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The author shows that extending the estimation window prior to structural breaks in cointegrated systems can be beneficial for forecasting performance and highlights under which conditions. In doing so, the author generalizes the Pesaran and Timmermann (2005)’s forecast error decomposition and shows that it depends on four terms: (1) a period ahead risk; (2) a bias due to a conditional mean shift; (3) a bias due to a variance mismatch; (4) a gap term valid only conditionally. The author also derives new expressions for the estimators of the adjustment matrix and a constant, which are auxiliary to the decomposition. Finally, the author introduces new simulation-based estimators for the finite sample forecast properties which are based on the derived decomposition. The author’s finding points out that, in some cases, parameter instability can be neglected by extending the window backward and forecasters can be insured against higher forecast risk under this model class as well, generalizing Pesaran and Timmermann (2005)’s result. The author’s result gives renewed importance to break tests, in order to distinguish cases when break-neglection is (not) appropriate.

Hashem Pesaran has made many seminal contributions, among others, in the time series econometrics estimation and forecasting under structural break, see Pesaran and Timmermann (2005, 2007), Pesaran, Pettenuzzo, and Timmermann (2006), and Pesaran, Pick, and Pranovich (2013). In this chapter, the authors focus on the estimation of regression parameters under multiple structural breaks with heteroskedasticity across regimes. The authors propose a combined estimator of regression parameters based on combining restricted estimator under the situation that there is no break in the parameters, with unrestricted estimator under the break. The operational optimal combination weight is between zero and one. The analytical finite sample risk is derived, and it is shown that the risk of the proposed combined estimator is lower than that of the unrestricted estimator under any break size and break points. Further, the authors show that the combined estimator outperforms over the unrestricted estimator in terms of the mean squared forecast errors. Properties of the estimator are also demonstrated in simulations. Finally, empirical illustrations for parameter estimators and forecasts are presented through macroeconomic and financial data sets.

From the standpoint of a policy maker who has access to a number of expert forecasts, the uncertainty of a combined or ensemble forecast should be interpreted as that of a typical forecaster randomly drawn from the pool. This uncertainty formula should incorporate forecaster discord, as justified by (i) disagreement as a component of combined forecast uncertainty, (ii) the model averaging literature, and (iii) central banks’ communication of uncertainty via fan charts. Using new statistics to test for the homogeneity of idiosyncratic errors under the joint limits with both T and n approaching infinity simultaneously, the authors find that some previously used measures can significantly underestimate the conceptually correct benchmark forecast uncertainty.

It is rare for the forecasts of one economic forecasting model to always be more accurate than the forecasts from an alternative model. This suggests the possibility of implementing a switching strategy that chooses, at each point in time, the forecasting model that is expected to be most accurate conditional on a set of instruments that are used to track the relative accuracy of the underlying forecasts. The authors analyze the factors determining the expected gains from such a switching rule over a strategy of always using one of the underlying forecasts. The authors derive bounds on the expected gains from switching for both the nested and non-nested cases and also analyze the case with a highly persistent (near-unit root) predictor variable.

A novel approach to modeling exchange rates is presented based on a set of models distinguished by the drivers of the rate and regime duration. The models are combined into a “meta model” using model averaging and non-nested hypothesis-testing techniques. The meta model accommodates periods of stability and slowly evolving or abruptly changing regimes involving multiple drivers. Estimated meta models for five exchange rates provide a compelling characterization of their determination over the last 40 years or so, identifying “phases” during which the influences from policy and financial market responses to news succumb to equilibrating macroeconomic pressures and vice versa.

This chapter investigates the performance of different dimension reduction approaches for large vector autoregressions in multi-step ahead forecasts. The authors consider factor augmented VAR models using principal components and partial least squares, random subset regression, random projection, random compression, and estimation via LASSO and Bayesian VAR. The authors compare the accuracy of iterated and direct multi-step point and density forecasts. The comparison is based on macroeconomic and financial variables from the FRED-MD data base. Our findings suggest that random subspace methods and LASSO estimation deliver the most precise forecasts.

We investigate whether smooth robust methods for forecasting can help mitigate pronounced and persistent failure across multiple forecast horizons. We demonstrate that naive predictors are interpretable as local estimators of the long-run relationship with the advantage of adapting quickly after a break, but at a cost of additional forecast error variance. Smoothing over naive estimates helps retain these advantages while reducing the costs, especially for longer forecast horizons. We derive the performance of these predictors after a location shift, and confirm the results using simulations. We apply smooth methods to forecasts of UK productivity and US 10-year Treasury yields and show that they can dramatically reduce persistent forecast failure exhibited by forecasts from macroeconomic models and professional forecasters.