On the Applicability of the Sieve Bootstrap in Time series Panels

In this paper we investigate the validity of the univariate autoregressive sieve bootstrap appliedto time series panels characterized by general forms of cross-sectional dependence, including butnot restricted to cointegration. Using the final equations approach we show that while it ispossible to write such a panel as a collection of infinite order autoregressive equations, theinnovations of these equations are not vector white noise. This causes the univariateautoregressive sieve bootstrap to be invalid in such panels. We illustrate this result with asmall numerical example using a simple bivariate system for which the sieve bootstrap is invalid,and show that the extent of the invalidity depends on the value of specific parameters. We alsoshow that Monte Carlo simulations in small samples can be misleading about the validity of theunivariate autoregressive sieve bootstrap. The results in this paper serve as a warning about thepractical use of the autoregressive sieve bootstrap in panels where cross-sectional dependence ofgeneral from may be present.