Forecasting with measurement errors in dynamic models
This paper explores the effects of measurement error on dynamic forecasting models. The paper sets out to illustrate a trade off that confronts forecasters and policymakers when they use data that are measured with error. On the one hand, observations on recent data give valuable clues as to the shocks that are hitting the system and will be propagated into the variables to be forecast (and which ultimately will inform monetary policy). But on the other, those recent observations are likely to be those least well measured. Two broad classes of results are illustrated. The first relates to cases where it is imagined that the forecaster takes the coefficients in the data generating process as a given, and has to choose how much of the historical time series of data to use to form a forecast. It is shown that if recent data is sufficiently badly measured, relative to older data, that it can be optimal in this case not to use old data at all. The second class of results is more general. Here, it is shown that for a general class of linear autoregressive forecasting models, the optimal weight to place on a data observation of some age, relative to the weight in the true data generating process, will depend on the measurement error in that data. The gains to be had in forecasting are illustrated using a model of UK business investment growth.
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