Regression Designs in Autoregressive Stochastic Processes

Optimal designs for regression models with autoregressive errors

In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least square estimator. The results are used to derive the optimal variance of the best linear estimator in the continuous time model and to construct efficient estimators and corresponding optimal designs for finite samples.

Simplified Simplicial Depth for Regression and Autoregressive Growth Processes

We simplify simplicial depth for regression and autoregressive growth processes in two directions. At first we show that often simplicial depth reduces to counting the subsets with alternating signs of the residuals. The second simplification is given by not regarding all subsets of residuals. By consideration of only special subsets of residuals, the asymptotic distributions of the simplified ...

Internal multiscale autoregressive processes, stochastic realization, and covariance extension

Periodic autoregressive stochastic volatility

This paper proposes a stochastic volatility model (PAR-SV ) in which the log-volatility follows a …rst-order periodic autoregression. This model aims at representing time series with volatility displaying a stochastic periodic dynamic structure, and may then be seen as an alternative to the familiar periodic GARCH process. The probabilistic structure of the proposed PAR-SV model such as periodi...

Multistep Prediction in Autoregressive Processes

In this paper, two competing types of multistep predictors, i+e+, plug-in and direct predictors, are considered in autoregressive ~AR! processes+When a working model AR~k! is used for the h-step prediction with h . 1, the plug-in predictor is obtained from repeatedly using the fitted ~by least squares! AR~k! model with an unknown future value replaced by their own forecasts, and the direct pred...