Robustifying forecasts from equilibrium-correction systems

Abstract

Cointegration analysis has led to equilibrium-correction econometric systems being ubiquitous. But in a non-stationary world subject to structural breaks, where model and mechanism differ, equilibrium-correction models are a risky device from which to forecast. Equilibrium shifts entail systematic forecast failure, as forecasts will tend to move in the opposite direction to data. We explain the empirical success of second-differenced devices and of model transformations based on additional differencing as reducing forecast-error biases, at some cost in increased forecast-error variances. The analysis is illustrated by an empirical application to narrow money holdings in the UK. r 2005 Elsevier B.V. All rights reserved. JEL classification: E41; C52

Factor‐augmented Error Correction Models*

“…The comparison between the ECM and FECM is more mixed, attributable perhaps to the fact that the factor space is estimated and may thus be susceptible to the presence of structural breaks (which are of course important for forecasting and are not taken account of here). In future research it would be interesting to consider modifications of the FECM model to take account of structural breaks -along the lines of a differenced FECM model (DFECM) to correspond to the Hendry (2006) formulation of a DVECM model described briefly in the introduction, in order to allow for change in the cointegrating or equilibrium information that may have occurred. per capita "private" gross national product, money supply, inflation and a short term interest rate.…”

“…Clements and Hendry (1995) explore this issue using alternative criteria for assessing forecasting accuracy including the trace mean squared forecast error criterion (TMSFE) and their preferred invariant generalised forecast error second moment (GFESM) criterion. More recent analysis by Hendry (2006) has argued in favour of using a differenced vector error correction model (DVECM) which introduces error-correction information into a double-differenced-VAR (DDVAR).…”

Identification and Forecasting in the Lee-Carter Model

“…The reason this works is that it gets around the problem that shifts to the deterministic term ν are rather pernicious to forecasting. Hendry (2006) This forecast is found to perform favourably to double differencing in that forecast variances do not build up. Comparing to the double differencing equation the difference is inclusion of the term α β∆ k T +h−1 which has zero mean and is therefore robust to level shifts and which also captures the dynamic term that was found to be of significance in-sample.…”

“…However, if there is a structural change in the level of the time-dependent parameter k t near the end of the sample or in the begining of the forecast period then forecasts will have poor properties. Hendry (2006) discusses how to forecast from cointegration models in the presence of level shifts. Suppose the estimated model satisfies the linear trend restriction δ = 0 so ∆k t = α βk t−1 + ν + ε t .…”

Evaluating Forecasts, Narratives and Policy Using a Test of Invariance

“…Furthermore, forecasting success may, but need not, 'corroborate' the forecasting model and its supporting theory: see Clements and Hendry (2005). Indeed, Hendry (2006) demonstrates a robust forecasting device that can outperform the forecasts from an estimated in-sample DGP after a location shift. Nevertheless, when several rival explanations exist, forecast failure can play an important role in distinguishing between them as discussed by Spanos (2007).…”