Bootstrap confidence intervals for a break date in linear regressions

Abstract

In this article, we consider bootstrap confidence intervals, namely percentile bootstrap for obtaining confidence intervals of a break date in linear regression models. Elliott and Mü‌ller [Confidence sets for the date of a single break in linear time series regressions. J Econometrics. 1997;141:1196–1218] point out that the simulated coverage probabilities are below the nominal rate when the limiting distribution is used to form confidence intervals of the break date. This is particularly so if the magnitude of a break is relatively small. We investigate the finite sample performance of bootstrap confidence intervals for the break date in linear regressions with serially correlated errors using Monte Carlo simulations. The simulation results confirm that bootstrap confidence intervals outperform those constructed by the conventional method. An empirical analysis is provided for illustrative purpose.

Keywords:

• Block bootstrap
• Monte Carlo simulations
• serial correlation
• sieve bootstrap
• stationary bootstrap
• stochastic regressor

Jel Classifications:

• C12
• C14

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The centred residuals ${\hat{u}}_i-\overline{\hat{u}},i=1,2,\dots ,T$ with $\overline{\hat{u}}=T^{-1}\sum _{t=1}^T{\hat{u}}_t$ is unnecessary because there exists a regressor of a series of ones in the DGP, which makes the sum of the OLS residuals zero.

2 Douglas [18] suggests rescaling the OLS residuals to equate the variances of the residuals and true errors. More precisely, multiply ${\hat{u}}_t$ by $\sqrt{{\hat{T}}_1/({\hat{T}}_1-p)}$ for $t=1,\dots ,{\hat{T}}_1$, and by $\sqrt{(T-{\hat{T}}_1)/(T-{\hat{T}}_1-p)}$ for $t={\hat{T}}_1+1,\dots ,T$, where p is the number of regressors.

3 Stock and Watson [35] applied Bai's [4] method to construct confidence intervals of the break date in simple regression models for various economic time series. Since the CIs are wide enough to cover the whole sample, they decided to report the 67% confidence intervals.

Additional information

Funding

This research was supported by the Soongsil University Research Fund of 201810001157.