Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility

Abstract

A number of recently published papers have focused on the problem of testing for a unit root in the case where the driving shocks may be unconditionally heteroskedastic. These papers have, however, assumed that the lag length in the unit root test regression is a deterministic function of the sample size, rather than data-determined, the latter being standard empirical practice. In this paper we investigate the finite sample impact of unconditional heteroskedasticity on conventional data-dependent methods of lag selection in augmented Dickey-Fuller type unit root test regressions and propose new lag selection criteria which allow for the presence of heteroskedasticity in the shocks. We show that standard lag selection methods show a tendency to over-fit the lag order under heteroskedasticity, which results in significant power losses in the (wild bootstrap implementation of the) augmented Dickey-Fuller tests under the alternative. The new lag selection criteria we propose are shown to avoid this problem yet deliver unit roots with almost identical finite sample size and power properties as the corresponding tests based on conventional lag selection methods when the shocks are homoskedastic.

Impacts of corn price and imported beef price on domestic beef price in South Korea

“…By using the first difference data, we find that the number of lags is same as 1 for all three different criterions. According to Tsay (1984), Potscher (1989), and Cavaliere et al (2015), BIC is consistent compared to AIC because AIC overestimates with positive probability. Therefore, we use BIC information.…”

Heteroskedasticity‐Robust Unit Root Testing for Trending Panels

“…While the choice of lag selection criteria may not necessarily affect asymptotic properties of unit root tests, it might however impact on finite sample performances of tests in the presence of heteroskedasticity. Cavaliere et al () have shown that standard lag selection criteria tend to over‐fit the lag order in the presence of heteroskedasticity and, hence, induce power losses in the (wild bootstrap version of the) univariate augmented Dickey–Fuller tests. Their modified lag selection criteria, which rescale the data by an estimate of the underlying time‐varying volatility process, significantly mitigate the power losses while retaining comparative size properties.…”

Wild bootstrap seasonal unit root tests for time series with periodic nonstationary volatility

“…Denoting this estimated lag length byp, we also then set p * =p in Step 4 of Algorithm 1 for all of the simulation results we report here. To obtain our estimatep we propose a seasonal generalisation of the heteroskedasticity-robust re-scaled modified information criterion [MIC] based method of Cavaliere et al (2015), designed to account for non-stationary volatility in the shocks by using re-scaled data. Our suggested approach consists of applying their re-scaling approach to each of the seasons separately.…”

“…Monte Carlo simulations for a variety of (periodic) non-constant volatility models suggest that the wild bootstrap HEGY tests perform very well in practice with only small finite sample differences between the two wild bootstrap schemes. We also outline how the re-scaled information-based lag length selection methods of Cavaliere et al (2015) can be adapted to the seasonal unit root testing case.…”