analysis of time series data can involve the inversion of large covariance matrices. for theclass of arma (p, q) processes there are no exact explicit expressions for these inverses, except for thema (1) process. in practice, the sample covariance matrix can be very large and inversion can becomputationally time consuming and so approximate explicit expressions for the inverse are desirable.thi...

Let Xt be an /-dimensional ARMA (p, q) process. Let g: U l -> W be a measurable function. Define a process Zt by Zt = g(Xt). Generally, Z.is not an ARMA process. However, we are interested in such functions g, for which Zt is also an AR process. It is important to know the orders of the process Zt. In the most cases we find only some bounds for them. From the practical point of view, our consid...

This paper presents a unified framework of stationary ARMA processes for discrete-valued time series based on Pegram’s [Pegram, G.G.S., 1980. An autoregressive model for multilag markov chains. J. Appl. Probab. 17, 350–362] mixing operator. Such a stochastic operator appears to be more flexible than the currently popular thinning operator to construct Box and Jenkins’ type stationary ARMAproces...

The purpose of this paper is to introduce a method of estimating parameters in nonnegative ARMA processes. The method is a generalization of the procedures which were derived for autoregressive and moving-average processes. The estimates are constructed in the form of minima of certain fractions or some functions of these minima. A theorem concerning the strong consistence of these estimates is...

We consider computationally-fast methods for estimating parameters in ARMA processes from binary time series data, obtained by thresholding the latent ARMA process. All methods involve matching estimated and expected autocorrelations of the binary series. In particular, we focus on the spectral representation of the likelihood of an ARMA process and derive a restricted form of this likelihood, ...

Recently, there has been much research on developing models suitable for analysing the volatility of a discrete-time process. Since the volatility process, like many others, is necessarily non-negative, there is a need to construct models for stationary processes which are non-negative with probability one. Such models can be obtained by driving autoregressive moving average (ARMA) processes wi...

Using the multiple threshold autoregressive and moving average (TARMA) model we analyze the nonlinearities in the dynamics of realized volatilities of daily stock returns of 30 companies in the Dow Jones index. We find that the realized volatility processes can be characterized by the high, moderate, and low regimes and that the persistence, variance and ARMA error term change with each regime....