Lajos Horváth

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We propose a class of estimators for the parameters of a GARCH(p, q) sequence. We show that our estimators are consistent and asymptot-ically normal under mild conditions. The quasi-maximum likelihood and the likelihood estimators are discussed in detail. We show that the maximum likelihood estimator is optimal. If the tail of the distribution of the(More)
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 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)
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)
The paper proposes two inferential tests for error correlation in the functional linear model, which complement the available graphical goodness-of-fit checks. To construct them, finite dimensional residuals are computed in two different ways, and then their autocorrelations are suitably defined. From these autocorrelation matrices, two quadratic forms are(More)
We propose new tests to detect a change in the mean of a time series. Like many existing tests, the new ones are based on the CUSUM process. Existing CUSUM tests require an estimator of a scale parameter to make them asymptotically distribution free under the no change null hypothesis. Even if the observations are independent, the estimation of the scale(More)