A review of nonparametric time series analysis

International Statistical Review

Volumn 65, Issue 1, 1997, Pages 49-72

  Härdie, Wolfgang ^a   Lütkepohl, Helmut ^a   Chen, Rong ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Bootstrap; Dependent observations; Hermite expansions; Kernel estimators; Smoothing techniques

Indexed keywords

EID: 0039460177     PISSN: 03067734     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1751-5823.1997.tb00367.x     Document Type: Article

References (135)

1. Akaike, H. (1969). Power spectrum estimation through autoregressive model fitting. Annals of the Institute of Statistical Mathematics, 21, 407-419.
2. Akaike, H. (1970). Statistical predictor identification. Ann. Inst. Statist. Math. 22, 203-217.
3. Akaike, H. (1974). A New Look at Statistical Model Identification, IEEE Transactions on Automatic Control, AC-19, 716-722.
4. Auestad, B. & Tjøstheim, D. (1990). Identification of nonlinear time series: First order characterization and order estimation, Biometrika, 77, 669-687.
5. Bartlett, M.S. (1950). Periodogram analysis and continuous spectra. Biometrika, 37, 1-16.
6. Becker, R.A., Chambers, J. M. & Wilks, A. R. (1988). The New S Language. New York: Chapman and Hall.
7. Berk, K.N. (1974). Consistent autoregressive spectral estimates. Annals of Statistics, 2, 489-502.
8. Bhansali, R.J. (1978). Linear prediction by autoregressive model fitting in the time domain. Annals of Statistics, 6, 224-231.
9. Bierens, H.J. (1983). Uniform consistency of kernel estimators of a regression function under generalized conditions. Journal of the American Statistical Association, 78, 699-707.
10. Bierens, H.J. (1987). Kernel estimators of regression functions, in T.F. Bewley (ed.) Advances in Econometrics: Fifth World Congress, Vol. 1. Cambridge: Cambridge University Press
11. Bierens, H.J. (1994). Topics in Advanced Econometrics: Estimation, testing, and specification of cross-section and time series models. Cambridge: Cambridge University Press
12. Billingsley, P. (1968). Convergence of Probability Measures. New York: Wiley.
13. Blackman, R.B. & Tukey, J.W. (1959). The Measurement of Power Spectrum from the Point of View of Communications Engineering. New York: Dover.
14. Bose, A. (1988). Edgeworth correction by bootstrap in autoregressions. Annals of Statistics, 16, 1709-1722.
15. Bowman, A.W. (1994). An alternative method of cross-validation for the smoothing of density estimates. Biometrika, 71, 353-360.
16. Breitung, J. & Gouriéroux, C. (1997). Rank tests for unit roots. Journal of Econometrics, forthcoming.
17. Brillinger, D.R. & Krishnaiah, P.R. (Ed.) (1983) Handbook of Statistics 3, Time Series in the Frequency Domain. Amsterdam: North-Holland.
18. Campbell, B. & Dufour, J.-M. (1993). Exact nonparametric orthogonality and random walk tests. Working paper, C.R.D.E., Montreal.
19. Chan, K.S. & Tong, H. (1986). On estimating thresholds in autoregressive models. Journal of Time Series Analysis, 7, 179-190.
20. Chatfield, C. (1984). The Analysis of Time Series: An Introduction, 3rd ed. London: Chapman and Hall.
21. Chen, R. (1996). A nonparametric multi-step prediction estimator in Markovian structures. Statistica Sinica, 6, 603-615.
22. Chen, R. & Hafner, C. (1995). Nonlinear time series analysis, in XploRe, an Interactive Statistical Computing Environment, (ed. Härdle, W., Klinke, S. & Turlach, B.). Heidelberg: Springer Verlag.
23. Chen, R., Härdle, W., Linton, O.B. & Severance-Lossin, E. (1996). Estimation in additive nonparametric regression. In COMPSTAT meeting Semmering, Härdle, W. & Schimek, M. (eds), Physika Verlag.
24. Chen, R., Liu, J.S. & Tsay, R.S. (1995). Additivity tests for nonlinear autoregressive models. Biometrika, 82, 369-383.
25. Chen, R. & Tsay, R. S. (1993a). Nonlinear additive ARX models. Journal of the American Statistical Association, 88, 955-967.
26. Chen, R. & Tsay, R. S. (1993b). Functional-coefficient autoregressive models. Journal of the American Statistical Association, 88, 298-308.
27. Cheng, B. & Tong, H. (1992). On consistent non-parametric order determination and chaos (with discussion). Journal of the Royal Statistical Society, Series B, 54, 427-474.
28. Cleveland, W. S. & Devlin, S. J. (1988). Locally weighted regression: An approach to regression analysis by local fitting. Journal of the American Statistical Association, 83, 596-610.
29. Collomb, G. & Härdle, W. (1986). Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations. Stochastic Processes and their Applications, 23, 77-89.
30. Csörgõ, S. & Mielniczuk, J. (1995a). Density estimation under long-range dependence. Ann. Statist. 23, 990-999.
31. Csörgõ, S. & Mielniczuk, J. (1995b). Nonparametric regression under long-range dependent normal errors. Ann. Statist. 23, 1000-1014.
32. Dahlhans, R. (1993). Fitting time series models to nonstationary processes. Institut für Angewandte Mathematik, Universität Heidelberg.
33. Dickey, D.A. & Fuller, W.A. (1979). Distribution of the estimators for autoregressive time series with unit root. Journal of the American Statistical Association, 74, 427-431.
34. Diebold, F. & Nason, J. (1990). Nonparametric exchange rate prediction. Journal of International Economics, 28, 315-332.
35. Diebolt, J. & Guegan, D. (1990). Probabilistic properties of the general nonlinear autoregressive process of order one. Technical report, No 128, L.S.T.A., Université de Paris VI.
36. Donoho, D.L. & Johnstone, I.M. (1992). Minimax estimation via wavelet shrinkage. Technical Report 402, Dept. Stat., Stanford University.
37. Donoho, D.L., Johnstone, I.M., Kerkyacharian, G. & Picard, D. (1995). Wavelet Shrinkage: Asymptopia? (with discussion). Journal of the Royal Statistical Society, Series B, 57, 301-369.
38. Drost, F.C., Klaassen, C.A.J. & Werker, B.J.M. (1994). Adaptive estimation in time series models. CentER Discussion Paper 9488, Tilburg University.
39. Efron, B. & Tibshirani, R.J. (1993). An Introduction to the Bootstrap. New York: Chapman & Hall.
40. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987-1008.
41. Engle, R.F. & Gonzáles-Rivera, G. (1991). Semiparametric ARCH models. Journal of Business and Economic Statistics, 9, 345-359.
42. Fan, J. (1993). Local linear regression and their minimax efficiency. Annals of Statistics, 21, 196-216.
43. Franke, J. & Härdle, W. (1992). On bootstrapping kernel spectral estimates. Annals of Statistics, 20, 121-145.
44. Friedman, J.H. (1988). Multivariate adaptive regression splines (with discussion). Ann. Statist., 19, 1-141.
45. Fuller, W.A. (1976). Introduction to Statistical Time Series. New York: Wiley.
46. Gallant, A.R. & Nychka, D.W. (1987). Seminonparametric maximum likelihood estimation. Econometrica, 55, 363-390.
47. Gallant, A.R. & Tauchen, G.E. (1989). Seminonparametric estimation of conditional constrained heterogeneous processes: Asset pricing applications, Econometrica, 57, 1091-1120.
48. Gasser, T. & Müller, H.G. (1979). Kernel estimation of regression functions. In Smoothing Techniques for Curve Estimation, eds. T. Gasser & M. Rosenblatt, 23-68.
49. Granger, C.W.J. & Hallman, G. (1991). Nonlinear transformations of integrated time series. Journal of Time Series Analysis, 12, 207-224.
50. Granger, C.W.J. & Teräsvirta, T. (1993). Modeling Nonlinear Economic Relationships. Oxford: Oxford University Press.
51. Györfi, L., Härdle, W., Sarda, P. & Vieu, P. (1989). Nonparametric Curve Estimation from Time Series. Lecture Notes in Statistics 60. Heidelberg: Springer-Verlag.
52. Haggan, V. & Ozaki, T. (1981). Modeling nonlinear vibrations using an amplitude-dependent autoregressive time series model. Biometrika, 68, 189-196.
53. Hall, P. & Hart. J.D. (1990a). Convergence rates in density estimation for data from infinite-order moving average processes. Probability Theory and Related Fields, 87, 253-274.
54. Hall, P. & Hart, J.D. (1990b). Nonparametric regression with long-range dependence. Stochastic Processes and their Applications, 36, 339-351.
55. Hall, P., Lihiri, S.N. & Truong, Y.K. (1994). On bandwidth choice for density estimation with dependent data. Manuscript.
56. Hall, P. & Patil, P. (1995). Formulae for mean integrated squared error of nonlinear wavelet-based density estimators. Ann. Statist. 23, 905-928.
57. Hamilton, J.D. (1994). Time Series Analysis, Princeton: Princeton University Press.
58. Härdle, W. (1990). Applied Nonparametric Regression. Cambridge: Cambridge University Press.
59. Härdle, W. & Hall, P. (1993). On the backfitting algorithm for additive regression models. Statistica Neerlandica, 47, 43-57.
60. Härdle, W., Klinke, S. & Turlach, B. (1995). XploRe, an Interactive Statistical Computing Environment. Heidelberg: Springer-Verlag.
61. Härdle, W. & Tsybakov, A.B. (1997). Local polynomial estimators of the volatility function. J. Econometrics, to appear.
62. Härdle, W., Tsybakov, A.B. & Yang, L. (1996). Nonparametric vector autoregression. Journal of Statistical Planning and Inference, to appear.
63. Härdle, W. & Vieu, P. (1992). Kernel regression smoothing of time series. Journal of Time Series Analysis, 13, 209-232.
64. Hart, J.D. (1991). Kernel regression estimation with time series errors. Journal of the Royal Statistical Society, Series B, 53, 173-187.
65. Hart, J.D. (1994). Automated kernel smoothing of dependent data by using time series cross-validation. Journal of the Royal Statistical Society, Series B, 56, 529-542.
66. Hart, J.D. (1996). Some automated methods of smoothing time-dependent data. J. Nonparametric Statistics, 6, 115-142.
67. Hart, J.D. & Vieu, P. (1990). Data-driven bandwidth choice for density estimation based on dependent data. Annals of Statistics, 18, 873-890.
68. Hart, J.D. & Wehrly, T.E. (1986). Kernel regression estimation using repeated measurement data. Journal of the American Statistical Association, 81, 1080-1088.
69. Hastie, T.J. & Tibshirani, R.J. (1990). Generalized Additive Models, Vol. 43 of Monographs on Statistics and Applied Probability. London: Chapman and Hall.
70. Hjellvik, V. & Tjøstheim, D. (1995). Nonparametric tests of linearity for time series. Biometrika, 82, 351-368.
71. Hutchinson, J.M., Lo, A.W. & Poggio, T. (1994). A nonparametric approach to pricing and hedging derivative securities via learning networks. Journal of Finance, 49, 851-889.
72. Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12, 231-254.
73. Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica, 59, 1551-1580.
74. Jones, D. A. (1978). Non-linear autoregressive processes. Journal of the Royal Statistical Society, Series A, 360, 71-95.
75. Katkovnik, V. Y. (1979). Linear and nonlinear methods for nonparametric regression analysis (in Russian). Avtomatika i Telemehanika, 35-46.
76. Kreiss, J.-P. (1987). On adaptive estimation in stationary ARMA processes. Annals of Statistics, 15, 112-133.
77. Kreiss, J.-P. and Franke, J. (1992). Bootstrapping stationary autoregressive moving-average models. Journal of Time Series Analysis, 13, 297-317.
78. Kuan, C.-M. & White, H. (1994). Artificial neural networks: An econometric perspective. Econometric Reviews, 13, 1-91.
79. Künsch, H.R. (1989). The jackknife and the bootstrap for general stationary observations. Annals of Statistics, 17, 1217-1241.
80. Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54, 159-178.
81. Lewis, R. & Reinsel, G.C. (1985). Prediction of multivariate time series by autoregressive model fitting. Journal of Multivariate Analysis, 16, 393-411.
82. Lewis, P.A.W. & Stevens, G. (1991). Nonlinear modeling of time series using multivariate adaptive regression splines (MARS), Journal of the American Statistical Association, 87, 864-877.
83. Linton, O. (1993). Adaptive estimation in ARCH models. Econometric Theory, 9, 539-569.
84. Linton, O. & Nielsen, J.P. (1995). A kernel method of estimating structured nonparametric regression based on marginal integration. Biometrika, 82, 93-100.
85. Liu, R.Y. and Singh, K. (1992). Moving blocks jackknife and bootstrap capture weak dependence. In Exploring the Limits of Bootstrap. R. Lepage & L. Billard (eds.). New York: Wiley, 225-248.
86. Lütkepohl, H. (1991). Introduction to Multiple Time Series Analysis. Berlin: Springèr-Verlag.
87. Lütkepohl, H. & Poskitt, D.S. (1996). Testing for causation using infinite order vector autoregressive processes. Econometric Theory, 12, 61-87.
88. Masry, E. & Tjøstheim, D. (1995a). Nonparametric estimation and identification of nonlinear ARCH time series: strong convergence and asymptotic normality. Econometric Theory, 11, 258-289.
89. Masry, E. & Tjøstheim, D. (1995b). Additive nonlinear ARX time series and projection estimates. Econometric Theory, to appear.
90. Murata, N., Yoshizawa, S. & Amari, S. (1994). Network information criterion - determining the number of hidden units for an artificial neural network model. IEEE Transactions on Neural Networks, 5, 865-871.
91. Park, B.U. & Marron, J.S. (1990). Comparison of data-driven bandwidth selectors. Journal of the American Statistical Association, 85, 66-72.
92. Park, B.U. & Turlach, B. (1992). Practical performance of several data driven bandwidth selectors (with discussion). Computational Statistics, 7, 251-270.
93. Parzen, E. (1961). Mathematical considerations in the estimation of spectra. Technometrics, 3, 167-190.
94. Parzen, E. (1974). Some recent advances in time series modeling. IEEE Transactions on Automatic Control, AC-19, 723-730.
95. Parzen, E. (1977). Multiple time series: Determining the order of approximating autoregressive schemes. In Multivariate Analysis-IV, P.R. Krishnaiah (ed.). Amsterdam: North-Holland, 389-409.
96. Pham, D.T. (1985). Bilinear Markovian representations and bilinear models. Stochastic Process. Appl. 20, 295-306.
97. Phillips, P.C.B. & Perron, P. (1988). Testing for a unit root in time series analysis. Biometrika, 75, 335-346.
98. Prakasa Rao, B.L.S. (1983). Nonparametric Functional Estimation. Orlando, FL: Academic Press.
99. Priestley, M.B. (1981). Spectral Analysis and Time Series. London: Academic Press.
100. Priestley, M. B. (1988). Non-linear and Non-stationary Time Series Analysis, New York: Academic Press.
101. Priestley, M.B. (1996). Wavelets and time-dependent spectral analysis. Journal of Time Series Analysis, 17, 85-103.
102. Robinson, P.M. (1983a). Review of various approaches to power spectrum estimation. In Handbook of Statistics, Vol. 3 (D.R. Brillinger and P.R. Krishnaiah eds.), pp. 343-368. Amsterdam: North-Holland.
103. Robinson, P.M. (1983b). Non-parametric estimation for time series models. Journal of Time Series Analysis, 4, 185-208.
104. Robinson, P.M. (1988). Semiparametric econometrics: A survey. Journal of Applied Econometrics, 3, 35-51.
105. Rosenblatt, M. (1970). Density estimation and Markov sequences. In Nonparametric Techniques in Statistical Inference, (M.L. Puri, ed.) 199-213. Cambridge University Press.
106. Roussas, G.G. (1969). Nonparametric estimation in Markov process. Annals of the Institute of Statistical Mathematics, 21, 73-87.
107. Rudemo, M. (1982). Empirical choice of histograms and kernel density estimators. Scandinavian J. of Statist., 9, 65-78.
108. Rumelhart, D.E., Hinton, G.E. & Williams, R.J. (1986). Learning internal representations by error propagation. In Parallel Distributed Processing: Explorations in the Microstructures of Cognition. D.E. Rumelhart & J.L. McClelland eds. Cambridge: M.I.T. Press, 1, pp. 318-362.
109. Said, S.E. & Dickey, D.A. (1984). Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika, 71, 599-607.
110. Saikkonen, P. & Luukkonen, R. (1997). Testing cointegration in infinite order vector autoregressive processes. Journal of Econometrics, forthcoming.
111. Schuster, A. (1898). On the investigation of hidden periodicities with application to a supposed 26-day period of meteorological phenomena. Terr. Mag. Atmos. Elect., 3, 13-41.
112. Sheather, S.J. (1983). A data-based algorithm for choosing the window width when estimating the density at a point. Computational Statistics and Data Analysis, 1, 229-238.
113. Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. London: Chapman and Hall.
114. Singh, R.S. & Ullah, A. (1985). Nonparametric time series estimation of joint DGP, conditional DGP and vector autoregression. Econometric Theory, 1, 27-52.
115. Skaug, H.J. & Tjøstheim, D. (1993). Non-parametric tests of serial independence. In The M. Priestley Birthday Volume (ed. T. Subba Rao), pp. 207-229.
116. Steigerwald, D.G. (1992). Adaptive estimation in time series regression models. Journal of Econometrics, 54, 251-275.
117. Stock, J.H. & M.W. Watson (1988). Testing for common trends. Journal of the American Statistical Association, 83, 1097-1107.
118. Stone, C.J. (1977). Consistent nonparametric regression. Annals of Statistics 5, 595-635.
119. Teräsvirta, T. (1994). Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association, 89, 208-218.
120. Tibshirani, R. (1988). Estimating transformations for regression via additivity and variance stabilization. Journal of the American Statistical Association, 83, 194-405.
121. Tjøstheim, D. (1990). Nonlinear time series and Markov chains. Advances in Applied Probability, 22, 587-611.
122. Tjøstheim, D. (1994). Nonlinear time series, a selective review. Scand. J. Statist. 21, 97-130.
123. Tjøstheim, D. & Auestad, B. (1994a). Non-parametric identification of non-linear time series: projection. Journal of the American Statistical Association, 89, 1398-1409.
124. Tjøstheim, D. & Auestad, B. (1994b). Non-parametric identification of non-linear time series: selecting significant lags. Journal of the American Statistical Association, 89, 1410-1419.
125. Tong, H. (1983). Threshold Models in Nonlinear Time Series Analysis. Lecture Notes in Statistics. Vol. 21, Heidelberg: Springer.
126. Tong, H. (1990). Nonlinear Time Series Analysis: A Dynamic Approach. Oxford: Oxford University Press.
127. Truong, Y.K. (1993). A nonparametric framework for time series analysis. New Directions in Time Series Analysis. New York: Springer.
128. Truong, Y.K. & Patil, P. (1996). On estimating possibly discontinous regression involving stationary time series. Manuscript.
129. Tsay, R. (1989). Testing and modeling threshold autoregressive processes. Journal of the American Statistical Association, 84, 231-240.
130. Tsybakov, A.B. (1986). Robust reconstruction of functions by the local approximation method. Problems of Information Transmission, 22, 133-146.
131. Tukey, J.W. (1949). The sampling theory of power spectrum estimates. Proceedings of the Symposium on Applications of Autocorrelation Analysis to Physical Problems, NAVEXOS-P-735, 47-67, Washington: Office of Naval Research.
132. Tweedie, R. L. (1975). Sufficient Conditions for Ergodicity and Recurrence of Markov Chain on a General State Space. Stochastic Processes and their Applications, 3, 385-403.
133. Weigend, A.S. & Nix, D. (1994). Predictions with confidence intervals (local error bars). Discussion Paper No. 34, Sonderforschungsbereich 373, Humboldt-Universität zu Berlin.
134. Werker, B.J.M. (1995). Statistical Methods in Financial Econometrics. CentER, Tilburg University.
135. Wong, C.-M. & Kohn, R. (1996). A Bayesian approach to estimating and forecasting additive nonparametric autoregressive models. Journal of Time Series Analysis, 17, 203-220.