Bootstrapping time series models

Econometric Reviews

Volumn 15, Issue 2, 1996, Pages 115-158

  Li, Hongyi ^a   Maddala, G S ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85071343153     PISSN: 07474938     EISSN: 15324168     Source Type: Journal    
DOI: 10.1080/07474939608800344     Document Type: Article

References (103)

1. Abadir, K. M., 1993. OLS bias in a non-stationary autoregression. Econometric Theory, 9: 81–93.
2. Abramovich, L., and Singh, K., 1985. Edgeworth corrected pivotal statistics and the bootstrap. Annals of Statistics, 13: 116–132.
3. Anderson, T. W., 1959. On asymptotic distribution of estimates of parameters of stochastic differences equations. Ann. Math. Statist., 30: 676–687.
4. Andrews, D.W.K., 1993. Exactly median-unbiased estimation of first-order autoregressive/unit-root models. Econometrica, 61: 139–165.
5. Babu, G. J., 1995. Bootstrap for non-standard cases. Journal of Statistical Planning and Inference, 43: 197–203.
6. Bai, C., and Olshen, R., 1988. Discussion of Hall's comparison of bootstrap confidence intervals. Annals of Statistics, 16: 953–956.
7. Barnard, G. A., 1963. Contribution to discussion. Journal of the Royal Statistical Society, B, 25: 294
8. Basawa, I. V., Mallik, A. K., McCormick, W. P., and Taylor, R. L., 1989. Bootstrapping explosive autoregressive processes. Annals of Statistics, 17: 1479–1486.
9. Basawa, I. V., Mallik, A. K., McCormick, W. P., and Taylor, R. L., 1991a. Bootstrapping unstable first order autoregressive processes. Annals of Statistics, 19: 1098–1101.
10. Basawa, I. V., Mallik, A. K., and McCormick, W., 1991b. and Taylor. R.L., Bootstrapping test of significance and sequential bootstrap estimation for unstable first order autoregressive processes. Commun. Statist. -Theory Meth., 20: 1015–1026.
11. Bernard, J. T., and Veall, M. R., 1987. The probability distribution of future demand. Journal of Business and Economic Statistics, 5: 417–424.
12. Beran, R., 1987. Prepivoting to reduce level error of confidence sets. Biometrika, 74: 457–468.
13. Beran, R., 1988. Prepivoting test statistics: A bootstrap view of asymptotic refinements. J. Amer. Statist. Assoc, 83: 687–697.
14. Beran, R., 1990. Refining bootstrap simultaneous confidence sets. J. Amer. Statist. Assoc, 85: 417–426.
15. Bhargava, A., 1986. On the theory of testing for unit roots in observed time series. Review of Economic Studies, 53: 369–384.
16. Bickel P. J., Freedman D. A., On Edgeworth expansions and the bootstrap 1980 Unpublished manuscript
17. Bickel, P. J., and Freedman, D. A., 1983. “ A Festschrift for Erich Lehmann ”. In Bootstrapping regression models with many parameters, Edited by: Bickel, P., Doksum, K., and Hodges, J. L., 28–48. Belmont, California: Wadsworth.
18. Bose, A., 1988. Edgeworth correction by bootstrap in autoregressions. Annals of Statistics, 16: 1709–1722.
19. Bose, A., 1990. Bootstrap in moving average models. Ann. Inst. Stat. Math., 42: 753–768.
20. Carlstein, E., 1986. The use of subseries values for estimating the variance of a general statistic from a stationary sequence. Annals of Statistics, 14: 1171–1179.
21. Chatterjee, S., and Bootstrapping, A.R.M.A., 1986. models: some simulations. IEEE Transactions, SMC-16: 294–299.
22. Davidson, J.E.H., 1981. Problems with the estimation of moving-average processes. Journal of Econometrics, 19: 295–310.
23. Davison, A. C., and Hall, P., 1993. On studentizing and blocking methods for implementing the bootstrap with dependent data. Australian Journal of Statistics, 35: 212–224.
24. DiCiccio, T., and Romano, J., 1988. A review of bootstrap confidence intervals (with discussion). Journal of the Royal Statistical Society, B, 50: 338–354.
25. Dickey, D. A., and Fuller, W. A., 1979. Distribution of the autoregressive time series with a unit root. Journal of the American Statistical Association, 74: 427–431.
26. Dickey, D. A., and Fuller, W. A., 1981. Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49: 1057–1072.
27. Dufour, J. M., 1990. Exact tests and confidence sets in linear regressions with autocorrelated errors. Econometrica, 58: 475–494.
28. Efron, B., 1979. Bootstrap methods: another look at the jackknife. The Annals of Statistics, 7: 1–26.
29. Efron, B., 1981. Censored data and the bootstrap. Journal of the American Statistical Association, 76: 312–319.
30. Efron, B., 1987. Better bootstrap confidence intervals. Journal of the American Statistical Association, 82: 171–200.
31. Efron, B., and Gong, G., 1983. A leisurely look at the bootstrap, the jackknife, and cross validation. American Statistican, 37: 36–48.
32. Efron, B., and Tibshirani, R., 1986. Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statistical Science, 1: 54–77.
33. Engle, R., and Granger, C.W.J., 1987. Cointegration and error correction: representations, estimation and testing. Econometrica, 55: 252–276.
34. Entorf H., Random Walks with drift, simultaneous equation errors, and small samples: simulating the birds-eye view 192 INSEE discussion paper, #9222
35. Ericsson, N. R., and Marquez, J., 1993. Encompassing the forecasts of U.S. trade balance models. Review of Economics and Statistics, 75: 19–31.
36. Eriksson, B., 1983. On the construction of confidence limits for the regression coefficients when the residuals are dependent. J. Statist. Comput. SimuL, 17: 297–309.
37. Fair, R. C., 1980. Estimating the expected predictive accuracy of econometric models. International Economic Review, 21: 355–378.
38. Fair, R. C., 1984. Specification, Estimation and Analysis of Macroeconomic Models, Cambridge: Harvard University Press.
39. Ferretti N., Romo J., Unit root bootstrap tests for AR(1) models Division of Economics, Universidad Carlos I11 de Madrid 1994 Working paper
40. Findley, D. F., 1986. “ Computer Science and Statistics: The Interface ”. In On bootstrap estimates of forecast mean square errors for autoregressive processes, Edited by: Allen, D. M., 11–17. North-Holland: Elsevier Science Publishers B.V.
41. Freedman, D. A., 1981. Bootstrapping regression models. The Annals of Statistics, 9: 1218–1228.
42. Freedman, D. A., 1984. On bootstrapping two-stage least-squares estimates in stationary linear models. The Annals of Statistics, 12: 827–842.
43. Freedman, D. A., and Peters, S. C., 1984. Bootstrapping a regression equation: some empirical results. Journal of the American Statistical Association, 79: 97–106.
44. Fuller, W. A., 1976. Introduction to Statistical Time Series, New York: Wiley.
45. Fuller, W. A., 1985. “ Nonstationary autoregressive time series ”. In Handbook of Statistics, Edited by: Hannan, E. J., Krishniah, P. R., and Rao, M. M., 1–23. North Holland.
46. van Giersbergen, N. P. A., and Kiviet, J. F., A Monte Carlo comparison of asymptotic and various bootstrap inference procedures in firstorder dynamic models. Paper presented at the European Meetings of the Econometric Society. August1993a, Uppsala.
47. van Giersbergen, N. P. A., and Kiviet, J. F., How to implement bootstrap hypothesis testing in regression models. Paper presented at EC2 Conference. 1993b. Oxford
48. Gregory, A. W., and Veall, M. R., 1985. Formulating Wald tests of nonlinear restrictions. Econometrica, 53: 1465–1468.
49. Hall, P., 1988a. On symmetric bootstrap confidence intervals. Journal of the Royal Statistical Society, B, 50: 35–45.
50. Hall, P., 1988b. Theoretical comparison of bootstrap confidence intervals. Ann. Statist, 16: 927–953.
51. Hall, P., 1989. Unusual properties of bootstrap confidence intervals in regression problems. Probability Theory and Related Fields, 81: 247–273.
52. Hall, P., 1992. The Bootstrap and Edgeworth Expansion, New York: Springer-Verlag.
53. Hall, P., and Horowitz, J. L., 1993. “ Corrections and blocking rules for the block bootstrap with dependent data ”. In Working Paper #93-11, Department of Economics, University of Iowa.
54. Hall, P., and Horowitz, J. L., 1994. Bootstrap critical values for tests based on generalized method of moments estimators. Forthcoming in Econo-metrica
55. Hall, P., and S, R., 1991. Wilson Two guidelines for bootstrap hypothesis testing. Biometrics, 47: 757–762.
56. Hartigan, J. A., 1969. Using subsample values as typical values. Journal of the American Statistical Association, 64: 1303–1317.
57. Hartigan, J. A., 1986. Comment on the paper by Efron and Tibshirani. Statistical Science, 1: 75–76.
58. Hinkley, D. V., 1988. Bootstrap methods (With Discussion). Journal of the Royal Statistical Society, B, 50: 321–337.
59. Hinkley, D. V., 1989. Bootstrap significance tests. Proceedings of the 47th Session of the International Statistical Institute, 3: 65–74.
60. Horowitz, J. L., 1994. Bootstrap-based critical values for the information matrix test. Journal of Econometrics, 61: 395–411.
61. Horowitz, J. L., and Savin, N. E., 1992. “ Non-invariance of the Wald test: The bootstrap to the rescue ”. In Manuscript, Univ. of Iowa.
62. Jeong, J., and Maddala, G. S., 1993. “ A perspective on application of bootstrap methods in econometrics ”. In Handbook of Statistics, Vol. 11, 573–610. North Holland Publishing Co.
63. Jeong, J., and Maddala, G. S., 1994. Testing the rationality of survey data using the weighted double-bootstrapped method of moments. Review of Economics and Statistics
64. Johansen, S., 1988. Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12: 231–255.
65. Johansen, S., 1991. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregression models. Econometrica, 59: 1551–1580.
66. Kabaila, P., 1993. On bootstrap predictive inference for autoregressive processes. Journal of Time Series Analysis, 14: 473–484.
67. Kiviet, J. F., 1984. “ Bootstrap inference in lagged-dependent variable models ”. In Working Paper, University of Amsterdam.
68. Kreiss, J.-P., and Franke, J., 1992. Bootstrapping stationary autoregressive moving-average models. Journal of Time Series Analysis, 13: 297–317.
69. Kunsch, H. R., 1989. The jackknife and the bootstrap for general stationary observations. The Annals of Statistics, 17: 1217–1241.
70. Kwok, B., and Veall, M. R., 1988. The Jackknife and regression with AR(1) errors. Economics Letters, 26: 247–252.
71. Lahiri, S. N., 1991. Second order optimality of stationary bootstrap. Statistics & Probability Letters, 11: 335–341.
72. Lahiri, S. N., 1992. “ Edgeworth correction by ‘moving block’ bootstrap for stationary and nonstationary data ”. In Exploring the Limits of Bootstrap, Edited by: LePage, R., and Billard, L., 183–214. New York: John Wiley&Sons, Inc.
73. Lahiri, S. N., 1993. On the moving block bootstrap under long range dependence. Statistics & Probability Letters, 18: 405–413.
74. Leger, C., Politis, D. N., and Romano, J. P., 1992. Bootstrap technology and applications. Technometrics, 34: 378–398.
75. Li, Y., 1994. Bootstrapping cointegrating regressions. Economics Letters, 32: 229–233.
76. Li, H., and Maddala, G. S., Bootstrapping cointegrating regressions. Dec. 16-181993. Paper presented at the Fourth Meeting of the European Conference Series in Quantitative Economics and Econometrics.
77. Liu, R. Y., 1988. Bootstrap procedures under some non-iid models. Annals of Statistics, 16: 1696–1708.
78. Liu, R. Y., and Singh, K., 1992. “ Moving blocks jackknife and bootstrap capture weak dependence ”. In Exploring the Limits of Bootstrap, Edited by: LePage, R., and Billard, L., 225–248. New York: John Wiley &Sons, Inc.
79. Masarotto, G., 1990. Bootstrap prediction intervals for autoregressions. International Journal of Forecasting, 6: 229–239.
80. Nankervis, J. C., and Savin, N. E., 1988. The Student's-f approximation in a stationary first order autoregressive model. Econometrica, 56: 119–145.
81. Nankervis, J. C., and Savin, N. E., 1994. “ The level and power of the bootstrap t-test in the AR(1) model with trend ”. In Manuscript, Department of Economics, University of Surrey and University of Iowa.
82. Park, J. Y., 1992. Canonical cointegrating regressions. Econometrica, 60: 119–143.
83. Peters, S. C., and Freedman, D. A., 1985. Using the bootstrap to evaluate forecasting equations. Journal of Forecasting, 4: 251–262.
84. Phillips, P.C.B., 1991. Optimal inference in cointegrated systems. Econometrica, 59: 283–306.
85. Phillips, P.C.B., 1990. and Hansen. Bruce E. Statistical inference in instrumental variables regression with I(1) process. Review of Economic Studies, 57: 99–125.
86. Phillips, P.C.B., and Joon, Y., 1988. Park Asymptotic equivalence of ordinary least squares and generalized least squares in regressions with integrated regressors. Journal of the American Statistical Association, 83: 111–115.
87. Politis, D. N., 1994. and Romano. Joseph P. The stationary bootstrap. Journal of American Statistical Association, 89: 1303–1313.
88. Quenouille, M. H., 1949. Approximate tests of correlation in time series. Journal of the Royal Statistical Society, B, 11: 68–83.
89. Rayner, R. K., 1990. Bootstrapping p values and power in the first-order autoregression: a Monte Carlo investigation. Journal of Business & Economic Statistics, 8: 251–263.
90. Rayner, R. K., 1991. Resampling methods for tests in regression models with autocorrelated errors. Economics Letters, 36: 281–284.
91. Rilstone, P., 1993. Some improvements for bootstrapping regression estimators under first-order serial correlation. Economics Letters, 42: 335–339.
92. Rubin, H., 1950. “ Consistency of maximum likelihood estimates in the explosive case ”. In Statistical Inference in Dynamic Economic Models Edited by: Koopmans, T. C., 356–364. New York
93. Runkle, D. E., 1987. Vector auto-regression and reality. Journal of Business & Economic Statistics, 5: 437–454.
94. Saikkonen, P., 1991. Asymptotically efficient estimation of cointegrating regressions. Econometric Theory, 7: 1–21.
95. Schwert, G. W., 1987. Effects of model specification on tests for unit roots in macroeconomic data. Journal of Monetary Economics, 20: 73–103.
96. Singh, K., 1981. On the asymptotic accuracy of Efron's bootstrap. Annals of Statistics, 9: 1187–1195.
97. Thombs, L. A., and Schucany, W. R., 1990. Bootstrap prediction intervals for autoregression. Journal of the American Statistical Association, 85: 486–492.
98. Veall, M. R., 1986. Bootstrapping regression estimators under first-order serial correlation. Economics Letters, 21: 41–44.
99. Veall, M. R., 1987. Bootstrapping the probability distribution of peak electricity demand. International Economic Review, 28: 203–212.
100. Veall, M. R., 1988. Discussion of Hall's paper. Annals of Statistics, 16: 979–981.
101. Vinod, H. D., and McCullough, B. D., 1996. Estimating cointegration parameters: an application of the double bootstrap. Journal of Statistical Planning and Inference., 43: 147–156.
102. Wet, T., and Wyk, J.W.J., 1986. Bootstrap confidence intervals for regression coefficients when the residuals are dependent. J. Statist. Comput. SimuL, 23: 317–327.
103. Zivot, E., 1993. “ A Bayesian analysis of the unit root hypothesis within an unobserved components model ”. In Discussion paper 93-15, Seattle: University of Washington.