Rescaled variance and related tests for long memory in volatility and levels. (English) Zbl 1027.62064
J. Econom. 112, No. 2, 265-294 (2003); corrigendum ibid. 126, No. 2, 571-572 (2005).
Summary: This paper studies properties of tests for long memory for general fourth order stationary sequences. We propose a rescaled variance test based on V/S statistics which is shown to have a simpler asymptotic distribution and to achieve a somewhat better balance of size and power than A. W. Lo’s [Econometrica 59, 1279-1313 (1991; Zbl 0781.90023)] modified R/S test and the KPSS test of D. Kwiatkowski et al. [J. Econom. 54, 159-178 (1992; Zbl 0871.62100)]. We investigate the theoretical performance of R/S, KPSS and V/S tests under short memory hypotheses and long memory alternatives, providing a Monte Carlo study and a brief empirical example. Assumptions of the same type are used in both short and long memory cases, covering all persistent dependence scenarios. We show that the results naturally apply and the assumptions are well adjusted to linear sequences (levels) and to squares of linear ARCH sequences (volatility).
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62P20 | Applications of statistics to economics |
| 62E20 | Asymptotic distribution theory in statistics |
| 62F05 | Asymptotic properties of parametric tests |
Keywords:
long memory; modified R/S statistic; KPSS statistic; V/S statistic; linear process; LARCH modelSoftware:
DiehardReferences:
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