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ESTIMATION OF THE PREDICTION ERROR VARIANCE AND AN R 2 MEASURE BY AUTOREGRESSIVE MODEL FITTING
Author(s) -
Bhansali R. J.
Publication year - 1993
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1993.tb00133.x
Subject(s) - mathematics , autoregressive model , estimator , measure (data warehouse) , realization (probability) , statistics , series (stratigraphy) , variance (accounting) , stationary process , predictability , asymptotic distribution , business , biology , paleontology , accounting , database , computer science
. For predicting the future values of a stationary process { x t } ( t = 0, pL 1, pL 2,…) on the basis of its past, two key parameters are the variance V ( h ), h ≥ 1, of the h ‐step prediction error and Z ( h ) ={ R (0) ‐ V ( h )}/ R (0), the corresponding measure, in an R 2 sense, of the predictability of the process from its past, where R (0) denotes the process variance. The estimation of V ( h ) and Z ( h ) from a realization of T consecutive observations of { x t } is considered, without requiring that the process follows a finite parameter model. Three different autoregressive estimators are examined and are shown to be asymptotically equivalent in the sense that as T ∝ they have the same asymptotic normal distribution. The question of bias in estimating these parameters is also examined and a bias correction is proposed. Finite sample behaviour is investigated by a simulation study.