On the Applicability of the Sieve Bootstrap in Time Series Panels*

Abstract

In this article, we investigate the validity of the univariate autoregressive sieve bootstrap applied to time series panels characterized by general forms of cross‐sectional dependence, including but not restricted to cointegration. Using the final equations approach we show that while it is possible to write such a panel as a collection of infinite order autoregressive equations, the innovations of these equations are not vector white noise. This causes the univariate autoregressive sieve bootstrap to be invalid in such panels. We illustrate this result with a small numerical example using a simple DGP for which the sieve bootstrap is invalid, and show that the extent of the invalidity depends on the value of specific parameters. We also show that Monte Carlo simulations in small samples can be misleading about the validity of the univariate autoregressive sieve bootstrap. The results in this article serve as a warning about the practical use of the autoregressive sieve bootstrap in panels where cross‐sectional dependence of general form may be present.

Exchange rate pass-through to import prices in Europe: a panel cointegration approach

“…The bootstrap version ofWesterlund's (2007) tests, meant to robustify them against cross-sectional dependence, is based on the univariate autoregressive sieve bootstrap. The latter has been shown bySmeekes and Urbain (2014) to be invalid for data generating processes characterized by strong cross-sectional dependence, as it does not reproduce the long-run covariance matrix of the data correctly.…”

Linear and nonlinear comovement in Southeast Asian local currency bond markets: a stepwise multiple testing approach

“…In addition,Palm et al (2011) showed the validity of the multivariate extension of Paparoditis and Politis' block bootstrap procedure for panel unit root tests in dependent panel settings. In contrast,Smeekes and Urbain's (2014) simulation results suggested the occurrence of size distortion in panel unit root tests based on the autoregressive (AR) sieve bootstrap in cross-sectionally dependent panels. This study, however, followsPalm et al's (2011) bootstrap algorithm, the application of which seems to be more appropriate for our data.…”

Computational framework for longevity risk management

“…With regard to the former, the VAR bootstrap scheme becomes infeasible in panel data where the number of cross-sectional units is large and the dimension of the system is too high. With regard to the latter, Palm (1977) shows that any VAR model can be written as a system of ARMA equations for each unit; starting from this consideration and using the results of Kreiss et al (2011), Smeeks and Urbain (2011) describe the AR sieve bootstrap algorithm for panel data. Chang (2004) has proven the validity of the AR sieve bootstrap in the context of panel data if there is only one contemporaneous source of dependence between the units; however, this 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 3 condition is likely to be violated in many empirical applications.…”

“…In this work we try to capture a more complex structure, incorporating in the bootstrap procedure the whole error matrix. In the case of panel data with a complex dependence structure, there are two different way to implement a bootstrap scheme: the first one is to apply a vector autoregressive (VAR) bootstrap, which extends the autoregressive procedure to the multidimensional case (Trapani, 2011); the second one consists of a univariate AR sieve bootstrap, with the modification that the residuals are re-sampled jointly across units to preserve the cross-sectional dependence (Smeeks and Urbain, 2011). With regard to the former, the VAR bootstrap scheme becomes infeasible in panel data where the number of cross-sectional units is large and the dimension of the system is too high.…”