The Lag-length Selection and Detrending Methods for HEGY Seasonal Unit-root Tests Using Stata

Abstract

The article extends the previous Hylleberg, Engle, Granger, and Yoo seasonal unit-root test commands (Baum and Sperling, 2001, https://ideas.repec.org/c/boc/bocode/s416502.html; Depalo, 2009, Stata Journal 9: 422-438), which allow for the use of both quarterly and monthly data. It is also possible to choose between ordinary least-squares and generalized leastsquares detrending (Rodrigues and Taylor, 2007, Journal of Econometrics 141: 548-573) procedures to deal with the deterministic part of the process. The command allows for the use of the sequential method proposed by Hall (1994, Journal of Business and Economic Statistics 12: 461-470) and Ng and Perron (1995, Journal of the American Statistical Association 90: 268-281), the adaptation of the modified Akaike information criteria to the case of seasonal unit-root tests (del Barrio Castro, Osborn, and Taylor, 2016, Econometric Reviews 35: 122-168) as well as the inclusion of Akaike information and Bayesian information criteria to determine the order of augmentation of the serial correlation in the augmented Hylleberg, Engle, Granger, and Yoo regression. Finally, the use of the command is illustrated with an empirical application to the case of monthly passenger airport arrivals to Palma de Mallorca. Taylor, and del Barrio Castro (2009), we can define six scenarios for the deterministic part μ St+s : no deterministic terms, zero-frequency intercept (one intercept), zero-frequency intercept and a trend, seasonal intercepts, seasonal intercepts and a zero-frequency trend, and seasonal intercepts and trends. Hence, in terms of μ St+s = δ z St+s,ζ , we have the following: Case 0: No deterministic terms: μ St+s = 0 Case 1: Only a constant: z St+s,1 = [1] with δ = (δ 0 ) Case 2: Constant and a zero-frequency trend: z St+s,2 = [1, St + s] with δ = δ 0 , δ 0 Case 3: Seasonal intercepts: z St+s,3 = [1, cos(2π(St + s)/S), sin(2π(St + s)/S), . . . , cos(2πS * (St + s)/S), sin(2πS * (St + s)/S), (−1) St+2 with δ = (δ 0 ,