The subject of this paper is autoregressive AR approximations of a stationary Gaus sian discrete time process based on a nite sequence of observations We adopt the non parametric minimax framework and study how well can the process be approximated by a nite order autoregressive model Our results show that a properly chosen model dimen sion leads to an optimal in order minimax estimator

Using a nonstationary, bivariate autoregressive process with iid innovations, this paper shows that the bootstrap vector autoregressive causality test is inconsistent in general in the sense that its weak limit is di¤erent from that of the original causality test.

There are many parameters which are very difficult to calibrate in the threshold autoregressive prediction model for nonlinear time series. The threshold value, autoregressive coefficients, and the delay time are key parameters in the threshold autoregressive prediction model. To improve prediction precision and reduce the uncertainties in the determination of the above parameters, a new DNA de...

A spatial autoregressive process is investigated, where the autoregressive coefficients are equal, and their sum is one. It is shown that the limiting distribution of the least squares estimator for this coefficient is normal and, in contrast to the doubly geometric process, the rate of convergence is n−5/4.

the classical method of process capability analysis necessarily assumes that collected data are independent; nonetheless, some processes such as biological and chemical processes are autocorrelated and violate the independency assumption. many processes exhibit a certain degree of correlation and can be treated by autoregressive models among which the autoregressive model of order one (ar (1)) ...

The most commonly used method for estimating the time domain parameters of an autoregressive process is to use the Yule-Walker equations. The Yule-Walker estimates of the parameters of an autoregressive process of order p, or AR(p), are known to often be highly biased. This can lead to inappropriate order selection and very poor forecasting. There is a Fourier transform relationship between the...