Testing periodically integrated autoregressive models

On the existence of Hilbert valued periodically correlated‎ autoregressive processes

‎In this paper we provide sufficient condition for existence of a‎ ‎unique Hilbert valued ($mathbb{H}$-valued) periodically‎ ‎correlated solution to the first order autoregressive model‎ ‎$X_{n}=rho _{n}X_{n-1}+Z_{n}$‎, ‎for $nin mathbb{Z}$‎, ‎and‎ ‎formulate the existing solution and its autocovariance operator‎. ‎Also we specially investigate equivalent condition for the‎ ‎coordinate process...

Testing the tail index in autoregressive models

We propose a class of nonparametric tests on the Pareto tail index of the innovation distribution in the linear autoregressive model. The simulation study illustrates a good performance of the tests. Such tests have various applications in a study of flood flows, rainflow data, behavior of solids, atmospheric ozone layer and reliability analysis, in communication engineering, in stock markets a...

Testing for Seasonal Unit Roots in Periodic Integrated Autoregressive Processes

Dierential Geometry of Autoregressive Fractionally Integrated Moving Average Models

The di erential geometry of autoregressive fractionally integrated moving average processes is developed. Properties of Toeplitz forms associated with the spectral density functions of these long memory processes are used to compute the geometric quantities. The role of these geometric quantities on the asymptotic bias of the maximum likelihood estimates of the model parameters and on the Bartl...

Testing an Autoregressive Structure in Binary Time Series Models

This paper introduces a Lagrange Multiplier (LM) test for testing an autoregressive structure in a binary time series model proposed by Kauppi and Saikkonen (2008). Simulation results indicate that the two versions of the proposed LM test have reasonable size and power properties when the sample size is large. A parametric bootstrap method is suggested to obtain approximately correct sizes also...