Unit-root tests for explosive behavior

Abstract

We present a new command, radf, that tests for explosive behavior in time series. The command computes the right-tail augmented Dickey and Fuller (1979, Journal of the American Statistical Association 74: 427–431) unitroot test and its further developments based on supremum statistics derived from augmented Dickey–Fuller-type regressions estimated using recursive windows (Phillips, Wu, and Yu, 2011, International Economic Review 52: 201–226) and recursive flexible windows (Phillips, Shi, and Yu, 2015, International Economic Review 56: 1043–1078). It allows for the lag length in the test regression and the width of rolling windows to be either specified by the user or determined using data-dependent procedures, and it performs the date-stamping procedures advocated by Phillips, Wu, and Yu (2011) and Phillips, Shi, and Yu (2015) to identify episodes of explosive behavior. It also implements the wild bootstrap proposed by Phillips and Shi (2020, Handbook of Statistics: Financial, Macro and Micro Econometrics Using R, Vol. 42, 61–80) to lessen the potential effects of unconditional heteroskedasticity and account for the multiplicity issue in recursive testing. The use of radf is illustrated with an empirical example.