In this paper, the two-stage procedure is considered for autoregressive parameters estimation in the p-order autoregressive model ( AR(p)). The point estimation and fixed-size confidence ellipsoids construction are investigated which are based on least-squares estimators. Performance criteria are shown including asymptotically risk efficient, asymptotically efficient, and asymptotically consist...

An inhomogeneous first–order integer–valued autoregressive (INAR(1)) process is investigated, where the autoregressive type coefficient slowly converges to one. It is shown that the process converges weakly to a Poisson or a compound Poisson distribution.

The asymptotic theory of the residual empirical process of autoregressions with an intercept is developed. In contrast to situations without intercept the asymptotic distribution does not depend on the location of the characteristic roots. This is important in applications, as the question of the distribution of the innovations then can be addressed without having to locate the characteristic r...

We present a model for representing stationary multivariate time series with arbitrary marginal distributions and autocorrelation structures and describe how to generate data quickly and accurately to drive computer simulations. The central idea is to transform a Gaussian vector autoregressive process into the desired multivariate time-series input process that we presume as having a VARTA (Vec...

Large sample properties are studied for a …rst-order autoregression (AR(1)) with a root greater than unity. It is shown that, contrary to the AR coe¢ cient, the leastsquares (LS) estimator of the intercept and its t-statistic are asymptotically normal without requiring the Gaussian error distribution, and hence an invariance principle applies. While the invariance principle does not apply to th...

The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. In this paper, we study the Lasso estimator for fitting autoregressive time series models. We adopt a double asymptotic framework where the maximal lag may increase with the sample size. We derive theoretical results establishing various types of consistency. In particular,...

The goal of this paper is to search for independent multidimensional processes subject to missing and mixed observations. The corresponding cocktail-party problem has a number of successful applications, however, the case of missing observations has been worked out only for the simplest Independent Component Analysis (ICA) task, where the hidden processes (i) are one-dimensional, and (ii) signa...

There are many types of autoregressive patterns in financial time series, and they form a transmission process. Here, we define autoregressive patterns quantitatively through an econometrical regression model. We present a computational algorithm that sets the autoregressive patterns as nodes and transmissions between patterns as edges, and then converts the transmission process of autoregressi...