Unbiasedness of Predictions from Etimated Vector Autoregressions
- 1 April 1985
- journal article
- research article
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 1 (3) , 387-402
- https://doi.org/10.1017/s0266466600011270
Abstract
Forecasts from a univariate autoregressive model estimated by OLS are unbiased, irrespective of whether the model fitted has the correct order; this property only requires symmetry of the distribution of the innovations. In this paper, this result is generalized to vector autoregressions and a wide class of multivariate stochastic processes (which include Gaussian stationary multivariate stochastic processes) is described for which unbiasedness of predictions holds: specifically, if a vector autoregression of arbitrary finite order is fitted to a sample from any process in this class, the fitted model will produce unbiased forecasts, in the sense that the prediction errors have distributions symmetric about zero. Different numbers of lags may be used for each variable in each autoregression and variables may even be missing, without unbiasedness being affected. This property is exact in finite samples. Similarly, the residuals from the same autoregressions have distributions symmetric about zero.Keywords
This publication has 55 references indexed in Scilit:
- Small-Sample Properties of Predictions from the Regression Model with Autoregressive ErrorsJournal of the American Statistical Association, 1983
- Effects of Not Knowing the Order of an Autoregressive Process on the Mean Squared Error of Prediction—IJournal of the American Statistical Association, 1981
- Properties of Predictors for Autoregressive Time SeriesJournal of the American Statistical Association, 1981
- The Asymptotic Mean Squared Error of Multistep Prediction from the Regression Model with Autoregressive ErrorsJournal of the American Statistical Association, 1979
- Maximum likelihood estimation of the GLS model with unknown parameters in the disturbance covariance matrixJournal of Econometrics, 1978
- Specification AnalysisJournal of the American Statistical Association, 1973
- Estimation of Seemingly Unrelated Regressions with Vector Autoregressive ErrorsJournal of the American Statistical Association, 1973
- Transformations for Estimation of Linear Models with Nested-Error StructureJournal of the American Statistical Association, 1973
- Fitting Time Series Models for PredictionTechnometrics, 1971
- The Unbiasedness of Zellner's Seemingly Unrelated Regression Equations EstimatorsJournal of the American Statistical Association, 1967