Asymptotic Inference of Autocovariances of Stationary Processes
نویسندگان
چکیده
Abstract: The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or L∞) and the quadratic (or L2) deviations. For these two cases, with proper centering and rescaling, the asymptotic distributions of the deviations are Gumbel and Gaussian, respectively. To establish such an asymptotic theory, as byproducts, we develop a normal comparison principle and propose a sufficient condition for summability of joint cumulants of stationary processes. We adopt a simulation-based block of blocks bootstrapping procedure that improves the finite-sample performance.
منابع مشابه
A central limit theorem for the sample autocorrelations of a Lévy driven continuous time moving average process
In this article we consider Lévy driven continuous time moving average processes observed on a lattice, which are stationary time series. We show asymptotic normality of the sample mean, the sample autocovariances and the sample autocorrelations. A comparison with the classical setting of discrete moving average time series shows that in the last case a correction term should be added to the cl...
متن کاملDistribution Theory for the Studentized Mean for Long, Short, and Negative Memory Time Series
We consider the problem of estimating the variance of the partial sums of a stationary time series that has either long memory, short memory, negative/intermediate memory, or is the firstdifference of such a process. The rate of growth of this variance depends crucially on the type of memory, and we present results on the behavior of tapered sums of sample autocovariances in this context when t...
متن کاملSample autocovariances of long-memory time series
We find the asymptotic distribution of the sample autocovariances of long-memory processes in cases of finite and infinite fourth moment. Depending on the interplay of assumptions on moments and the intensity of dependence, there are three types of convergence rates and limit distributions. In particular, a normal approximation with the standard rate does not always hold in practically relevant...
متن کاملMultiple Local Whittle Estimation in Stationary Systems
Moving from univariate to bivariate jointly dependent long memory time series introduces a phase parameter ( ), at the frequency of principal interest, zero; for short memory series = 0 automatically. The latter case has also been stressed under long memory, along with the "fractional di¤erencing" case =( 2 1) =2; where 1; 2 are the memory parameters of the two series. We develop time domain co...
متن کاملSimultaneous Quantile Inference for Non-stationary Long-memory Time Series
We consider the simultaneous or functional inference of time-varying quantile curves for a class of non-stationary long-memory time series. New uniform Bahadur representations and Gaussian approximation schemes are established for a broad class of non-stationary long-memory linear processes. Furthermore, an asymptotic distribution theory is developed for the maxima of a class of non-stationary ...
متن کامل