Optimal Forecasts in the Presence of Structural Breaks

Abstract

This paper considers the problem of forecasting under continuous and discrete structural breaks and proposes weighting observations to obtain optimal forecasts in the MSFE sense. We derive optimal weights for continuous and discrete break processes. Under continuous breaks, our approach recovers exponential smoothing weights. Under discrete breaks, we provide analytical expressions for the weights in models with a single regressor and asympotically for larger models. It is shown that in these cases the value of the optimal weight is the same across observations within a given regime and differs only across regimes. In practice, where information on structural breaks is uncertain a forecasting procedure based on robust weights is proposed. Monte Carlo experiments and an empirical application to the predictive power of the yield curve analyze the performance of our approach relative to other forecasting methods.

Structural-break models under mis-specification: Implications for forecasting

“…However, for our analysis, we restrict ourselves to a sample of methods in which averaging approaches play an important role. For detailed explanation, see Pesaran et al (2013) and Hansen (2009). We start with averaging forecasts from different sub-windows (AveW) studied in Pesaran and Pick (2011).…”

“…In our comparative study, we choose m = T (1 − v min ) + 1 windows with v min = 0.05. The second method we discuss is the optimal weight method (Optwgt) studied in Pesaran et al (2013). This method gives past observations weights which minimize prediction mean squared error of the onestep ahead forecast.…”

“…This is a model-specific approach, however. The third method is the robust weight method (Rwgt) studied in Pesaran et al (2013). This method integrates the optimal weights from Optwgt with respect to a uniformly distributed break dates over a possible range, say [b, b], where b and b are the lower and upper ranges in which the break resides.…”

“…In our study, we consider two pairs of [b, b] to check the sensitivity of the PMSE to the choice of b and b. That is, we conduct Rwgt with b = 0.5 and b = 0.98 (Rwgt1) and with b = 0 and b = 1 (Rwgt2), following Pesaran et al (2013). We also conduct the reverse ordered CUSUM method (ROC) studied in Pesaran and Timmermann (2002) and Tian and Anderson (2014).…”

“…Then, the literature naturally considered certain forecast averaging methods, for example, as in Pesaran and Timmermann (2007). In particular, they include averaging over different estimation windows (Pesaran and Pick, 2011), the optimal and robust weighting forecasting approach (Pesaran et al, 2013), reverse ordered CUSUM weighting (Pesaran and Timmermann, 2002), and more weighting on the recent data (Tian and Anderson, 2014), and weighted averaging between the models with and without breaks based on a Mallows criterion (Hansen, 2009). …”