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This chapter introduces the best linear predictor (BLP) with the asymptotic minimum mean squared forecasting error (MSFE) among linear predictors of variables in cointegrated systems. Accordingly, the authors show that (i) if the autocorrelation coefficient of the cointegration error between the prediction time and the predicted targeting time is larger than ½ (representing a short prediction period), then the BLP is deduced from the random walk model; and (ii) in other cases (representing a long prediction period), the BLP is deduced from the cointegration model. Under this scheme, we suggest a switching predictor that automatically selects the random walk or cointegration model according to the size of the estimated autocorrelation coefficient. These results effectively explain the superiority reversal in the short- and long-term prediction of the exchange rate between the random walk and the structural/cointegration model (known as the Meese–Rogoff or disconnect puzzle).

We address an interesting case – the predictability of excess US asset returns from macroeconomic factors within a flexible regime-switching VAR framework – in which the presence of regimes may lead to superior forecasting performance from forecast combinations. After documenting that forecast combinations provide gains in predictive accuracy and that these gains are statistically significant, we show that forecast combinations may substantially improve portfolio selection. We find that the best-performing forecast combinations are those that either avoid estimating the pooling weights or that minimize the need for estimation. In practice, we report that the best-performing combination schemes are based on the principle of relative past forecasting performance. The economic gains from combining forecasts in portfolio management applications appear to be large, stable over time, and robust to the introduction of realistic transaction costs.

Marcet, and Nicolini (2003) and Milani (2014) demonstrate within the adaptive learning framework that a forecast error-based endogenous gain mechanism that switches between constant gain and decreasing gain may be more effective than the former alone in explaining time-varying parameters. In this paper, we propose an alternative endogenous gain scheme, henceforth referred to as CEG, that is based on recent coefficient estimates by the economic agents. We then show within a controlled simulation environment that CEG outperforms both constant gain learning as well as the aforementioned switching gain algorithm in terms of mean squared forecast errors (MSFE). In addition, we demonstrate within the context of a New Keynesian model that forecasts generated under CEG perform better in certain dimensions, particularly for inflation data, compared to constant gain learning. Combined with the fact that the proposed gain scheme ports easily to existing likelihood based inferential techniques used in constant gain learning, it is readily applicable to richer, more dynamic economic models.

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.

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.

We examine the role of structural breaks in forecasting stock return volatility. We begin by testing for structural breaks in the unconditional variance of daily returns for the S&P 500 market index and ten sectoral stock indices for 9/12/1989–1/19/2006 using an iterative cumulative sum of squares procedure. We find evidence of multiple variance breaks in almost all of the return series, indicating that structural breaks are an empirically relevant feature of return volatility. We then undertake an out-of-sample forecasting exercise to analyze how instabilities in unconditional variance affect the forecasting performance of asymmetric volatility models, focusing on procedures that employ a variety of estimation window sizes designed to accommodate potential structural breaks. The exercise demonstrates that structural breaks present important challenges to forecasting stock return volatility. We find that averaging across volatility forecasts generated by individual forecasting models estimated using different window sizes performs well in many cases and appears to offer a useful approach to forecasting stock return volatility in the presence of structural breaks.

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.

Many recent chapters have investigated whether data from internet search engines such as Google can help improve nowcasts or short-term forecasts of macroeconomic variables. These chapters construct variables based on Google searches and use them as explanatory variables in regression models. We add to this literature by nowcasting using dynamic model selection (DMS) methods which allow for model switching between time-varying parameter regression models. This is potentially useful in an environment of coefficient instability and over-parameterization which can arise when forecasting with Google variables. We extend the DMS methodology by allowing for the model switching to be controlled by the Google variables through what we call “Google probabilities”: instead of using Google variables as regressors, we allow them to determine which nowcasting model should be used at each point in time. In an empirical exercise involving nine major monthly US macroeconomic variables, we find DMS methods to provide large improvements in nowcasting. Our use of Google model probabilities within DMS often performs better than conventional DMS methods.

This paper investigates forecasting US Treasury bond and Dollar Eurocurrency rates using the stochastic unit root (STUR) model of Leybourne et al. (1996), and the stochastic cointegration (SC) model of Harris et al. (2002, 2006). Both models have time-varying parameter representations and are conceptually attractive for modelling interest rates as both allow for conditional heteroscedasticity. I find that for many of the series considered STUR and SC models generate statistically significant gains in out-of-sample forecasting accuracy relative to simple orthodox models. The results obtained highlight the usefulness of these extensions and raise some issues for future research.