On Some Asymptotic Results for Multivariate Autoregressive Models with Estimated Parameters

Abstract

In this paper the asymptotic equivalence of the estimated predictor and the optimal predictor of k-dimensional pth order autoregressive process in the stable case with dependent error variables bas been shown. An expression for the mean square error of the estimated predictor has also been derived.

Bootstrap prediction regions for multivariate autoregressive processes

“…On the grounds of the results in Samaranayake and Hasza (1988) and Basu and Sen Roy (1986) (see also Lütkepohl, 1993, Sect. 3.5) we find that, for a Gaussian process…”

Hybrid Forecasting with Estimated Temporally Aggregated Linear Processes

“…A preferable assumption would have been that estimation is based on the same sample that we intend to use for prediction, but exploiting only data up to the forecasting origin; Samaranayake and Hasza (1988) and Basu and Sen Roy (1986) have shown that many results obtained in the presence of the independence hypothesis remain valid under this more reasonable assumption. A preferable assumption would have been that estimation is based on the same sample that we intend to use for prediction, but exploiting only data up to the forecasting origin; Samaranayake and Hasza (1988) and Basu and Sen Roy (1986) have shown that many results obtained in the presence of the independence hypothesis remain valid under this more reasonable assumption.…”

“…Most results obtained in this direction have to do with the combination of the estimation and the characteristic errors; we refer the reader to Baillie (1979), Reinsel (1980), Yamamoto (1980Yamamoto ( , 1981, Dufour (1985), Basu and Sen Roy (1986), Lütkepohl (1987), and Samaranayake and Hasza (1988). On the one hand, the stochastic nature of the time series models under consideration implies that the forecasts produced with them carry in their wake an error that cannot be minimized even if the parameters of the model are known with total precision; we refer to this as the characteristic error of the model.…”

“…All these errors that one incurs at the time of carrying out a forecasting task are of different nature and much effort has been dedicated in the literature to quantifying them in the case of linear multivariate VARMA processes. Most results obtained in this direction have to do with the combination of the estimation and the characteristic errors; we refer the reader to Baillie (1979), Reinsel (1980), Yamamoto (1980Yamamoto ( , 1981, Dufour (1985), Basu and Sen Roy (1986), Lütkepohl (1987), and Samaranayake and Hasza (1988). Explicit approximate expressions for these errors in the VARMA context are available in the monograph Lütkepohl (2005).…”

Prediction problems related to a first-order autoregressive process in the presence of outliers

“…Then since ε t 's and hence x t 's are continuous, n γ(0) is non-zero with probability one for sufficiently large n. Thus from Basu and Sen Roy (1986),…”