For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogram and local Whittle estimators, has been exhaustively examined and their properties well established. However, except for some specific cases, little is known about the estimation of the memory...

We discuss the covariance structure and long-memory properties of stationary solutions of the bilinear equation Xt=[zeta]tAt+Bt,(*), where are standard i.i.d. r.v.'s, and At,Bt are moving averages in Xs, st. Stationary solution of (*) is obtained as an orthogonal Volterra expansion. In the case...

The aggregation procedure when a sample of length N is divided into blocks of length m=o(N), m--[infinity] and observations in each block are replaced by their sample mean, is widely used in statistical inference. Taqqu et al. (1995, Fractals, 3, 785-798), and Teverovsky and Taqqu (1997, J. Time...

type="main" xml:id="jtsa12056-abs-0001"This article presents a general method for studentizing weighted sums of a linear process where weights are arrays of known real numbers and innovations form a martingale difference sequence. Asymptotical normality for such sums was established in Abadir et...

This paper deals with the estimation of the long-run variance of a stationary sequence. We extend the usual Bartlett-kernel heteroskedasticity and autocorrelation consistent (HAC) estimator to deal with long memory and antipersistence. We then derive asymptotic expansions for this estimator and...

We consider the long-memory and leverage properties of a model for the conditional variance V-sub-t-super-2 of an observable stationary sequence X-sub-t, where V-sub-t-super-2 is the square of an inhomogeneous linear combination of X-sub-s, s < t, with square summable weights b-sub-j. This model, which we call linear autoregressive conditionally heteroskedastic (LARCH), specializes, when V-sub-t-super-2 depends only on X-sub-t - 1, to the asymmetric ARCH model of Engle (1990, Review of Financial Studies 3, 103--106), and, when V-sub-t-super-2 depends only on finitely many X-sub-s, to a version of the quadratic ARCH model of Sentana (1995, Review of Economic Studies 62, 639--661), these authors having discussed leverage potential in such models. The model that we consider was suggested by Robinson (1991, Journal of Econometrics 47, 67--84), for use as a possibly long-memory conditionally heteroskedastic alternative to i.i.d. behavior, and further studied by Giraitis, Robinson and Surgailis (2000, Annals of Applied Probability 10, 1002--1004), who showed that integer powers X-sub-t-super-&ell;, &ell; ≥ 2 can have long-memory autocorrelations. We establish conditions under which the cross-autocovariance function between volatility and levels, h-sub-t = cov<fen><cp type="lpar">V-sub-t-super-2,X-sub-0<cp type="rpar"></fen>, decays in the manner of...</cp></cp></t,>

This paper discusses asymptotic normality of certain classes of M- and R-estimators of the slope parameter vector in linear regression models with long memory moving average errors, extending recent results of Koul (1992) and Koul and Mukherjee (1993). Like in the case of the long memory...