Asymptotic and nootstrap inference for AR(∞) processes with conditional heteroskedasticity

Econometric Reviews

Volumn 26, Issue 6, 2007, Pages 609-641

  Gonalves, Slvia ^a   Kilian, Lutz ^b,c  

^a Canada H3A 2T7   (Canada)

^b UNIVERSITY OF MICHIGAN   (United States)

^c CEPR ^*  (United States)

Author keywords

Autoregression; Bootstrap; GARCH

Indexed keywords

EID: 36949024935     PISSN: 07474938     EISSN: 15324168     Source Type: Journal    
DOI: 10.1080/07474930701624462     Document Type: Article

References (53)

1. Andrews, D. W. K (1991). Heteroskedastic and autocorrelation consistent covariance matrix estimation. Econometrica 59:817-858.
2. Bekaert, G., Hodrick, R. J. (2001). Expectations hypothesis tests. Journal of Finance 56:1357-1394.
3. Berk, K. (1974). Consistent autoregressive spectral estimates. Annals of Statistics 2:489-502.
4. Bhansali, R. (1978). Linear prediction by autoregressive model fitting in the time domain. Annals of Statistics 6:224-231.
5. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31:307-327.
6. Braun, P. A., Mittnik, S. (1993). Misspecifications in vector autoregressions and their effects on impulse responses and variance decompositions. Journal of Econometrics 59:319-341.
7. Brillinger, D. R. (1981). Time Series: Data Analysis and Theory. San Francisco: Siam.
8. Buhlmann, P. (1995). Moving-average representation for autoregressive approximations. Stochastic Processes and Their Applications 60:331-342.
9. Bùhlmann, P. (1997). Sieve bootstrap for time series. Bernoulli 3:123-148.
10. Canova, F. (1995). Vector autoregressions: specification, estimation, inference and forecasting. In: Pesaran, H., Wickens, M., eds. The Handbook of Applied Econometrics. Vol. 1. London: Basil Blackwell.
11. Choi, E., Hall, P. (2000). Bootstrap confidence regions computed on autoregressions of arbitrary order. Journal of the Royal Statistical Society, Series B 62:461-477.
12. Davidson, J. (1994). Stochastic Limit Theory. New York: Oxford University Press.
13. Diebold, F. X., Kilian, L. (2001). Measuring predictability: theory and macroeconomic applications. Journal of Applied Econometrics 16:657-669.
14. Durrett, R. (1996). Probability: Theory and Examples. 2nd ed. Belmont, California: Duxury Press.
15. Eicker, F. (1963). Asymptotic normality and consistency of the least squares estimators for families of linear regressions. Annals of Mathematical Statistics 34:447-456.
16. Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50:987-1007.
17. Freedman, D. A. (1981). Bootstrapping regression models. Annals of Statistics 9:1218-1228.
18. Galbraith, J. W. (2003). Content horizons for univariate time-series forecasts. International Journal of Forecasting 19:43-55.
19. Geman, S., Hwang, C.-R. (1982). Nonparametric maximum likelihood estimation by the method of sieves. Annals of Statistics 10:401-414.
20. Giné, E., Zinn, J. (1990). Bootstrapping general empirical measures. Annals of Probability 18:851-869.
21. Gonçalves, S., Kilian, L. (2004). Bootstrapping autoregressions with conditional heteroskedasticity of unknown form. Journal of Econometrics 123:89-120.
22. Gonçalves, S., White, H. (2004). Maximum likelihood and the bootstrap for nonlinear dynamic models. Journal of Econometrics 119:199-220.
23. Grenander, U. (1981). Abstract Inference. New York: Wiley.
24. Hannan, E. J. (1970). Multiple Time Series. New York: Wiley.
25. Hannan, E. J., Deistler, M. (1988). The Statistical Theory of Linear Systems. New York: Wiley.
26. Hansen, B. E. (2000). Testing for structural change in conditional models. Journal of Econometrics 97:93-115.
27. Hodrick, R. J. (1992). Dividend yields and expected stock returns: alternative procedures for inference and measurement. Review of Financial Studies 5:357-386.
28. Hong, Y., Lee, Y.-J. (2003). Consistent testing for serial correlation of unknown form under general conditional heteroskedasticity. Manuscript, Department of Economics, Cornell University.
29. Inoue, A., Kilian, L. (2002). Bootstrapping smooth functions of slope parameters and innovation variances in VAR(∞) models. International Economic Review 43:309-332.
30. Kreiss, J. P. (1997). Asymptotic properties of residual bootstrap for autoregressions. Mimeo, Institute for Mathematical Stochastics, Technical University of Braunschweig, Germany.
31. Künsch, H. R. (1989). The jackknife and the bootstrap for general stationary observations. Annals of Statistics 17:1217-1241.
32. Kuersteiner, G. M. (2001). Optimal instrumental variables estimation for ARMA models. Journal of Econometrics 104:359-405.
33. Lewis, R., Reinsel, G. (1985). Prediction of multivariate time series of autoregressive model fitting. Journal of Multivariate Analysis 16:393-411.
34. Liu, R. Y. (1988). Bootstrap procedure under some non-i.i.d. models. Annals of Statistics 16:1696-1708.
35. Lütkepohl, H. (1988a). Asymptotic distribution of the moving-average coefficients of an estimated vector autoregressive process. Econometric Theory 4:77-85.
36. Lütkepohl, H. (1988b). Prediction tests for structural stability. Journal of Econometrics 39:267-296.
37. Lütkepohl, H., Poskitt, D. S. (1991). Estimating orthogonal impulse responses via vector autoregressive models. Econometric Theory 7:487-496.
38. Lütkepohl, H., Poskitt, D. S. (1996). Testing for causation using infinite order vector autoregressive processes. Econometric Theory 12:61-87.
39. Lütkepohl, H., Saikkonen, P. (1997). Impulse response analysis in infinite-order cointegrated vector autoregressive processes. Journal of Econometrics 81:127-157.
40. Mammen, E. (1993). Bootstrap and wild bootstrap for high dimensional linear models. Annals of Statistics 21:255-285.
41. McCullagh, P. (1987). Tensor Methods in Statistics. London: Chapman and Hall.
42. Ng, S., Perron, P. (1995). Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag. Journal of the American Statistical Association 90:268-281.
43. Nicholls, D. F., Pagan. A. R. (1983). Heteroskedasticity in models with lagged dependent variables. Econometrica 51:1233-1242.
44. Paparoditis, E. (1996). Bootstrapping autoregressive and moving average parameter estimates of infinite order vector autoregressive processes. Journal of Multivariate Analysis 57:277-296.
45. Politis, D. N., Romano, J. P., Wolf, M. (1999). Subsampling. New York: Springer-Verlag.
46. Saikkonen, P. (1992). Estimation and testing of cointegrated systems by an autoregressive approximation. Econometric Theory 8:1-27.
47. Saikkonen, P., Lütkepohl, H. (1996). Infinite-order cointegrated vector autoregressive processes. Econometric Theory 12:814-844.
48. Saikkonen, P., Luukkonen, R. (1997). Testing cointegration in infinite order vector autoregressive processes. Journal of Econometrics 81:93-126.
49. Stock, J. H., Watson, M. W. (2001). Vector autoregressions. Journal of Economic Perspectives 15(Fall):101-115.
50. Weiss, A. A. (1988). ARMA models with ARCH errors. Journal of Time Series Analysis 5:129-143.
51. White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48:817-838.
52. White, H. (2000). Asymptotic Theory for Econometricians. Revised Edition. San Diego: Academic Press.
53. Wu, C. F. J. (1986). Jackknife bootstrap and other resampling methods in regression analysis. Annals of Statistics 14:1261-1295.