Gao, Jiti (2007): Nonlinear time series: semiparametric and nonparametric methods. Published in: Chapman & Hall/CRC , Vol. 108, No. Monographs on Statistics and Applied Probability (2 September 2007): pp. 1-237.
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Abstract
Useful in the theoretical and empirical analysis of nonlinear time series data, semiparametric methods have received extensive attention in the economics and statistics communities over the past twenty years. Recent studies show that semiparametric methods and models may be applied to solve dimensionality reduction problems arising from using fully nonparametric models and methods. Answering the call for an up-to-date overview of the latest developments in the field, "Nonlinear Time Series: Semiparametric and Nonparametric Methods" focuses on various semiparametric methods in model estimation, specification testing, and selection of time series data.After a brief introduction, this book examines semiparametric estimation and specification methods and then applies these approaches to a class of nonlinear continuous-time models with real-world data. It also assesses some newly proposed semiparametric estimation procedures for time series data with long-range dependence. Even though this book only deals with climatological and financial data, the estimation and specifications methods discussed can be applied to models with real-world data in many disciplines. This resource covers key methods in time series analysis and provides the necessary theoretical details. The latest applied finance and financial econometrics results and applications presented in this book enable researchers and graduate students to keep abreast of developments in the field.
Item Type: | MPRA Paper |
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Original Title: | Nonlinear time series: semiparametric and nonparametric methods |
English Title: | Nonlinear Time Series: Semiparametric and Nonparametric Methods |
Language: | English |
Keywords: | Estimation in time series, linear time series, model specification, nonlinear time series, nonparametric method, semiparametric method |
Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes |
Item ID: | 39563 |
Depositing User: | Jiti Gao |
Date Deposited: | 05 Feb 2013 01:17 |
Last Modified: | 27 Sep 2019 14:37 |
References: | Agarwal, G. G., and Studden, W. J., 1980. Asymptotic integrated mean square error using least squares and bias minimizing splines. Annals of Statistics 8, 1307–1325. Ahn, D. H., and Gao, B., 1999. A parametric nonlinear model of term structure dynamics. Review of Financial Studies 12, 721–762. A ̈ıt-Sahalia, Y., 1996a. Nonparametric pricing of interest rate derivative securities. Econometrica 64, 527–560. A ̈ıt-Sahalia, Y., 1996b. Testing continuous-time models of the spot in- terest rate. Review of Financial Studies 9, 385–426. A ̈ıt-Sahalia, Y., 1999. Transition densities for interest rate and other nonlinear diffusions. Journal of Finance 54, 1361–1395. A ̈ıt-Sahalia, Y., Bickel, P., and Stoker, T., 2001. Goodness-of-fit tests for regression using kernel methods. Journal of Econometrics 105, 363–412. A ̈ıt-Sahalia, Y., and Lo, A., 1998. Nonparametric estimation of state– price densities implicit in financial asset prices. Journal of Finance 53, 499–547. A ̈ıt-Sahalia, Y., and Lo, A., 2000. Nonparametric risk management and implied risk aversion. Journal of Econometrics 94, 9–51. Akaike, H., 1973. Information theory and an extension of the maximum likelihood principle. In 2nd International Symposium on Information Theory (Edited by B. N. Petrov and F. Csa ́ki), 267–281. Akad ́emiai Kiado, Budapest. Andersen, T. G., and Lund, J., 1997. Estimation in continuous–time stochastic volatility models of the short term interest rate. Journal of Econometrics 77, 343–378. Andersen, T. G., and Sørensen, B. E., 1996. GMM estimation of a stochastic volatility model: a Monte Carlo study. Journal of Business and Economic Statistics 14, 328–352. Andrews, D. W., 1991. Asymptotic normality of series estimators for nonparametric and semiparametric regression models. Econometrica 59, 307–345. Andrews, D. W., 1993. Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821–856. Andrews, D. W., 1997. A conditional kolmogorov test. Econometrica 65, 1097–1028. Andrews, D. W., and Ploberger, W., 1994. Optimal tests when a nui- sance parameter is present only under the alternative. Econometrica 62, 1383–1414. Anh, V., Angulo, J., and Ruiz–Medina, M., 1999. Possible long–range dependence in fractional random fields. Journal of Statistical Planning & Inference 80, 95–110. Anh, V., and Heyde, C. (ed.), 1999. Special issue on long–range depen- dence. Journal of Statistical Planning & Inference 80, 1. Anh, V., and Inoue, A., 2005. Financial markets with memory I: dy- namic models. Stochastic Analysis & Its Applications 23, 275–300. Anh, V., Inoue, A., and Kasahara, Y., 2005. Financial markets with memory II: innovation processes and expected utility maximization. Stochastic Analysis & Its Applications 23, 301–328. Anh, V., Wolff, R. C. L., Gao, J., and Tieng, Q., 1999. Local linear re- gression with long–range dependent errors. Australian & New Zealand Journal of Statistics 41, 463–479. Arapis, M., and Gao, J., 2006. Empirical comparisons in short–term in- terest rate models using nonparametric methods. Journal of Financial Econometrics 4, 310–345. Auestad, B., and Tjøstheim, D., 1990. Identification of nonlinear time series: first order characterization and order determination. Biometrika 77, 669–687. Avramidis, P., 2005. Two–step cross–validation selection method for partially linear models. Statistica Sinica 15, 1033–1048. Bachelier, L., 1900. Th ́eorie e la Speculation. Reprinted in Cootner (ed.), 17–78. Baillie, R., and King, M. L. (eds.), 1996. Special Issue of the Journal of Econometrics. Annals of Econometrics 73. Bandi, F., and Phillips, P. C. B., 2003. Fully nonparametric estimation of scalar diffusion models. Econometrica 71, 241–283. Beran, J., 1994. Statistics for Long Memory Processes. Chapman and Hall, London. Beran, J., and Feng, Y., 2002. Local polynomial fitting with long- memory, short-memory and antipersistent errors. Annals of the Institute of Statistical Mathematics 54, 291–311. Beran, J., and Ghosh, S., 1998. Root–n–consistent estimation in par- tial linear models with long–memory errors. Scandinavian Journal of Statistics 25, 345–357. Beran, J., Ghosh, S., and Sibbertsen, P., 2003. Nonparametric M- estimation with long–memory errors. Journal of Statistical Planning & Inference 117, 199–205. Berkes, I., Horva ́th, L., Kokoszka, P., and Shao, Q., 2006. On discrimi- nating between long–range dependence and changes in mean. Annals of Statistics 34, 1116–1140. Bickel, P., and Zhang, P., 1992. Variable selection in nonparametric regression with categorical covariates. Journal of the American Sta- tistical Association 87, 90–97. Black, F., and Scholes, M., 1973. The pricing of options and corporate liabilities. Journal Political Economy 3, 637–654. Bloomfield, P., 1976. Fourier Analysis of Time Series: An Introduction. John Wiley, New York. Boente, G., and Fraiman, R., 1988. Consistency of a nonparametric estimate of a density function for dependent variables. Journal of Multivariate Analysis 25, 90–99. Breidt, F. J., Crato, N. and de Lima, P. J. F., 1998. The detection and estimation of long–memory in stochastic volatility. Journal of Econometrics 83, 325–348. Brennan, M., and Schwartz, E., 1980. A continuous–time approach to the pricing of bonds. Journal of Banking and Finance 3, 133–145. Broto, C., and Ruiz, E., 2004. Estimation methods for stochastic vola- tility models: a survey. Journal of Economic Surveys 18, 613–649. Brockwell, P., and Davis, R., 1990. Time Series: Theory and Methods. Springer, New York. Cai, Z., Fan, J., and Li, R., 2000. Efficient estimation and inferences for varying–coefficient models. Journal of the American Statistical Asso- ciation 95, 888–902. Cai, Z., Fan, J., and Yao, Q., 2000. Functional-coefficient regression models for nonlinear time series. Journal of the American Statistical Association 95, 941–956. Cai, Z., and Hong, Y., 2003. Nonparametric methods in continuous– time finance: a selective review. In Recent Advances and Trends in Nonparametric Statistics (Edited by M. G. Akritas and D. Politis), 283–302. North–Holland, Amsterdam. Carroll, R. J., Fan, J., Gijbels, I., and Wand, M. P., 1997. Generalized partially linear single–index models. Journal of the American Statis- tical Association 92, 477–489. Casas, I., and Gao, J., 2005. Specification testing in semiparametric continuous–time diffusion models: theory and practice. Working paper available from www.maths.uwa.edu.au/ ̃jiti/casgao05.pdf. Casas, I., and Gao, J., 2006. Estimation in continuous–time stochastic volatility models with long–range dependence. Working paper avail- able from www.maths.uwa.edu.au/ ̃jiti/cgjbes.pdf. Chan, K., Karolyi, F., Longstaff, F., and Sanders, A., 1992. An empir- ical comparison of alternative models of the short–term interest rate. Journal of Finance 47, 1209–1227. Chan, N. H., 2002. Time Series: Applications to Finance. Wiley Inter- science, Hoboken, New Jersey. Chapman, D., and Pearson, N., 2000. Is the short rate drift actually nonlinear ? Journal of Finance 54, 355–388. Chen, H., and Chen, K., 1991. Selection of the splined variables and con- vergence rates in a partial spline model. Canadian Journal of Statis- tics 19, 323–339. Chen, R., Liu, J., and Tsay, R., 1995. Additivity tests for nonlinear autoregression. Biometrika 82, 369–383. Chen, R., and Tsay, R., 1993. Nonlinear additive ARX models. Journal of the American Statistical Association 88, 955–967. Chen, S. X., and Gao, J., 2004. An adaptive empirical likelihood test for parametric time series regression. Journal of Econometrics (forth- coming and available from www.maths.uwa.edu.au/ ̃jiti/cg04.pdf). Chen, S. X., and Gao, J., 2005. On the use of the kernel method for specification tests of diffusion models. Working paper available from www.maths.uwa.edu.au/ ̃jiti/cg05.pdf. Chen, S. X., Ha ̈rdle, W., and Li, M., 2003. An empirical likelihood goodness–of–fit test for time series. Journal of the Royal Statistical Society Series B 65, 663–678. Chen, X., and Fan, Y., 1999. Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series. Journal of Econometrics 91, 373–401. Chen, X., and Fan, Y., 2005. Pseudo–likelihood ratio tests for model selection in semiparametric multivariate copula models. Canadian Journal of Statistics 33, 389–414. Cheng, B., and Robinson, P. M., 1994. Semiparametric estimation from time series with long–range dependence. Journal of Econometrics 64, 335–353. Cheng, B., and Tong, H., 1992. On consistent nonparametric order de- termination and chaos. Journal of the Royal Statistical Society Series B 54, 427–449. Cheng, B., and Tong, H., 1993. Nonparametric function estimation in noisy chaos. In Developments in Time Series Analysis (Edited by T. Subba Rao), 183–206. Chapman and Hall, London. Comte, F., 1996. Simulation and estimation of long memory continuous time models. Journal of Time Series Analysis 17, 19–36. Comte, F., and Renault, E., 1996. Long memory in continuous-time models. Journal of Econometrics 73, 101–149. Comte, F., and Renault, E., 1998. Long memory in continuous–time stochastic volatility models. Mathematical Finance 8, 291–323. Corradi, V., and Swanson, N. R., 2005. Bootstrap specification tests for diffusion processes. Journal of Econometrics 124, 117–148. Corradi, V., and White, H., 1999. Specification tests for the variance of a diffusion process. Journal of Time Series Analysis 20, 253–270. Cox, J., Ingersoll, E., and Ross, S., 1985. An intertemporal general equilibrium model of asset prices. Econometrica 53, 363–384. Dahlhaus, R., 1989. Efficient parameter estimation for self–similar pro- cesses. Annals of Statistics 17, 1749–1766. Delgado, M. A., and Hidalgo, J., 2000. Nonparametric inference on structural breaks. Journal of Econometrics 96, 113–144. Deo, R., and Hurvich, C. M., 2001. On the log–periodogram regres- sion estimator of the memory parameter in long memory stochastic volatility models. Econometric Theory 17, 686–710. Dette, H., 1999. A consistent test for the functional form of a regression based on a difference of variance estimators. Annals of Statistics 27, 1012–1040. Dette, H., 2002. A consistent test for heteroscedasticity in nonparametric regression based on the kernel method. Journal of Statistical Planning & Inference 103, 311–329. Dette, H., and Von Lieres und Wilkau, C., 2001. Testing additivity by kernel-based methods—what is a reasonable test ? Bernoulli 7, 669–697. Dette, H., and Von Lieres und Wilkau, C., 2003. On a test for a para- metric form of volatility in continuous time financial models. Finance Stochastics 7, 363–384. DeVore, R. A., and Lorentz, G. G., 1993. Constructive Approximation. Springer, New York. Dickey, D. A., and Fuller, W. A., 1979. Distribution of estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427–431. Ding, Z., and Granger, C. W. J., 1996. Modelling volatility persistence of speculative returns: a new approach. Journal of Econometrics 73, 185–215. Ding, Z., Granger, C. W. J., and Engle, R., 1993. A long memory prop- erty of stock market returns and a new model. Journal of Empirical Finance 1, 83–105. Dong, C., Gao, J., and Tong, H., 2006. Semiparametric penalty function method in partially linear model selection. Forthcoming in Statistica Sinica (available from www.maths.uwa.edu.au/ ̃jiti/dgt.pdf). Doukhan, P., 1995. Mixing–Properties and Examples. Lecture Notes in Statistics. Springer–Verlag, New York. Durham, G. B., 2004. Likelihood specification analysis of continuous– time models of the short–term interest rate. Forthcoming in the Jour- nal of Financial Economics. Eastwood, B., and Gallant, R., 1991. Adaptive truncation rules for seminonparametric estimates achieving asymptotic normality. Econometric Theory 7, 307–340. Engle, R. F., 2001. Financial econometrics–a new dicipline with new methods. Journal of Econometrics 100, 53–56. Engle, R. F., and Granger, C. W. J., 1987. Co–integration and error correction: representation, estimation and testing. Econometrica 55, 251–276. Engle, R. F., Granger, C. W. J., Rice, J. A., and Weiss, A., 1986. Semiparametric estimates of the relation between weather and electricity sales. Journal of the American Statistical Association 81, 310–320. Eubank, R. L., 1988. Spline Smoothing and Nonparametric Regression. Marcel Dekker, Inc., New York. Eubank, R. L., 1999. Nonparametric Regression and Spline Smoothing. Marcel Dekker, Inc., New York. Eubank, R. L., and Hart, J. D., 1992. Testing goodness-of-fit in regres- sion via order selection. Annals of Statistics 20, 1412–1425. Eubank, R. L., and Spiegelman, C. H., 1990. Testing the goodness of fit of a linear model via nonparametric regression techniques. Journal of the American Statistical Association 85, 387–392. Eumunds, D. E., and Moscatelli, V. B., 1977. Fourier approximation and embeddings of Sobolev space. Dissertationae Mathematicae. Pol- ish Scientific Publishers, Warsaw. Fan, J., 1996. Test of significance based on wavelet thresholding and Neyman’s truncation. Journal of the American Statistical Association 91, 674–688. Fan, J., 2005. A selective overview of nonparametric methods in financial econometrics. With comments and a rejoinder by the author. Statistical Science 20, 317–357. Fan, J., and Gijbels, I., 1996. Local Polynomial Modelling and Its Applications. Chapman and Hall, London. Fan, J., Ha ̈rdle, W., and Mammen, E., 1998. Direct estimation of low dimensional components in additive models. Annals of Statistics 26, 943–971. Fan, J., and Huang, L. S., 2001. Goodness-of-fit tests for parametric regression models. Journal of the American Statistical Association 453, 640–652. Fan, J., and Huang, T., 2005. Profile likelihood inferences on semiparametric varying–coefficient partially linear models. Bernoulli 11, 1031–1057. Fan, J., and Jiang, J., 2005. Nonparametric inferences for additive mod- els. Journal of the American Statistical Association 100, 890–907. Fan, J., Jiang, J., Zhang, C., and Zhou, Z., 2003. Time–dependent diffusion models for term structure dynamics. Statistica Sinica 13, 965–992. Fan, J., and Li, R., 2001. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statis- tical Association 96, 1348–1360. Fan, J., and Li, R., 2002. Variable selection for Cox’s proportional haz- ards model and frailty model. Annals of Statistics 30, 74–99. Fan, J., and Yao, Q., 1998. Efficient estimation of conditional variance functions in stochastic regression. Biometrika 85, 645–660. Fan, J., and Yao, Q., 2003. Nonlinear Time Series: Nonparametric and Parametric Methods. Springer, New York. Fan, J., and Zhang, C., 2003. A re-examination of Stanton’s diffusion estimation with applications to financial model validation. Journal of the American Statistical Association 461, 118–134. Fan, J., Zhang, C. M., and Zhang, J., 2001. Generalized likelihood ratio statistics and Wilks phenomenon. Annals of Statistics 29, 153–193. Fan, Y., and Li, Q., 1996. Consistent model specification tests: omitted variables and semiparametric functional forms. Econometrica 64, 865– 890. Fan, Y., and Li, Q., 1999. Central limit theorem for degenerate U– statistics of absolutely regular processes with applications to model specification testing. Journal of Nonparametric Statistics 10, 245–271. Fan, Y., and Li, Q., 2000. Consistent model specification tests: kernel- based tests versus Bierens’ ICM tests. Econometric Theory 16 1016– 1041. Fan, Y., and Li, Q., 2003. A kernel-based method for estimating additive partially linear models. Statistica Sinica 13, 739–762. Fan, Y., and Linton, O., 2003. Some higher–theory for a consistent nonparametric model specification test. Journal of Statistical Plan- ning and Inference 109, 125–154. Fox, R., and Taqqu, M. S., 1986. Large–sample properties of parame- ter estimates for strongly dependent stationary Gaussian time series. Annals of Statistics 14, 512–532. Franke, J., Kreiss, J. P., and Mammen, E., 2002. Bootstrap of kernel smoothing in nonlinear time series. Bernoulli 8, 1–38. Franses, P. H., and van Dijk, D., 2000. Nonlinear Time Series Models in Empirical Finance. Cambridge University Press. Frisch, U., 1995. Turbulence. Cambridge University Press. Galka, A., 2000. Topics in Nonlinear Time Series Analysis with Implications for EEG Analysis. World Scientific, Singapore. Gallant, A. R., 1981. On the bias in flexible functional forms and an essentially unbiased form: the Fourier flexible form. Journal of Econometrics 15, 211–245. Gallant, A. R., and Souza, G., 1991. On the asymptotic normality of Fourier flexible form estimates. Journal of Econometrics 50, 329–353. Gao, J., 1998. Semiparametric regression modelling of nonlinear time series. Scandinavian Journal of Statistics 25, 521–539. Gao, J., 2000. A semiparametric approach to pricing interest rate derivative securities. Presentation at Quantitative Methods in Finance & Bernoulli Society 2000 Conference, Sydney, 4–9 December, 2000. Gao, J., 2004. Modelling long–range dependent Gaussian processes with application in continuous–time financial models. Journal of Applied Probability 41, 467–482. Gao, J., and Anh, V., 1999. Semiparametric regression with long-range dependent error processes. Journal of Statistical Planning & Inference 80, 37–57. Gao, J., and Anh, V., 2000. A central limit theorem for a random quadratic form of strictly stationary processes. Statistics & Probability Letters 49, 69–79. Gao, J., Anh, V., and Heyde, C., 2002. Statistical estimation of non- stationary Gaussian processes with long–range dependence and inter- mittency. Stochastic Processes & Their Applications 99, 295–321. Gao, J., Anh, V., Heyde, C., and Tieng, Q., 2001. Parameter estimation of stochastic processes with long–range dependence and intermittency. Journal of Time Series Analysis 22, 517–535. Gao, J., Anh, V., and Wolff, R. C. L., 2001. Semiparametric approximation methods in multivariate model selection. Journal of Complexity 17, 754–772. Gao, J., and Gijbels, I., 2006. Selection of smoothing parametes in nonparametric and semiparametric testing. Working paper available from www.maths.uwa.edu.au/ ̃jiti/gg51.pdf. Gao, J., Gijbels, I., and Van Bellegem, S., 2006. Nonparametric simultaneous testing for structural breaks. Working paper available from www.maths.uwa.edu.au/ ̃jiti/ggvb.pdf. Gao, J., and Hawthorne, K., 2006. Semiparametric estimation and test- ing of the trend of temperature series. Econometrics Journal 9, 333– 356. Gao, J., and King, M. L., 2004. Adaptive testing in continuous–time diffusion models. Econometric Theory 20, 844–882. Gao, J., and King, M. L., 2005. Model estimation and specification testing in nonparametric and semiparametric models. Working paper available from www.maths.uwa.edu.au/ ̃jiti/jems.pdf. Gao, J., King, M. L., Lu, Z., and Tjøstheim, D., 2006. Nonparametric time series specification with nonstationarity. Working paper available from www.maths.uwa.edu.au/ ̃jiti/gklt.pdf. Gao, J., and Liang, H., 1995. Asymptotic normality of pseudo-LS estimator for partially linear autoregressive models. Statistics & Probability Letters 23, 27–34. Gao, J., and Liang, H., 1997. Statistical inference in single-index and partially nonlinear regression models. Annals of the Institute of Sta- tistical Mathematics 49, 493–517. Gao, J., Lu, Z., and Tjøstheim, D., 2006. Estimation in semiparametric spatial regression. Annals of Statistics 36, 1395–1435. Gao, J., and Shi, P., 1997. M-type smoothing splines in nonparametric and semiparametric regression models. Statistica Sinica 7, 1155–1169. Gao, J., and Tong, H., 2004. Semiparametric nonlinear time series model selection. Journal of the Royal Statistical Society Series B 66, 321–336. Gao, J., and Tong, H., 2005. Nonparametric and semiparametric regres- sion model selection. Unpublished technical report. Working paper available from www.maths.uwa.edu.au/ ̃jiti/kao43.pdf. Gao, J., Tong, H., and Wolff, R. C. L., 2002a. Adaptive orthogonal series estimation in additive stochastic regression models. Statistica Sinica 12, 409–428. Gao, J., Tong, H., and Wolff, R. C. L., 2002b. Model specification tests in nonparametric stochastic regression models. Journal of Multivari- ate Analysis 83, 324–359. Gao, J., and Wang, Q., 2006. Specification testing of nonlinear time series with long–range dependence. Working paper available from www.maths.uwa.edu.au/ ̃jiti/gw61.pdf. Gao, J., and Yee, T., 2000. Adaptive estimation in partially linear (semiparametric) autoregressive models. Canadian Journal of Sta- tistics 28, 571–586. Geweke, J., and Porter–Hudak, S., 1983. The estimation and appli- cation of long memory time series models. Journal of Time Series Analysis 4, 221–237. Gijbels, I., and Goderniaux, A. C., 2004. Bandwidth selection for change- point estimation in nonparametric regression. Technometrics 46, 76– 86. Gonza ́lez–Manteiga, W., Quintela–del–R ́ıo, A., and Vieu, P., 2002. A note on variable selection in nonparametric regression with dependent data. Statistics & Probability Letters 57, 259–268. Go ̈tze, F., Tikhomirov, A., and Yurchenko, V., 2004. Asymptotic ex- pansion in the central limit theorem for quadratic forms. Preprint 04–004, Probability and Statistics, The University of Bielefeld, Germany. Gozalo, P. L., 1993. A consistent model specification test for nonparametric estimation of regression function models. Econometric Theory 9, 451–477. Gozalo, P. L., and Linton, O. B., 2001. Testing additivity in generalized nonparametric regression models with estimated parameters. Journal of Econometrics 104, 1–48. Granger, C. W. J., Inoue, T., and Morin, N., 1997. Nonlinear stochastic trends. Journal of Econometrics 81, 65–92. Granger, C. W. J., and Joyeux, R., 1980. An introduction to long–range time series models and fractional differencing. Journal of Time Series Analysis 1, 15–30. Granger, C. W. J., and Tera ̈svirta, T., 1993. Modelling Nonlinear Dy- namic Relationships. Oxford University Press. Granger, C. W. J., Tera ̈svirta, T., and Tjøstheim, D., 2006. Nonlinear Time Series Econometrics. Oxford University Press. Gr ́egoire, G., and Hamrouni, Z., 2002. Two nonparametric tests for change-point problem. Journal of Nonparametric Statistics 14, 87– 112. Hall, P., and Hart, J., 1990. Nonparametric regression with long–range dependence. Stochastic Processes and Their Applications 36, 339–351. Hall, P., Lahiri, S., and Polzehl, J., 1996. On the bandwidth choice in nonparametric regression with both short– and long–range dependent errors. Annals of Statistics 23, 1921–1936. Hannan, E. J., 1973. The asymptotic theory of linear time–series models. Journal of Applied Probability 10, 130–145. Hansen, B., 2000a. Sample splitting and threshold estimation. Econometrica 68, 575–603. Hansen, B., 2000b. Testing for structural change in conditional means. Journal of Econometrics 97, 93–115. Ha ̈rdle, W., 1990. Applied Nonparametric Regression. Cambridge University Press, Boston. Ha ̈rdle, W., Hall, P., and Ichimura, H., 1993. Optimal smoothing in single-index models. Annals of Statistics 21, 157-178. Ha ̈rdle, W., Hall, P., and Marron, J., 1988. How far are automatically chosen regression smoothing parameters from their optimum (with discussion) ? Journal of the American Statistical Association 83, 86– 99. Ha ̈rdle, W., Hall, P., and Marron, J., 1992. Regression smoothing parameters that are not far from their optimum. Journal of the American Statistical Association 87, 227–233. Ha ̈rdle, W., and Kneip, A., 1999. Testing a regression model when we have smooth alternatives in mind. Scandinavian Journal of Statistics 26, 221–238. Ha ̈rdle, W., Liang, H., and Gao, J., 2000. Partially Linear Models. Springer Series: Contributions to Statistics. Physica-Verlag, New York. Ha ̈rdle, W., Lu ̈tkepohl, H., and Chen, R., 1997. A review of nonpara- metric time series analysis. International Statistical Review 65, 49–72. Ha ̈rdle, W., and Mammen, E., 1993. Comparing nonparametric versus parametric regression fits. Annals of Statistics 21, 1926–1947. Ha ̈rdle, W., and Vieu, P., 1992. Kernel regression smoothing of time series. Journal of Time Series Analysis 13, 209–232. Hart, J., 1997. Nonparametric Smoothing and Lack-of-Fit Tests. Springer, New York. Harvey, A. C., 1998. Long memory in stochastic volatility. In Forecasting Volatility in Financial Markets (Edited by J. Knight and S. Satchell), 307–320. Butterworth–Heinemann, Oxford. Hengartner, N. W., and Sperlich, S., 2003. Rate optimal estimation with the integration method in the presence of many covariates. Working paper. Heyde, C., and Gay, R., 1993. Smoothed periodogram asymptotics and estimation for processes and fields with possible long–range depen- dence. Stochastic Processes and Their Applications 45, 169–182. Hidalgo, F. J., 1992. Adaptive semiparametric estimation in the presence of autocorrelation of unknown form. Journal of Time Series Anal-ysis 13, 47–78. Hjellvik, V., and Tjøstheim, D., 1995. Nonparametric tests of linearity for time series. Biometrika 82, 351–368. Hjellvik, V., Yao, Q., and Tjøstheim, D., 1998. Linearity testing using local polynomial approximation. Journal of Statistical Planning and Inference 68, 295–321. Hong, Y., and Li, H., 2005. Nonparametric specification testing for continuous–time models with application to spot interest rates. Review of Financial Studies 18, 37–84. Hong, Y., and White, H., 1995. Consistent specification testing via nonparametric series regression. Econometrica 63, 1133–1159. Horowitz, J., 2003. Bootstrap methods for Markov processes. Econometrica 71, 1049–1082. Horowitz, J. L., and Ha ̈rdle, W., 1994. Testing a parametric model against a semiparametric alternative. Econometric Theory 10, 821– 848. Horowitz, J., and Mammen, E., 2004. Nonparametric estimation of an additive model with a link function. Annals of Statistics 32, 2412– 2443. Horowitz, J., and Spokoiny, V. G., 2001. An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69, 599–632. Huang, J., and Yang, L., 2004. Identification of non-linear additive autoregressive models. Journal of the Royal Statistical Society Series B 66, 463–477. Hull, J., and White, A., 1987. The pricing of options on assets with stochastic volatilities. Journal of Finance 2, 281–300. Hurst, H. E., 1951. Long–term storage capacity of reservoirs. Transac- tions of the American Society of Civil Engineers 116, 770–799. Hurvich, C., and Beltrao, K., 1993. Asymptotics for the low-frequency ordinates of the periodogram of a long–memory time series. Journal of Time Series Analysis 14, 455–472. Hurvich, C., Deo, R., and Brodsky, J., 1998. The mean squared error of Geweke and Porter-Hudak’s estimator of the memory parameter of a long-memory time series. Journal of Time Series Analysis 19, 19–46. Hurvich, C., and Tsai, C. L., 1995. Relative rates of convergence for efficient model selection criteria in linear regression. Biometrika 82, 418–425. Hyndman, R., King, M. L., Pitrun, I., and Billah, B., 2005. Local linear forecasts using cubic smoothing splines. Australian & New Zealand Journal of Statistics 47, 87–99. Jayasuriya, B., 1996. Testing for polynomial regression using nonpara- metric regression techniques. Journal of the American Statistical As- sociation 91, 1626–1631. Jiang, G., 1998. Nonparametric modelling of US interest rate term structure dynamics and implication on the prices of derivative securities. Journal Financial and Quantitative Analysis 33, 465–497. Jiang, G., and Knight, J., 1997. A nonparametric approach to the estimation of diffusion processes with an application to a short-term interest rate model. Econometric Theory 13, 615–645. Jones, C. S., 2005. Nonlinear mean reversion in the short–term interest rate. Forthcoming in the Review of Financial Studies. Kantz, H., and Schreiber, T., 2004. Nonlinear Time Series Analysis. 2nd Edition. Cambridge University Press. Karlsen, H., Myklebust, T., and Tjøstheim, D., 2006. Nonparametric estimation in a nonlinear cointegration model. Forthcoming in Annals of Statistics. Karlsen, H., and Tjøstheim, D., 1998. Nonparametric estimation in null recurrent time series. Sonderforschungsbereich 373, 50. Humboldt University, Berlin. Karlsen, H., and Tjøstheim, D., 2001 Nonparametric estimation in null recurrent time series. Annals of Statistics 29, 372–416. Kashin, B. S., and Saakyan, A. A., 1989. Orthogonal Series. Translations of Mathematical Monographs, Vol. 75, American Mathematical Society. King, M. L., and Shively, T., 1993. Locally optimal testing when a nuisance parameter is present only under the alternative. Review of Economics and Statistics 75 1–7. Kohn, R., Marron, J., and Yau, P., 2000. Wavelet estimation using Bayesian basis selection and basis averaging. Statistica Sinica 10, 109– 128. Koul, H., and Stute, W., 1998. Regression model fitting with long memory errors. Journal of Statistical Planning & Inference 71, 35–56. Kreiss, J. P., Neumann, M. H., and Yao, Q., 2002. Bootstrap tests for simple structures in nonparametric time series regression. Preprint, Institu ̈t fu ̈r Mathematische Stochastik, Technische Universita ̈t, Braunschweig, Germany. Kristensen, D., 2004. Estimation in two classes of semiparametric diffu- sion models. Working paper available from Department of Economics, The University of Wisconsin–Madison, USA. Ku ̈nsch, H., 1986. Discrimination between monotonic trends and long- range dependence. Journal of Applied Probability 23, 1025–1030. Lavergne, P., 2001. An equality test across nonparametric regressions. Journal of Econometrics 103, 307–344. Lavergne, P., and Vuong, Q. H., 1996. Nonparametric selection of re- gressors: the nonnested case. Econometrica 64, 207–219. Lavergne, P., and Vuong, Q. H., 2000. Nonparametric significance testing. Econometric Theory 16, 576–601. Li, K. C., 1985. From Stein’s unbiased risk estimates to the method of generalized cross-validation. Annals of Statistics 13, 1352–1377. Li, K. C., 1986. Asymptotic optimality of CL and generalized cross-validation in ridge regression with application to spline smoothing. Annals of Statistics 14, 1101–1112. Li, K. C., 1987. Asymptotic optimality for Cp, CL, cross-validation and generalized cross-validation: discrete index set. Annals of Statistics 15, 958–975. Li, M., Pearson, N. D., and Poteshman, A. M., 2005. Facing up to conditioned diffusions. Forthcoming in the Journal of Financial Eco- nomics. Li, Q., 1999. Consistent model specification tests for time series econometric models. Journal of Econometrics 92, 101–147. Li, Q., and Hsiao, C., 1998. Testing serial correlation in semiparametric panel data models. Journal of Econometrics 87, 207–237. Li, Q., Hsiao, C., and Zinn, J., 2003. Consistent specification tests for semiparametric & nonparametric models based on series estimation methods. Journal of Econometrics 112, 295–325. Li, Q., and Racine, J., 2006. Nonparametric Econometrics: Theory and Practice. Princeton University Press. Li, Q., and Wang, S., 1998. A simple consistent bootstrap tests for a parametric regression functional form. Journal of Econometrics 87, 145–165. Li, Q., and Wooldridge, J., 2002. Semiparametric estimation of partially linear models for dependent data with generated regressors. Econo- metric Theory 18, 625–645. Lieberman, O., and Phillips, P. C. B., 2004. Expansions for the distribution of the maximum likelihood estimator of the fractional difference parameter. Econometric Theory 20, 464–484. Lieberman, O., and Phillips, P. C. B., 2005. Expansions for approximate maximum likelihood estimators of the fractional difference parameter. Econometrics Journal 8, 367–379. Ling, S., and Tong, H., 2005. Testing for a linear MA model against threshold MA models. Annals of Statistics 33, 2529–2552. Linton, O. B., 1997. Efficient estimation of additive nonparametric regression models. Biometrika 84, 469–473. Linton, O. B., 2000. Efficient estimation of generalized additive nonparametric regression models. Econometric Theory 16, 502–523. Linton, O. B., 2001. Estimating additive nonparametric models by partial Lq norm: the curse of fractionality. Econometric Theory 17, 1037– 1050. Linton, O. B., and Ha ̈rdle, W., 1996. Estimation of additive regression models with known links. Biometrika 83, 529–540. Linton, O. B., and Mammen, E., 2005. Estimation in semiparametric ARCH(∞) models by kernel smoothing methods. Econometrica 73, 1001–1030. Mammen, E., Linton, O. B., and Nielsen, J. P., 1999. The existence and asymptotic properties of a backfitting projection algorithm under weak conditions. Annals of Statistics 27, 1443-1490. Mandelbrot, B., and Van Ness, J., 1968. Fractional Brownian motion, fractional noises and applications. SIAM Review 10, 422–437. Masry, E., and Tjøstheim, D., 1995. Nonparametric estimation and identification of nonlinear ARCH time series. Econometric Theory 11, 258–289. Masry, E., and Tjøstheim, D., 1997. Additive nonlinear ARX time series and projection estimates. Econometric Theory 13, 214–252. Merton, R. C., 1973. The theory of rational option pricing. Bell Journal of Economics, 4, 141–183. Mikosch, T., and Starica, C., 2004. Nonstationarities in financial time series, the long–range dependence and the IGARCH effects. Review of Economics and Statistics, 86, 378–390. Nicolau, J., 2003. Bias reduction in nonparametric diffusion coefficient estimation. Econometric Theory 19, 754–777. Nielsen, J. P., and Linton, O. B., 1998. An optimization interpretation of integration and back–fitting estimators for separable nonparametric models. Journal of the Royal Statistical Society Series B 60, 217–222. Nishiyama, Y., and Robinson, P., 2000. Edgeworth expansions for semiparametric averaged derivatives. Econometrica 68, 931–980. Nishiyama, Y., and Robinson, P., 2005. The bootstrap and the Edgeworth correction for semiparametric averaged derivatives. Econometrica 73, 903–948. Pagan, A., and Ullah, A., 1999. Nonparametric Econometrics. Cambridge University Press, New York. Park, J., and Phillips, P. C. B., 2001. Nonlinear regressions with inte- grated time series. Econometrica 69, 117–162. Phillips, P. C. B., 1987. Time series regression with a unit root. Econometrica 55, 277–302. Phillips, P. C. B., and Park, J., 1998. Nonstationary density estimation and kernel autoregression. Cowles Foundation Discussion Paper, No. 1181, Yale University. Pollard, D., 1984. Convergence of Stochastic Processes. Springer, New York. Pritsker, M., 1998. Nonparametric density estimation and tests of continuous time interest rate models. Review of Financial Studies 11, 449–487. Robinson, P. M., 1988. Root–N–consistent semiparametric regression. Econometrica 56, 931–964. Robinson, P. M., 1989. Hypothesis testing in semiparametric and nonparametric models for econometric time series. Review of Economic Studies 56, 511–534. Robinson, P. M., 1994. Time series with strong dependence. In Advances in Econometrics (Edited by C. A. Sims), Sixth World Congress Vol. 1, 47–96. Cambridge University Press, Cambridge. Robinson, P. M., 1995a. Log-periodogram regression of time series with long-range dependence. Annals of Statistics 23, 1048–1072. Robinson, P. M., 1995b. Gaussiaan semiparametric estimation of long– range dependence. Annals of Statistics 23, 1630–1661. Robinson, P. M., 1997. Large-sample inference for nonparametric regression with dependent errors. Annals of Statistics 25, 2054–2083. Robinson, P. M., 2001. The memory of stochastic volatility models. Journal of Econometrics 101, 195–218. Robinson, P. M. (ed.), 2003. Time series with long memory. Advanced Texts in Econometrics. Oxford University Press, Oxford. Robinson, P. M., 2005. The distance between rival nonstationarity frac- tional processes. Journal of Econometrics 128, 283–300. Robinson, P. M., and Zaffaroni, P., 1998. Nonlinear time series with long memory: a model for stochastic volatility. Journal of Statistical Planning & Inference 68, 359–371. Rockafeller, R. T., 1970. Convex Analysis. Princeton University Press, New Jersey. Roussas, G., and Ioannides, D., 1987. Moment inequalities for mixing sequences of random variables. Stochastic Analysis and Applications 5, 61–120. Ruppert, D., Wand, M. P., and Carroll, R. J., 2003. Semiparametric Regression. Cambridge University Press, Cambridge. Samarov, A. M., 1993. Exploring regression structure using nonpara- metric functional estimation. Journal of the American Statistical Association 423, 836–847. Schumaker, L., 1981. Spline Functions. John Wiley, New York. Shao, J., 1993. Linear model selection by cross–validation. Journal of the American Statistical Association 422, 486–494. Shao, J., 1997. An asymptotic theory for linear model selection (with comments). Statistica Sinica 7, 221–264. Shi, P., and Tsai, C. L., 1999. Semiparametric regression model selections. Journal of Statistical Planning & Inference 77, 119–139. Shimotsu, K., and Phillips, P. C. B., 2005. Exact local Whittle estimation of fractional integration. Annals of Statistics 33, 1890–1933. Shimotsu, K., and Phillips, P. C. B., 2006. Local Whittle estimation of fractional integration and some of its variants. Journal of Econometrics 130, 209–233. Shiryaev, A. N., 1999. Essentials of Stochastic Finance. World Scientific, Singapore. Shively, T., and Kohn, R., 1997. A Bayesian approach to model selection in stochastic coefficient regression models and structural time series models. Journal of Econometrics 76, 39–52. Shively, T., Kohn, R., and Ansley, C. F., 1994. Testing for linearity in a semiparametric regression model. Journal of Econometrics 64, 7–96. Shively, T., Kohn, R., and Wood, S., 1999. Variable selection and func- tion estimation in additive nonparametric regression using a data- based prior. With comments and a rejoinder by the authors. Journal of the American Statistical Association 94, 777–806. Silverman, B. W., 1986. Density Estimation for Statistics and Data Analysis. Chapman and Hall, London. Sperlich, S., Tjøstheim, D., and Yang, L., 2002. Nonparametric esti- mation and testing of interaction in additive models. Econometric Theory 18, 197–251. Stanton, R., 1997. A nonparametric model of term structure dynamics and the market price of interest rate risk. Journal of Finance 52, 1973–2002. Stock, J., 1994. Unit roots, structural breaks and trends. In Handbook of Econometrics (Edited by R. Engle and D. McFadden) 4, 2740–2841. Elsevier Science, Amsterdam. Stone, M., 1977. An asymptotic equivalence of choice of model by cross-validation and Akaike’s criterion. Journal of the Royal Statistical So- ciety Series B 39, 44–47. Stute, W., 1997. Nonparametric model checks for regression. Annals of Statistics 25, 613–641. Stute, W., Thies, S., and Zhu, L., 1998. Model checks for regression: an innovation process approach. Annals of Statistics 26, 1916–1934. Stute, W., and Zhu, L., 2002. Model checks for generalized linear models. Scandinavian Journal of Statistics 29, 535–545. Stute, W., and Zhu, L., 2005. Nonparametric checks for single-index models. Annals of Statistics 33, 1048–1083. Sun, Y., and Phillips, P. C. B., 2003. Nonlinear log–periodogram re- gression for perturbed fractional processes. Journal of Econometrics 115, 355–389. Sundaresan, S., 2001. Continuous–time methods in finance: a review and an assessment. Journal of Finance 55, 1569–1622. Tanaka, K., 1996. Time Series Analysis: Nonstationary and Noninvertible Distribution Theory. John Wiley & Sons, New York. Taylor, S., 1986. Modelling Financial Time Series. John Wiley, Chichester. U.K. Taylor, S. J., 1994. Modelling stochastic volatility: a review and comparative study. Mathematical Finance 4, 183–204. Tera ̈svirta, T., Tjøstheim, D., and Granger, C., 1994. Aspects of modelling nonlinear time series. In Handbook of Econometrics (Edited by R. F. Engle and D. L. McFadden) 4, 2919–2957. Elsevier Science, Amsterdam. Tjøstheim, D., 1994. Nonlinear time series: a selective review. Scandinavian Journal of Statistics 21, 97–130. Tjøstheim, D., 1999. Nonparametric specification procedures for time series. Asymptotics, nonparametrics, and time series 158, 149–199. Statistics: Textbooks and Monographs. Dekker, New York. Tjøstheim, D., and Auestad, B., 1994a. Nonparametric identification of nonlinear time series: projections. Journal of the American Statistical Association 89, 1398–1409. Tjøstheim, D., and Auestad, B., 1994b. Nonparametric identification of nonlinear time series: selecting significant lags. Journal of the Amer- ican Statistical Association 89, 1410–1419. Tong, H., 1976. Fitting a smooth moving average to noisy data. IEEE Transactions on Information Theory, IT-26, 493–496. Tong, H., 1990. Nonlinear Time Series. Oxford University Press, Oxford. Truong, Y. K., and Stone, C. J., 1994. Semiparametric time series regression. Journal Time Series Analysis 15, 405–428. Tsay, R., 2005. Analysis of Financial Time Series. Second Edition. Wiley Interscience, Hoboken, New Jersey. Tschernig, R., and Yang, L., 2000. Nonparametric lag selection for time series. Journal of Time Series Analysis 21, 457–487. Vasicek, O., 1977. An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–188. Viano, M., Deniau, C., and Oppenheim, G., 1994. Continuous–time fractional ARMA processes. Statistics & Probability Letters 21, 323– 336. Viano, M., Deniau, C., and Oppenheim, G., 1995. Long-range depen- dence and mixing for discrete time fractional processes. Journal of Time Series Analysis 16, 323–338. Vieu, P., 1994. Choice of regressors in nonparametric estimation. Computational Statistics & Data Analysis 17, 575–594. Vieu, P., 1995. Order choice in nonlinear autoregressive models. Statistics 26, 307–328. Vieu, P., 2002. Data–driven model choice in multivariate nonparametric regression. Statistics 36, 231–245. Wahba, G., 1978. Improper priors, spline smoothing and the problem of guarding against model errors in regression. Journal of the Royal Statistical Society Series B 40, 364–372. Wahba, G., 1990. Spline Models for Observational Data. SIAM, Philadelphia. Wand, M. P., and Jones, M. C., 1995. Kernel Smoothing. Chapman and Hall, London. Whang, Y. J., 2000. Consistent bootstrap tests of parametric regression functions. Journal of Econometrics 98, 27–46. Whang, Y. J., and Andrews, D. W. K., 1993. Tests of specification for parametric and semiparametric models. Journal of Econometrics 57, 277–318. Wong, C. M., and Kohn, R., 1996. A Bayesian approach to estimating and forecasting additive nonparametric autoregressive models. Jour- nal of Time Series Analysis 17, 203–220. Wong, F., Carter, C., and Kohn, R., 2003. Efficient estimation of covariance selection models. Biometrika 90, 809–830. Wood, S., Kohn, R., Shively, T., and Jiang, W., 2002. Model selection in spline nonparametric regression. Journal of the Royal Statistical Society Series B 64, 119–139. Wooldridge, J., 1992. A test for functional form against nonparametric alternatives. Econometric Theory 8, 452–475. Xia, Y., Li, W. K., Tong, H., and Zhang, D., 2004. A goodness-of-fit test for single-index models (with comments). Statistica Sinica 14, 1–39. Xia, Y., Tong, H., and Li, W. K., 1999. On extended partially linear single–index models. Biometrika 86, 831–842. Xia, Y., Tong, H., Li, W. K., and Zhu, L. X., 2002. An adaptive estimation of dimension reduction space. Journal of the Royal Statistical Society Series B 64, 363–410. Yang, L., 2002. Direct estimation in an additive model when the components are proportional. Statistica Sinica 12, 801–821. Yang, L., 2006. A semiparametric GARCH model for foreign exchange volatility. Journal of Econometrics 130, 365–384. Yang, L., and Tschernig, R., 2002. Non– and semiparametric identifica- tion of seasonal nonlinear autoregression models. Econometric Theory 18, 1408–1448. Yang, Y., 1999. Model selection for nonparametric regression. Statistica Sinica 9, 475–500. Yao, Q., and Tong, H., 1994. On subset selection in nonparametric stochastic regression. Statistica Sinica 4, 51–70. Yatchew, A. J., 1992. Nonparametric regression tests based on least squares. Econometric Theory 8, 435–451. Yau, P., and Kohn, R., 2003. Estimation and variable selection in nonparametric heteroscedastic regression. Statistics & Computing 13, 191–208. Yau, P., Kohn, R., and Wood, S., 2003. Bayesian variable selection and model averaging in high-dimensional multinomial nonparametric regression. Journal of Computational & Graphical Statistics 12, 23– 54. Zhang, C. M., and Dette, H., 2004. A power comparison between non- parametric regression tests. Statistics & Probability Letters 66, 289– 301. Zhang, P., 1991. Variable selection in nonparametric regression with continuous covariates. Annals of Statistics 19, 1869–1882. Zhang, P., 1993. Model selection via multifold cross–validation. Annals of Statistics 21, 299–313. Zheng, J. X., 1996. A consistent test of functional form via nonparametric estimation techniques. Journal of Econometrics 75, 263–289. Zheng, X., and Loh, W. Y., 1995. Consistent variable selection in linear models. Journal of the American Statistical Association 90, 151–156. Zheng, X., and Loh, W. Y., 1997. A consistent variable selection criterion for linear models with high–dimensional covariates. Statistica Sinica 7, 311–325. Zhu, L., 2005. Nonparametric Monte Carlo Tests and Their Applications. Lecture Notes in Statistics. 182. Springer, New York. |
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