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The impact of measurement errors on ARMA prediction
Author(s) -
Koreisha Sergio G.,
Fang Yue
Publication year - 1999
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/(sici)1099-131x(199903)18:2<95::aid-for717>3.0.co;2-e
Subject(s) - observational error , invertible matrix , statistics , econometrics , range (aeronautics) , noise (video) , component (thermodynamics) , mathematics , forecast error , set (abstract data type) , state space representation , state space , autoregressive–moving average model , signal (programming language) , computer science , algorithm , autoregressive model , artificial intelligence , materials science , image (mathematics) , physics , pure mathematics , composite material , thermodynamics , programming language
Measurement errors can have dramatic impact on the outcome of empirical analysis. In this article we quantify the effects that they can have on predictions generated from ARMA processes. Lower and upper bounds are derived for differences in minimum mean squared prediction errors (MMSE) for forecasts generated from data with and without errors. The impact that measurement errors have on MMSE and other relative measures of forecast accuracy are presented for a variety of model structures and parameterizations. Based on these results the need to set up the models in state space form to extract the signal component appears to depend upon whether processes are nearly non‐invertible or non‐stationary or whether the noise‐to‐signal ratio is very high. Copyright © 1999 John Wiley & Sons, Ltd.