smooth transition autoregressive models Biometrika 75 pp 491 – 499.

382. Judge G, Hill C, Griffiths W, Lee T, Lutkepol H 1988 An introduction to the theory and practice of econometrics 2nd edition John Wiley and Sons Inc New York USA.

383. Hardle W 1990 Applied nonparametric regression Econometric Society Monograph Cambridge University Press Cambridge UK.

384. Lancaster T 1990 The econometric analysis of transition data Cambridge University Press Cambridge UK.

385. Tong H 1990 Nonlinear time series: A dynamical system approach Clarendon Press Oxford UK.

386. Johansen S 1992 Cointegration in partial systems and the efficiency of single equation analysis Journal of Econometrics 52 pp 389 – 402.

387. Banerjee A, Dolado J J, Galbraith J W, Hendry D F 1993 Cointegration, error correction, and the econometric analysis of nonstationary data Oxford University Press Oxford UK.

388. Cleveland W S 1993 Visualizing data Hobart Press Summit New Jersey USA.

389. Pesaran M H, Potter S M (editors) 1993 Nonlinear dynamics, chaos and econometrics John Willey and Sons Inc New York USA.

390. Hamilton J D 1994 Time series analysis Princeton University Press Princeton, NJ USA.

391. Peters E E 1994 Fractal market analysis: Applying chaos theory to investment and economics John Wiley and Sons Inc New York USA.

392. Enders W 1995 Applied econometric time series John Wiley and Sons Inc New York USA.

393. Johansen S 1995 Likelihood based inference in co-integrated vector autoregressive models Oxford University Press Oxford UK.

394. Karatzas I, Shreve S 1995 Methods of mathematical finance Columbia University Press New York USA.

395. Moore G E 1995 Lithography and the future of Moore’s law Proceedings SPIE Symposium Optical Microlithography Conference VIII 2440 2.

396. Moore G E 2003 No exponential is forever – but we can delay forever ISSCC.

397. Campbell J Y, Lo A W, MacKinlay A C 1996 The econometrics of financial markets Princeton University Press Princeton USA.

398. Mosekilde E 1996 Topics in nonlinear dynamics: Applications to physics, biology and economic systems World Scientific Publishing Pte Ltd Singapore.

399. Rogers L C G, Talay D (editors) 1997 Numerical methods in finance Cambridge University Press Cambridge UK.

400. Campbell J, Lo A, MacKinlay C 1997 The econometrics of financial markets Princeton University Press Princeton NJ USA.

401. Greene W H 1997, 1999, 2003 Econometric analysis 1st edition, 4th edition, 5th edition Prentice Hall Upper Saddle River USA.

402. Hasem P M, Pesaran B 1997 Working with Microfit 4.0: Interactive econometric analysis Oxford University Press Oxford UK.

403. Lo A W, MacKinlay A C 1997 The econometrics of financial markets Princeton University Press Princeton New Jersey USA.

404. Anderson H M, Vahid F 1998 Testing multiple equation systems for common nonlinear factors Journal of Econometrics 84 pp 1 – 37.

405. Hubbard B B 1998 The world according to wavelets A K Peters Wellesley MA USA.

406. Mallat S A 1998 Wavelet tour of signal processing Academic Press San Diego CA USA.

407. Teolis A 1998 Computational signal processing with wavelets Birkhauser Switzerland.

408. Anishenko V S, Vadivasova T E, Astakhov V V 1999 Nonlinear dynamics of chaotic and stochastic systems Saratov University Publishing House Saratov Russian Federation.

409. Escribano, Jorda 1999 Improved testing and specification of smooth transition regression models in Nonlinear time series analysis of economic and financial data Rothman (editor) Kluwer Academic Press Amsterdam The Netherlands.

410. Hasem P M, Shin Y 1999 An autoregressive distributed lag modelling approach to cointegration analysis in Econometrics and economic theory in the 20th century: The Ranger Frisch centennial symposium Strom S, Holly A, Diamond P (editors) Cambridge University Press Cambridge UK www.econ.cam.ac.uk/faculty/pesaran/ADL.pdf .

411. Hasem P M, Shin Y, Smith R J 2001 Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 (3) pp 289 – 326.

412. Potter S 1999 Non-linear time series modelling: An introduction Typescript Federal Reserve Bank of New York NY USA.

413. Rothman (editor) 1999 Nonlinear time series analysis of economic and financial data Kluwer Academic Press Amsterdam The Netherlands.

414. Hayashi F 2000 Econometrics Princeton University Press Princeton NJ USA.

415. Durbin J, Koopman S J 2000 Time series analysis of non-Gaussian observations based on state-space models from both classical and Bayesian perspectives Journal of Royal Statistical Society Series B 62 pp 3 – 56.

416. Durbin J, Koopman S J 2002 A simple and efficient simulation smoother for state space time series analysis Biometrika 89 pp 603 – 615.

417. Durbin J, Koopman S J 2012 Time series analysis by state space methods 2nd edition Oxford University Press Oxford UK.

418. Ilinski K 2001 Physics of finance: Gauge modelling in non-equilibrium pricing John Wiley and Sons Inc New York USA ISBN-10: 0471877387 pp 1 – 300.

419. Kuznetsov S P 2001 Dynamic chaos Izdatel’stvo Fiziko-Matematicheskoi Literatury Moscow Russian Federation pp 1 – 296.

420. Tufte E R 2001 The visual display of quantitative information 2nd edition Graphics Press Cheshire CT USA.

421. Nicolau J 2002 Stationary processes that look like random walks – The bounded random walk process in discrete and continuous time Econometric Theory 18 pp 99 – 118.

422. Ledenyov V O, Ledenyov O P, Ledenyov D O 2002 A quantum random number generator on magnetic flux qubits Proceedings of the 2nd Institute of Electrical and Electronics Engineers Conference IEEE-NANO 2002 Chicago Washington DC USA IEEE Catalog no 02TH86302002 Library of Congress number: 2002106799 ISBN: 0-7803-7538-6.

423. Woolridge J M 2002 Econometric analysis of cross section and panel data MIT Press Cambridge MA USA.

424. Koop G 2003 Bayesian econometrics John Wiley and Sons Inc New York USA.

425. Selover D D, Jensen R V, J. Kroll J 2003 Studies in Nonlinear Dynamics & Econometrics 7 1.

426. Davidson R, MacKinnon J 2004 Econometric theory and methods Oxford University Press Oxford UK.

427. Cameron A C, Trivedi P K 2005 Microeconometrics: Methods and applications Cambridge University Press Cambridge UK.

428. Protter P E 2005 Stochastic integration and differential equations Springer Germany.

429. Backhaus K et al 2006 Multivariate analysemethoden. Eine anwendungsorientierte einführung Springer Berlin Heidelberg Germany.

430. Damodaran A 2006 Applied corporate finance. A user’ manual 2nd edition John Wiley & Sons Inc New Jersey USA.

431. Ernst D, Häcker J 2007 Applied international corporate finance Vahlen München Germany.

432. Angrist J D, Pischke J-S 2008 Mostly harmless econometrics: An empiricist’s companion Princeton University Press USA.

433. Vialar Th, Goergen A 2009 Complex and chaotic nonlinear dynamics Springer-Verlag Berlin Heidelberg Germany ISBN 978-3-540-85977-2 pp 1 – 752.

434. Weatherall J O 2013 Physics of Wall Street Houfton New York USA.

Selected Research Papers in Macroeconomics, Microeconomics & Nanoeconomics Sciences:

435. Ledenyov V O, Ledenyov D O 2012a Shaping the international financial system in century of globalization Cornell University NY USA www.arxiv.org 1206.2022.pdf pp 1 – 20.

436. Ledenyov V O, Ledenyov D O 2012b Designing the new architecture of international financial system in era of great changes by globalization Cornell University NY USA www.arxiv.org 1206.2778.pdf pp 1 – 18.

437. Ledenyov D O, Ledenyov V O 2012a On the new central bank strategy toward monetary and financial instabilities management in finances: econophysical analysis of nonlinear dynamical financial systems Cornell University NY USA www.arxiv.org 1211.1897.pdf pp 1 – 8.

438. Ledenyov D O, Ledenyov V O 2012b On the risk management with application of econophysics analysis in central banks and financial institutions Cornell University NY USA www.arxiv.org 1211.4108.pdf pp 1 – 10.

439. Ledenyov D O, Ledenyov V O 2013a On the optimal allocation of assets in investment portfolio with application of modern portfolio management and nonlinear dynamic chaos theories in investment, commercial and central banks Cornell University NY USA www.arxiv.org 1301.4881.pdf pp 1 – 34.

440. Ledenyov D O, Ledenyov V O 2013b On the theory of firm in nonlinear dynamic financial and economic systems Cornell University NY USA www.arxiv.org 1206.4426v2.pdf pp 1 – 27.

441. Ledenyov D O, L