Monitoring memory parameter change-points in long-memory time series

Sequential Test for Change-Point in Long Memory Process

“…We set the largest monitoring sample size T varying among 200, 500 { } and the training sample size [Tτ] � [0.25T]. In order to compute the critical values of monitoring statistics, we use the sieve bootstrap method proposed by Chen et al [6]. e sieve bootstrap frequency was set to be B � 300, and all simulations are obtained by 1000 replications at α � 5% nominal level.…”

“…For a practitioner, it is of importance in terms of model building and forecasting to know whether a given time series has a certain kind of persistence, either stationary I(d) with 0 ≤ d < (1/2) or non-stationary I(d) with d > (1/2), or whether the persistent breaks from stationary to non-stationary persistence or vice versa. e classical (I(0)/I(1)) framework has been an issue of substantial empirical interest, especially concerning in ation rate series [5], foreign exchange rates [6], government budget de cits [7], and real output [8], and a number of testing procedures have been suggested that aim to distinguish such behavior. ese include, inter alia, ratio tests [9], LBI tests [10], CUSUM of squares-based test [11], moving ratio tests [12], and Wilcoxon rank test [13].…”

“…Chen et al [17] proposed a moving ratio statistic (MRS) to monitor change in persistence in long memory process. Chen et al [6] proposed a two-stage moving ratio statistic to monitor long memory parameter change-point. Recently, Chen et al [18] proposed the socalled DF di erence statistic to sequentially detect unit root to long memory process change-point.…”

“…is indicates that the numerator of statistic U T (s) is O p (T 1+2(d 2 − d 1 ) ). On the other hand, (6) gives that the denominator of statistic U T (s) is O p (T). us,…”