Bootstrap unit-root test for random walk with drift: The bsrwalkdrift command

Abstract

In this article, we introduce the command bsrwalkdrift, which is primarily intended to perform a bootstrap unit-root test under the null hypothesis of random walk with drift. The method implemented in this command is considerably more precise than the corresponding case of the conventional augmented Dickey–Fuller test, which can be inaccurate when the true value of the drift term is small relative to the standard deviation of the innovations. The command also has an option to account for deterministic linear trend and another option to perform bootstrap unit-root tests under the null hypothesis of random walk without drift.

The Significant Effects of the COVID-19 on Leisure and Hospitality Sectors: Evidence From the Small Businesses in the United States

“…Table 1 reports the findings of the bootstrap unit-root test for a random walk with drift proposed by Dorta and Sanchez ( 16 ) at the national level for small businesses revenues and openings of two sectors: (i) leisure and hospitality and (ii) accommodation and food services. The results indicate that small businesses revenues and openings in two sectors follow the random walk with drift process.…”

“…We utilize the bootstrap unit-root test for a random walk with drift introduced by Dorta and Sanchez ( 16 ). The Dorta-Sanchez unit-root test corrects the possible bias in the data generation process (DGP) that corresponds to a random walk with a non-zero drift for small and medium sample sizes.…”

“…Park ( 17 ) uses the ADF unit-root test for autoregressive (AR) unit-root models with bootstrapped critical values to address possible sample bias. At this stage, Dorta and Sanchez ( 16 ) calculate the bootstrapped critical values for the unit-root test methodology of Park ( 17 ). Poor sample size can also be an issue in our case, given that there are sub-periods in the sample during the COVID-19 period (See Figure 1 ).…”

“…If the t statistic is lower than the bootstrapped critical values, the unit root hypothesis will be rejected. Furthermore, the p -values on comparing bootstrapped critical values and t statistics are also provided ( 16 ). Finally, the optimal number of lags is also determined by the Akaike Information Criteria (AIC).…”

“…At this stage, we consider the data at the national and state levels. For this purpose, we utilize the bootstrap unit-root test for a random walk with the drift of Dorta and Sanchez ( 16 ). The bootstrapped critical values decrease the size distortions following the bootstrap procedure in Park ( 17 ).…”