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We study so–called augmented GARCH sequences, which include many sub-models of considerable interest, such as polynomial and exponential GARCH. To model the returns of speculative assets, it is particularly important to understand the behaviour of the squares of the observations. The main aim of this paper is to present a strong approximation for the sum of(More)
We consider a linear regression model with errors modelled by martingale difference sequences, which include heteroskedastic augmented GARCH processes. We develop asymptotic theory for two monitoring schemes aimed at detecting a change in the regression parameters. The first method is based on the CUSUM of the residuals and was studied earlier in the(More)
We study the almost sure convergence of the Bartlett estimator for the asymp-totic variance of the sample mean of a stationary weekly dependent process. We also study the a. s. behavior of this estimator in the case of long-range dependent observations. In the weakly dependent case, we establish conditions under which the estimator is strongly consistent.(More)
Microstructure noise in security prices biases the results of empirical asset pricing specifications, particularly when security-level explanatory variables are cross-sectionally correlated with the amount of noise. We focus on tests of whether measures of illiquidity, which are likely to be correlated with the noise, are priced in the cross-section of(More)
The paper develops a comprehensive asymptotic theory for the estimation of a change– point in the mean function of functional observations. We consider both the case of a constant change size, and the case of a change whose size approaches zero, as the sample size tends to infinity. We show how the limit distribution of a suitably defined change– point(More)
We discuss the limiting behavior of the serial correlation coefficient in mildly explosive autoregression, where the error sequence is in the domain of attraction of an α–stable law, α ∈ (0, 2]. Therein, the autoregressive coefficient ρ = ρ n > 1 is assumed to satisfy the condition ρ n → 1 such that n(ρ n − 1) → ∞ as n → ∞. In contrast to the vast majority(More)
Consider a linear model setting in which the explanatory variables are specified by time series. To sequentially test for the stability of the regression parameters in time, we introduce a detector which is based on the first excess time of a CUSUM-type statistic over a suitably defined threshold function. The main aim of this paper is to derive the limit(More)