Abstract
In this paper an overview of the existing literature about bootstrapping for estimation and prediction in time series is presented. Some of the methods are detailed, organized according to the aim they are designed for (estimation or prediction) and to the fact that some parametric structure is assumed, or not, for the dependence. Finally, some new bootstrap (kernel based) method is presented for prediction when no parametric assumption is made for the dependence.
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References
Boldin, M.V. (1982). Estimation of the distribution of the noise in an autoregressive scheme.Theory of Probability and its Applications,27, 866–871.
Bühlmann, P. (1994). Blockwise bootstrap empirical processes for stationary sequences.Annals of Statistics,22, 995–1012.
Bühlmann, P. (1997). Sieve bootstrap for time serics.Bernoulli,3, 123–148.
Bühlmann, P. (1998). Sieve bootstrap for smoothing in nonstationary time series.Annals of Statistics 26, 48–83.
Bühlmann, P. and H.R. Künsch (1995). The blockwise bootstrap for general parameters of a stationary time series.Scandinavian Journal of Statistics,22, 35–54.
Cao, R., M. Febrero-Bande, W. Gonzálcz-Manteiga, J.M. Prada-Sánchez and I. García-Jurado (1997). Saving computer time in constructing consistent boot-strap prediction intervals for autoregressive processes.Communications in Statistics-Simulation and Computation,26, 961–978.
Carlstein, E., K-A. Do, P. Hall, T., Hesterberg and H.R. Künsch (1995). Matchedblock bootstrap for dependent data. Preprint.
Efron, B. (1979). Bootstrap methods: another look at the jackknife.Annals of Statistics,7, 1–26.
Ferretti, N. and J. Romo (1996). Unit root bootstrap test for AR(1) models.Biometrika,83, 849–860.
Franke, J., J-P. Kreiss and E. Mammen (1996). Bootstrap of kernel smoothing in nonlinear time series. Preprint.
Fuller, W.A. (1976).Introduction to statistical time series. John Wiley, New York.
Gannoun, A. (1990). Estimation non paramétrique de la médiane conditionnelle. Application la prévision.Comptes Rendus de l'Académie des Sciences, Paris,310, 295–298.
García-Jurado, I., W. González-Manteiga, J.M., Prada-Sánchez, M. Febrero-Bande and R. Cao (1995). Predicting using Box-Jenkins, nonparametric and boot-strap techniques.Technometrics,37, 303–310.
Hall, P., J.L. Horowitz and B-Y. Jing (1995). On blocking rules for the bootstrap with dependent data.Biometrika 82, 561–574.
Heimann, G. and J-P. Kreiss (1996). Bootstrapping general first order autoregression.Statistics and Probability Letters,30, 87–98.
Kreiss, J-P. and J. Franke (1992). Bootstrapping stationary autoregressive moving average models.Journal of Time Series Analysis,13, 297–317.
Kulperger, R.J. (1996). Bootstrapping empirical distribution functions of residuals from autoregressive model fitting.Communications in Statistics (Simulation and Computation),25, 657–670.
Künsch, H.R. (1989). The jackknife and the bootstrap for general stationary observations.Annals of Statistics,17, 1217–1241.
Liu, R.Y. and K. Singh (1992). Moving blocks jackknife and bootstrap capture weak dependence.Exploring the limits of bootstrap (R. LePage and L Billard, eds), John Wiley, New York, 225–248.
Naik-Nimbalkar, U.V. and M.B. Rajarshi (1994). Validity of blockwise bootstrap for empirical processes with stationary observations.Annals of Statistics,22 980–994.
Paparoditis, E. (1996). Bootstrapping autoregressive and moving average parameters estimates of infinite order vector autoregressive processes.Journal of Multivariate Analysis,57, 277–296.
Politis, D.N. and J.R. Romano (1994a). The stationary bootstrap.Journal of the American Statistical Association,89, 1303–1313.
Politis, D.N. and J.R. Romano (1994b). Large sample confidence regions based on subsamples under minimal assumptions.Annals of Statistics,22, 2031–2050.
Poitis, D.N. and J.R. Romano (1994c). Limit theorems for weakly dependent Hilbert space valued random variables with application to the stationary bootstrap.Statistica Sinica,4, 461–476.
Radulović, D. (1996). The bootstrap for the mean of strong mixing sequences under minimal conditions.Statistics and Probability Letters,28, 65–72.
Stine, R.A. (1987). Estimating properties of autoregressive forccasts.Journal of the American Statistical Association,82, 1072–1078.
Stute, W. (1995). Bootstrap of a lincar model with AR-error structure.Metrika,42, 395–410.
Stute, W. and B. Gründer (1992). Bootstrap approximations to prediction intervals for explosive AR(1)-processes.Lecture Notes in Economics and Mathematical Systems,376, Springer-Verlag, Berlin, 121–130.
Thombs, L.A. and W.R. Schucany (1990). Bootstrap prediction intervals for autoregression.Journal of the American Statistical Association,85, 486–492.
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This research was partially supported by the “Dirección General de Investigación Científica y Tćnica” Grants PB94-0494 and PB95-0826 and by the “Xunta de Galicia” Grant XUGA 10501B97.
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Cao, R. An overview of bootstrap methods for estimating and predicting in time series. Test 8, 95–116 (1999). https://doi.org/10.1007/BF02595864
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DOI: https://doi.org/10.1007/BF02595864
Key Words
- Autoregressive processes
- blockwise bootstrap
- moving average processes
- moving blocks bootstrap
- resampling methods
- stationary bootstrap