Spurious Regression

Ventosa-Santaulària, Daniel (2008): Spurious Regression. Published in: Journal of Probability and Statistics , Vol. 2009, No. 802975 (2009)

Abstract

The spurious regression phenomenon in Least Squares occurs for a wide range of Data Generating Processes, such as driftless unit roots, unit roots with drift, long memory, trend and broken-trend stationarity. Indeed, spurious regressions have played a fundamental role in the building of modern time series econometrics and have revolutionized many of the procedures used in applied macroeconomics. Spin-offs from this research range from unit-root tests to cointegration and error-correction models. This paper provides an overview of results about spurious regression, pulled from disperse sources, and explains their implications.

• Item Type: MPRA Paper
• Language: English
• Keywords: Spurious Regression, Stationarity, Unit Root, Long Memory.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

ADELMAN, I. (1965): “Long Cycles: Fact or Artifact,” American Economic Review, 55, 444–463.

AGHION, P., AND S. N. DURLAUF (2005): Handbook of Economic Growth, Volume 1A. North-Holland.

ALDRICH, J. (1995): “Correlations genuine and spurious in Pearson and Yule,” Statistical Science, 10(4), 364–376.

ALOGOSKOUFIS, G., AND R. SMITH (1991): “The Phillips Curve, The Persistence of Inflation, and the Lucas Critique: Evidence from Exchange-Rate Regimes,” The American Economic Review, 81(5), 1254–1275.

ARINO, M., AND F. MARMOL (2004): “A permanent-transitory decomposition for ARFIMA processes,” Journal of Statistical Planning and Inference, 124, 87–97.

AUE, A., L. HORV´A TH, M. HUˇS KOV´A, AND P. KOKOSZKA (2008): “Testing for changes in polynomial regression,” Bernoulli, 14(3), 637–660.

BAI, J., AND P. PERRON (1998): “Estimating and Testing LinearModels withMultiple Structural Changes,” Econometrica, 66, 47–78.

BANERJEE, A., J. DOLADO, J. GALBRAITH, AND D. HENDRY (1993): CoIntegration, Error Correction, and the Econometric Analysis of Non-Stationary Data. Oxford University Press.

BARDSEN, G., E. JANSEN, AND R. NYMOEN (2004): “Econometric Evaluation of the New Keynesian Phillips Curve,” Oxford Bulletin of Economics and Statistics, 66(s1), 671–686.

BERKES, I., L. HORV´A TH, P. KOKOSZKA, AND Q. SHAO (2006): “On discriminating between long-range dependence and changes in mean,” Annals of Statistics, 34(3), 1140–1165.

BERNARD, A., AND S. DURLAUF (1995): “Convergence in International Output,” Journal of Applied Econometrics, 10(2), 97–108.

BERNARD, A., AND S. DURLAUF (1996): “Interpreting tests of the Convergence Hypothesis,” Journal of Econometrics, 71, 161–173.

BHATTACHARYA, R., V. GUPTA, AND E. WAYMIRE (1983): “The Hurst effect under trends,” Journal of Applied Probability, pp. 649–662.

BREIDT, F., N. CRATO, AND P. DE LIMA (1998): “The detection and estimation of long memory in stochastic volatility,” Journal of Econometrics, 83(1-2), 325–348.

BREUSCH, T., AND A. PAGAN (1980): “The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics,” Review of Economic Studies, 47, 239–254.

CAMPELL, J., AND P. PERRON (1991): “What Macroeconomist Should Know about Unit Roots,” in NBER Macroeconomics Annual, ed. by O. Blanchard, and S. Fisher, pp. 141–201. MIT Press.

CAPPUCCIO, N., AND D. LUBIAN (1997): “Spurious Regressions Between I(1) Processes with Long Memory Errors,” Journal of Time Series Analysis, 18, 341–354.

CARRION–I–SILVESTRE, J., AND A. SANS´O (2006): “Joint hypothesis specification for unit root tests with a structural break*,” Econometrics Journal, 9(2), 196–224.

CATI, R., M. GARCIA, AND P. PERRON (1999): “Unit roots in the presence of abrupt governmental interventions with an application to Brazilian data,” Journal of Applied Econometrics, 14(1), 27–56.

CAVALIERE, G., AND R. TAYLOR (2006): “Testing for a Change in Persistence in the Presence of a Volatility Shift,” Oxford Bulletin of Economics and Statistics, 68(s1), 761–781.

CHEUNG, Y. (1993): “Long memory in foreign-exchange rates,” Journal of Business & Economic Statistics, pp. 93–101.

COCHRANE, J. (1994): “Permanent and Transitory Components of GNP and Stock Prices,” The Quarterly Journal of Economics, 109(1), 241–265.

COE, P., AND J. NASON (2004): “Long-run monetary neutrality and long-horizon regressions,” Journal of Applied Econometrics, 19(3), 355–373.

COENEN, G., AND J. VEGA (2001): “The Demand for M3 in the Euro Area,” Journal of Applied Econometrics, 16(6), 727–748.

CORBAE, D., AND S. OULIARIS (1988): “Cointegration and Tests of Purchasing Power Parity,” The Review of Economics and Statistics, 70(3), 508–511.

CRATO, N., AND P. DE LIMA (1994): “Long-range dependence in the conditional variance of stock returns,” Economics Letters, 45(3), 281–285.

CROWDER, W. (1997): “The Long-Run Fisher Relation in Canada,” The Canadian Journal of Economics, 30(4b), 1124–1142.

CUDDINGTON, J., AND H. LIANG (2000): “Purchasing power parity over two centuries,” Journal of International Money and Finance, 19(5), 753–757.

CULVER, S., AND D. PAPELL (1997): “Is there a unit root in the inflation rate? Evidence from sequential break and panel data models,” Journal of Applied Econometrics, 12(4), 435–444.

D’ADDA, C., AND A. SCORCU (2003): “On the time stability of the output-capital ratio,” Economic Modelling, 20(6), 1175–1189.

DAVIDSON, J., D. HENDRY, F. SRBA, AND S. YEO (1978): “Econometric Modelling of The Aggregate Time Series Relationship betwen the consumers: Expenditure and Income in the United Kindom,” Economic Journal, 88, 661–92.

DE JONG, R. (2003): “Logarithmic Spurious Regressions,” Economics Letters, 81(1), 13–21.

DELOACH, S. (2001): “More Evidence in Favor of the Balassa-Samuelson Hypothesis,” Review of International Economics, 9(2), 336–342.

DIBA, B., AND H. GROSSMAN (1988): “Explosive Rational Bubbles in Stock Prices?,” The American Economic Review, 78(3), 520–530.

DICKEY, D., AND W. FULLER (1979): “Distribution of the Estimators for Autoregressive Time Series with a Unit Root,” Journal of the American Statistical Association, 74, 427–31.

_____(1981): “Likelihood ratio statistics for autoregressive time series with a unit root,” Econometrica, pp. 1057–1072.

DICKEY, D., AND S. PANTULA (1987): “Determining the Order of Differencing in Autoregressive Processes,” Journal of Business & Economic Statistics, 5(4), 455–461.

DRINE, I., AND C. RAULT (2003): “Do panel data permit the rescue of the Balassa-Samuelson hypothesis for Latin American countries?,” Applied Economics, 35(3),351–359.

DURLAUF, S. (1996): “On The Convergence and Divergence of Growth Rates,” The Economic Journal, 106(437), 1016–1018.

_____(2001): “Manifesto for a Growth Econometrics,” Journal of Econometrics, 100(1), 65–69.

DURLAUF, S., AND P. PHILLIPS (1988): “Trends versus RandomWalks in Time Series Analysis,” Econometrica, 56(6), 1333–1354.

DURLAUF, S., AND D. QUAH (1998): The New Empirics of Economic Growth. National Bureau of Economic Research Cambridge, Mass., USA.

ELLIOTT, G., T. ROTHENBERG, AND J. STOCK (1996): “Efficient tests for an autoregressive unit root,” Econometrica: Journal of the Econometric Society, pp. 813–836.

ENDERS, W., AND S. HURN (1994): “Theory and Tests of Generalized Purchasing-Power Parity: Common Trends and Real Exchange Rates in the Pacific Rim,” Review of International Economics, 2(2), 179–190.

ENGLE, R., AND C. GRANGER (1987): “Co-integration and Error Correction: Representation, Estimation, and Testing,” Econometrica, 55, 251–276.

ENTORF, H. (1997): “Random Walks Wiht Drifts: Nonsense Regression and Spurious Fixed-Effect Estimation,” Journal of Econometrics, 80, 287–296.

EVANS, M., AND K. LEWIS (1995): “Do Expected Shifts in Inflation Affect Estimates of the Long-Run Fisher Relation?,” The Journal of Finance, 50(1), 225–253.

FAMA, E. (1965): “The behavior of stock-market prices,” Journal of business, 38(1), 34.

FARIA, J., AND M. LEÓN-LEDESMA (2003): “Testing the Balassa-Samuelson Effect: Implications for Growth and the PPP,” Journal ofMacroeconomics, 25(2), 241–253.

FAUST, J., AND E. LEEPER (1997): “When Do Long-Run Identifying Restrictions Give Reliable Results?,” Journal of Business & Economic Statistics, 15(3), 345–353.

FERSON, W., S. SARKISSIAN, AND T. SIMIN (2003): “Is Stock Return Predictability Spurious?,” Journal of Investment Management, 1(3), 1–10.

FUHRER, J., AND G. MOORE (1995): “Inflation Persistence,” The Quarterly Journal of Economics, 110(1), 127–159.

FURMAN, E., AND R. ZITIKIS (2008): “Weighted risk capital allocations,” Insurance Mathematics and Economics, 43(2), 263–269.

_____(2009a): “General Stein-Type Decompositions of Covariances: Revisiting the Capital Asset Pricing Model,” Proceedings of the 58th Annual Meeting of the Midwest Finance Association, Vol.6. 8 pages. Chicago, Illinois, USA.

_____(2009b): “Weighted Pricing Functionals,” Actuarial Research Clearing House (ARCH). pp. 31. Proceedings of the 43rd Actuarial Research Conference, University of Regina, Saskatchewan, Canada.

GALÍ , J., M. GERTLER, AND J. LÓPEZ-SALIDO (2005): Robustness of the Estimates of the Hybrid New Keynesian Phillips Curve. Banco de España.

GARCIA, R., AND P. PERRON (1996): “An Analysis of the Real Interest Rate Under Regime Shifts,” The Review of Economics and Statistics, 78(1), 111–125.

GILES, D. E. (2007): “Spurious Regressions with Time-Series Data: Further Asymptotic Results,” Communications in Statistics-Theory and Methods, 36(5), 967–979.

GIRAITIS, L., P. KOKOSZKA, AND R. LEIPUS (2001): “Testing for long memory in the presence of a general trend,” Journal of Applied Probability, pp. 1033–1054.

GIRAITIS, L., P. KOKOSZKA, R. LEIPUS, AND G. TEYSSIERE (2003): “Rescaled variance and related tests for long memory in volatility and levels,” Journal of Econometrics, 112(2), 265–294.

GODFREY, L. (1988): Misspecification Tests in Econometrics: The Lagrange Multiplier Principle and Other Methods. Cambridge University Press.

GRANGER, C. (1969): “Investigating Causal Relations by Econometric Models and Cross-spectral Methods,” Econometrica, 37(3), 424–438.

______(1980): “Long Memory Relationships and the Aggregation of Dynamic Models,” Journal of Econometrics, 14, 227–38.

______(1981): “Some Properties of Time Series Data and their Use in Econometric Model Specification,” Journal of Econometrics, 16, 121–130.

GRANGER, C., N. HYUNG, AND Y. JEON (2001): “Spurious regressions with stationary series,” Applied Economics, 33(7), 899–904.

GRANGER, C., AND R. JOYEUX (1980): “An Introduction to Long-Memory Time Series Models and Fractional Differencing,” Journal of Time Series Analysis, 1, 15– 29.

GRANGER, C., AND P. NEWBOLD (1974): “Spurious Regressions in Econometrics,” Journal of Econometrics, 2, 11–20.

GRANGER, C., AND A. WEISS (1983): Time Series Analysis of Error-Correction Models. Academic Press.

HALDRUP, N. (1998): “An Econometric Analysis of I (2) Variables,” Journal of Economic Surveys, 12(5), 595–650.

HAMILTON, J. (1994): Time Series Analisys. Princeton. (2000): “A Parametric Approach to Flexible Nonlinear Inference,” Econometrica, 69, 801–812.

HAMORI, S., AND A. TOKIHISA (1997): “Testing for a unit root in the presence of a variance shift,” Economics Letters, 57(3), 245–253.

HANSEN, B., AND P. PHILLIPS (1990): “Estimation and Inference in Models of Cointegration: A Simulation Study,” Advances in Econometrics, 8, 225–248.

HASSLER, U. (1996): “Spurious regressions when stationary regressors are included,” Economics Letters, 50(1), 25–31.

HASSLER, U. (2000): “Simple Regressions with Linear Time Trends,” Journal of Time Series Analysis, 21, 27–32.

HASSLER, U. (2003): “Nonsense Regressions Due to Neglected Time Varying Means,” Statistical Papers, 44, 169–182.

HENDRY, D. (1980): “Econometrics-Alchemy or Science?,” Economica, 47(188), 387–406.

HENDRY, D., AND G. ANDERSON (1977): “Testing Dynamic Specification in Small Simultaneous Systems: An Application to a Model of Building Society Behaviour in the United Kingdom,” Frontiers in Quantitative Economics, 3, 361–383.

HENDRY, D., AND G. MIZON (1978): “Serial Correlation as Convenience Simplification, Not a Nuissance: A comment on a Study of the Demand for Money by the Bank of England,” Economic Journal, 88, 549–63.

HENDRY, D., AND M. MORGAN (1995): The Foundations of Econometric Analysis. Cambridge University Press.

HENDRY, D., A. PAGAN, AND J. SARGAN (1984): “Dynamic Specification,” Handbook of Econometrics, 2, 1023–1100.

HIPEL, AND MCLEOD (1978): “Preservation of the Rescaled Adjusted Range Parts 1, 2 and 3,” Water Resources Research, 14, 491–518.

HOSKING, J. (1981): “Fractional Differencing,” Biometrika, 68, 165–76.

HURST, H. (1951): “Long Term Storage Capacity Reservoirs,” Transcations of The American Society of Civil Engineers, 116, 770–799.

JACH, A., AND P. KOKOSZKA (2008): “Wavelet-domain test for long-range dependence in the presence of a trend,” Statistics, 42(2), 101–113.

JARQUE, C., AND A. BERA (1980): “Efficient Tests for Normality, Homoskedasticity and Serial Independence of Regression Residuals,” Economics Letters, 6, 255–259.

JEVONS, W. (1884): “Commercial Crises and Sunspots,” Investigations in Currencies and Finance (MacMillan, London), pp. 221–243.

JUSELIUS, K. (1996): “A Structured VAR under Changing Monetary Policy,” Journal of Business and Economics Statistics, 16, 400–412.

______(1999): “Price Convergence in the Medium and Long Run: An I (2) Analysis of Six Price Indices,” Cointegration, Causality and Forecasting: A Festschrift to Clive Granger, Oxford University Press, Oxford.

KAO, C. (1999): “Spurious regression and residual-based tests for cointegration in panel data,” Journal of Econometrics, 90(1), 1–44.

KEENAN, K. (1985): “A Tukey nonadditivity type test for time series nonlinearity,” Biometrika, 72, 39–44.

KIM, T., S. LEE, AND P. NEWBOLD (2003): “Spurious Regressions With Processes Around Linear Trends or Drifts,” Discussion Papers in Economics.

KIM, T., S. LEE, AND P. NEWBOLD (2004): “Spurious Regressions With Stationary Processes Around Linear Trends,” Economics Letters, 83, 257–262.

KIM, T., S. LEE, AND P. NEWBOLD (2005): “Spurious Nonlinear Regressions in Econometrics,” Economics Letters, 87, 301–306.

KIM, T., S. LEYBOURNE, AND P. NEWBOLD (2002): “Unit root tests with a break in innovation variance,” Journal of Econometrics, 109(2), 365–387.

_______(2004): “Behaviour of Dickey-Fuller Unit-Root Tests Under Trend Misspecification,” Journal of Time Series Analysis, 25(5), 755–764.

KING, R., C. PLOSSER, J. STOCK, AND M. WATSON (1991): “Stochastic Trends and Economic Fluctuations,” The American Economic Review, 81(4), 819–840.

KOUSTAS, Z. (1996): “Unemployment hysteresis in Canada: an approach based on long-memory time series models,” Applied Economics, 28(7), 823–831.

KWIATKOWSKI, D., P. PHILLIPS, P. SCHMIDT, AND Y. SHIN (1992): “Testing the null hypothesis of stationarity against the alternative of a unit root,” Journal of econometrics, 54(1-3), 159–178.

LEE, J. (2006): “Fractionally integrated long horizon regressions,” Studies in Nonlinear Dynamics & Econometrics.

LEGENDRE, A. (1805): Nouvelles méthodes pour la détermination des orbites des cometes. F. Didot.

LEYBOURNE, S., T. C. MILLS, AND P. NEWBOLD (1998): “Spurious rejections by Dickey–Fuller tests in the presence of a break under the null,” Journal of Econometrics, 87(1), 191–203.

LEYBOURNE, S., AND P. NEWBOLD (2000): “Behavior of Dickey-Fuller t-tests when there is a break under the alternative hypothesis,” Econometric Theory, 16(05), 779– 789.

LEYBOURNE, S., AND P. NEWBOLD (2003): “Spurious Rejections by Cointegration Tests Induced by Structural Breaks,” Applied Economics, 35, 1117–1121.

LI, Q., AND D. PAPELL (1999): “Convergence of International Output Time Series Evidence for 16 OECD Countries,” International Review of Economics and Finance, 8, 267–280.

LIU, Y., M. PAN, AND L. HSUEH (1993): “A modified R/S analysis of long-term dependence in currency futures prices,” Journal of International Financial Markets, Institutions & Money, 3(2), 97–113.

LO, A. (1991): “Long-term memory in stock market prices,” Econometrica, pp. 1279–1313.

LOBATO, I., AND P. ROBINSON (1996): “Averaged periodogram estimation of long memory,” Journal of Econometrics, 73(1), 303–324.

LOBATO, I., AND N. SAVIN (1998): “Real and spurious long-memory properties of stock-market data,” Journal of Business & Economic Statistics, pp. 261–268.

LUMSDAINE, R., AND D. PAPELL (1997): “Multiple Trend Breaks and the Unit-Root Hypothesis,” The Review of Economics and Statistics, 79(2), 212–218.

MANDELBROT, B., AND M. TAQQU (1979): “Robust R/S analysis of long run serial correlation,” in Proc. 42nd Session ISI, pp. 69–99.

MARMOL, F. (1995): “Spurious Regressions Between I(d) Processes,” Journal of Time Series Analysis, 16, 313–321.

MARMOL, F. (1996): “Nonsense Regressions between Integrated Processes of Different Orders.,” Oxford Bulletin of Economics & Statistics, 58(3), 525–36.

MARMOL, F. (1998): “Spurious Regression Theory with Nonstationary Fractionally Integrated Processes,” Journal of Econometrics, 84, 233–250.

MCLEOD, A., AND W. LI (1983): “Diagnosting checking ARMA time series models using squared residual autocorrelation,” Journal of Time Series Analysis, 4, 169–176.

MEHL, A. (2000): “Unit Root Tests with Double Trend Breaks and the 1990s Recession in Japan,” Japan and the World Economy, 12(4), 363–379.

MIKOSCH, T. (2003): Modeling dependence and tails of financial time series. Chapman & Hall/CRC, Extreme Values in Finance, Telecommunications, and the Environment.

MIKOSCH, T., AND C. DE VRIES (2006): “Tail Probabilities for Regression Estimators,” Laboratory of Actuarial Mathematics, University of Copenhagen.

MIKOSCH, T., AND C. ST˘ARIC˘A (2000): “Is it really long memory we see in financial returns,” Extremes and integrated risk management, 12, 149–168.

______(2004): “Nonstationarities in financial time series, the long-range dependence, and the IGARCH effects,” Review of Economics and Statistics, 86(1), 378–390.

MONTAÑÉS, A., AND M. REYES (1998): “Effect of a Shift in the Trend Function on Dickey-Fuller Unit Root Tests,” Econometric Theory, 14, 355–363.

MONTAÑÉS, A., AND M. REYES (1999): “The asymptotic behaviour of the Dickey-Fuller tests under the crash hypothesis,” Statistics and Probability Letters, 42(1), 81–89.

MOON, R., A. RUBIA, AND R. VALKANOV (2006): “Long-Horizon Regressions when the Predictor is Slowly Varying,” Journal of Business and Economic Statistics.

MORGAN, M. (1990): The History of Econometric Ideas. Cambridge University Press.

MUSCATELLI, V., AND F. SPINELLI (2000): “The long-run stability of the demand for money: Italy 1861–1996,” Journal of Monetary Economics, 45(3), 717–39.

NELSON, C., AND H. KANG (1981): “Spurious Periodicity in Inappropriately Detrended Time Series,” Econometrica, 49(3), 741–751.

NELSON, C., AND C. PLOSSER (1982): “Trends and Random Walks in Macroeconomic Time Series: some evidence and Implications,” Journal of Monetary Economics, 10, 139–169.

NEWEY, W., AND K. WEST (1987): “A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix,” Econometrica: Journal of the Econometric Society, pp. 703–708.

NG, S., AND P. PERRON (2001): “Lag length selection and the construction of unit root tests with good size and power,” Econometrica, pp. 1519–1554.

NIELSEN, H. (2002): “An I (2) Cointegration Analysis of Price and Quantity Formation in Danish Manufactured Exports,” Oxford Bulletin of Economics and Statistics, 64(5), 449–472.

NORIEGA, A., AND D. VENTOSA-SANTAUL`A RIA (2006a): “Spurious Cointegration: the Engle-Granger test in the presence of Structural Breaks,” Banco deM´exicoWorking Paper No 2006-12.

______(2006b): “Spurious Regression Under Broken Trend Stationarity,” Journal of Time Series Analysis, 27, 671–684.

______(2007): “Spurious Regression And Trending Variables,” Oxford Bulletin of Economics and Statistics, 7, 4–7.

PARK, J., AND P. PHILLIPS (1989): “Statistical Inference in Regressions with Integrated Processes: Part 2,” Econometric Theory, 5(1), 95–131.

PEARSON, K. (1897): “On a Form of Spurious Correlation Which May Arise When Indices Are Used in the Measurement of Organs,” Proceedings of the Royal Society of London, 60, 489–498.

PEDRONI, P. (2004): “Panel Cointegration; Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the Purchasing Power Parity Hypothesis,” Econometric Theory, 20(3), 597–625.

PERRON, P. (1989): “The Great Crash, The Oil Price Shock and the Unit Root Hypothesis,” Econometrica, 57, 1361–1401.

_____(1990): “Testing for a unit root in a time series with a changing mean,” Journal of Business & Economic Statistics, pp. 153–162.

______(1997): “Further evidence on breaking trend functions in macroeconomic variables,” Journal of Econometrics, 80(2), 355–385.

PERRON, P., AND S. NG (1996): “Useful modifications to some unit root tests with dependent errors and their local asymptotic properties,” The Review of Economic Studies, pp. 435–463.

PERRON, P., AND T. VOGELSANG (1992): “Nonstationarity and Level Shifts with an Application to Purchasing Power Parity,” Journal of Business and Economic Statistics, 10(3), 301–320.

PHILLIPS, P. (1986): “Understanding Spurious Regressions in Econometrics,” Journal of Econometrics, 33, 311–340.

______(1998): “New Tools for Understanding Spurious Regressions,” Econometrica, 66, 1299–1325.

______(2001): “Trending Time Series and Macroeconomic Activity: some present and future challenges,” Journal of Econometrics, 100, 21–27.

_______(2003): “Laws and Limits of Econometrics*,” The Economic Journal, 113(486), 26–52.

_______(2005): “Econometric Analysis of Fisher’s Equation,” The American Journal of Economics and Sociology, 64(1), 125–68.

PHILLIPS, P., AND B. HANSEN (1990): “Statistical Inference in Instrumental Variables Regression with I (1) Processes,” The Review of Economic Studies, 57(1), 99–125.

PHILLIPS, P., AND H. MOON (1999): “Linear Regression Limit Theory for Nonstationary Panel Data,” Econometrica, 67(5), 1057–1111.

PHILLIPS, P., AND P. PERRON (1988): “Testing for a Unit Root in Time Series Regression,” Biometrika, 75, 335–346.

PLOSSER, C., AND G. SCHWERT (1978): “Money, Income and Sunspots: measuring economic relationships and the effects of differencing,” Journal of Monetary Economics, 4, 637–660.

RAMSEY, J. (1969): “Tests for specification errors in classical linear least squares regression analysis,” Journal of the Royal Statistical Society B, 31, 155–182.

ROBINSON, P. (1994): “Efficient Tests of Nonstationary Hypotheses.,” Journal of the American Statistical Association, 89(428).

SARGAN, G. (1964): Wages and prices in United Kingdom: a study in econometric methodology. Buttewoth, London.

SEN, A. (2001): “Behaviour of Dickey–Fuller F-tests under the trend-break stationary alternative,” Statistics and Probability Letters, 55(3), 257–268.

_______(2003): “On unit-root tests when the alternative is a trend-break stationary process,” Journal of Business and Economic Statistics, 21(1), 174–184.

_______(2008): “Behaviour of Dickey–Fuller tests when there is a break under the unit root null hypothesis,” Statistics and Probability Letters, 78(6), 622–628.

STOCK, J. (1987): “Asymptotic properties of least squares estimators of cointegrating vectors,” Econometrica, pp. 1035–1056.

SUN, Y. (2004): “A Convergent t-statistic in spurious regressions,” Econometric Theory, 20(05), 943–962.

_______(2006): “Spurious regressions between stationary generalized long memory processes,” Economics Letters, 90(3), 446–454.

SUN, Y., AND P. PHILLIPS (2004): “Understanding the Fisher equation,” Journal of Applied Econometrics, 19(7), 869–886.

TAYLOR, J. (1979): “Estimation and Control of a Macroeconomic Model with Rational Expectations,” Econometrica, 47(5), 1267–1286.

TAYLOR, R. (2005): “Fluctuation Tests for a Change in Persistence,” Oxford Bulletin of Economics and Statistics, 67(2), 207–230.

TEVEROVSKY, V., AND M. TAQQU (1997): “Testing for long-range dependence in the presence of shifting means or a slowly declining trend, using a variance-type estimator,” Journal of Time Series Analysis, 18, 279–304.

TSAY, W., AND C. CHUNG (2000): “The spurious regression of fractionally integrated processes,” Journal of Econometrics, 96(1), 155–182.

VALKANOV, R. (2003): “Long-horizon regressions: theoretical results and applications,” Journal of Financial Economics, 68(2), 201–232.

VENTOSA-SANTAULÀRIA, D. (2009): “Spurious Instrumental Variables,” Forthcoming: Communications in Statistics. Theory and Methods.

VENTOSA-SANTAULÀRIA, D., AND J. VERA-VALDÉS (2008): “Granger-Causality in the presence of structural breaks,” Economics Bulletin, 3(61), 1–14.

WHITE, H. (1989): “An additional hidden unit test for neglected nonlinearity in multilayer feedforward networks,” Proceedings of the international joint conference on neural networks, Washington, DC (IEEE Press, New York), 2, 451–455.

_________(1992): Estimation, Inference and Specification Analysis. New York. Cambridge University Press.

WU, J. (2000): “Mean Reversion of the Current Account: Evidence from the Panel Data Unit Root Test,” Economics Letters, 66(2), 215–222.

WU, J., S. CHEN, AND H. LEE (2001): “Are current account deficits sustainable? Evidence from panel cointegration,” Economics Letters, 72(2), 219–224.

YULE, G. (1897): “On the theory of correlation,” Journal of the Royal Statistical Society, 60(4), 812–854.

_____(1926): “Why do we Sometimes get Nonsense-Correlations between Time-Series?–A Study in Sampling and the Nature of Time-Series,” Journal of the Royal Statistical Society, 89(1), 1–63.

ZHANG, A., R. GABRYS, AND P. KOKOSZKA (2007): “Discriminating between long memory and volatility shifts,” Statistics, 36(4), 253–275.

ZHU, Z. (1998): “The random walk of stock prices: evidence from a panel of G-7 countries,” Applied Economics Letters, 5(7), 411–413.

ZIVOT, E., AND D. ANDREWS (1992): “Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit Root Hypothesis,” Journal of Business And Economic Statistics, 10, 251–270.