Forecasting with equilibrium-correction models during structural breaks

Abstract

a b s t r a c tWhen location shifts occur, cointegration-based equilibrium-correction models (EqCMs) face forecasting problems. We consider alleviating such forecast failure by updating, intercept corrections, differencing, and estimating the future progress of an 'internal' break. Updating leads to a loss of cointegration when an EqCM suffers an equilibrium-mean shift, but helps when collinearities are changed by an 'external' break with the EqCM staying constant. Both mechanistic corrections help compared to retaining a prebreak estimated model, but an estimated model of the break process could outperform. We apply the approaches to EqCMs for UK M1, compared with updating a learning function as the break evolves.

Unpredictability in economic analysis, econometric modeling and forecasting

“…Clements and Hendry (2001) use that analysis to explain the outcomes of forecasting competitions, where the simplicity of a model is viewed as essential for success (see e.g., Makridakis and Hibon, 2000), but argue that is due to confounding parsimony with robustness, as such competitions did not include non-parsimonious but robust models. Castle, Fawcett and Hendry (2010) highlight the forecasting advantages of transforming a non-parsimonious model to be robust after breaks, and show that it can then even outperform the highly parsimonious yet robust device ∆ x T +1|T = ∆x T after a break at time T − 1: how a congruent encompassing in-sample model is used in the forecast period matters when there are location shifts.…”

“…Castle et al (2010) show that location shifts reduce the collinearities between variables, having the greatest impact on the smallest eigenvalues, and since mean square forecast errors (MSFEs) depend most on λ 1 /λ n , changes in collinearity after a break adversely increase forecast uncertainty. This effect cannot be avoided by deleting the collinear variables, nor is the problem mitigated by orthogonalizing the variables, which can transform an external break (one affecting marginal processes) to an internal one (shifting the conditional model of interest).…”

How Biased Are U.S. Government Forecasts of the Federal Debt?

“…Notably, the specific algorithm for IIS can make or break IIS's usefulness; cf. Doornik (2009a), Castle, Fawcett, and Hendry (2010), and Hendry and Doornik (2014). IIS is a statistically valid procedure for integrated, cointegrated data; see Johansen and Nielsen (2009).…”

Model Discovery and Trygve Haavelmo’s Legacy

“…While an unanticipatable event obviously cannot be forecast, once a shift has occurred, some models are, and others are not, robust. In particular, EqCMs fail systematically as forecasts continue to revert to the previous (and so incorrect) equilibrium mean: see Castle, Fawcett, and Hendry (2010). However, the difference of an EqCM is robust once past a location shift: see Hendry (2006).…”