OPTIMAL FORECAST COMBINATION UNDER REGIME SWITCHING*

This article proposes a new forecast combination method that lets the combination weights be driven by regime switching in a latent state variable. An empirical application that combines forecasts from survey data and time series models finds that the proposed regime switching combination scheme performs well for a variety of macroeconomic variables. Monte Carlo simulations shed light on the type of data‐generating processes for which the proposed combination method can be expected to perform better than a range of alternative combination schemes. Finally, we show how time variations in the combination weights arise when the target variable and the predictors share a common factor structure driven by a hidden Markov process.     

A Bayesian method of combining judgmental and model-based density forecasts

This paper introduces a formal method of combining expert and model density forecasts when the sample of past forecasts is unavailable. It works directly with the expert forecast density and endogenously delivers weights for forecast combination, relying on probability rules only. The empirical part of the paper illustrates how the framework can be applied in forecasting US inflation by mixing density forecasts from an autoregressive model and the Survey of Professional Forecasters.     

Forecast combination for discrete choice models: predicting FOMC monetary policy decisions

This paper provides a methodology for combining forecasts based on several discrete choice models. This is achieved primarily by combining one-step-ahead probability forecasts associated with each model. The paper applies well-established scoring rules for qualitative response models in the context of forecast combination. Log scores, quadratic scores and Epstein scores are used to evaluate the forecasting accuracy of each model and to combine the probability forecasts. In addition to producing point forecasts, the effect of sampling variation is also assessed. This methodology is applied to forecast US Federal Open Market Committee (FOMC) decisions regarding changes in the federal funds target rate. Several of the economic fundamentals influencing the FOMC’s decisions are integrated, or I(1), and are modeled in a similar fashion to Hu and Phillips (J Appl Econom 19(7):851– 867, 2004). The empirical results show that combining forecasted probabilities using scores generally outperforms both equal weight combination and forecasts based on multivariate models.     

Forecast combination when outcomes are difficult to predict

We show that when outcomes are difficult to forecast in the sense that forecast errors have a large common component that (a) optimal weights are not affected by this common component, and may well be far from equal to each other but (b) the relative mean square error loss from averaging over optimal combination can be small. Hence, researchers could well estimate combining weights that indicate that correlations could be exploited for better forecasts only to find that the difference in terms of loss is negligible. The results then provide an additional explanation for the commonly encountered practical situation of the averaging of forecasts being difficult to improve upon.     

Generalized Method of Moment estimation of multivariate multifractal models

Multifractal processes have recently been introduced as a new tool for modeling the stylized facts of financial markets and have been found to consistently provide certain gains in performance over basic volatility models for a broad range of assets and for various risk management purposes. Due to computational constraints, multivariate extensions of the baseline univariate multifractal framework are, however, still very sparse so far. In this paper, we introduce a parsimoniously designed multivariate multifractal model, and we implement its estimation via a Generalized Methods of Moments (GMM) algorithm. Monte Carlo studies show that the performance of this GMM estimator for bivariate and trivariate models is similar to GMM estimation for univariate multifractal models. An empirical application shows that the multivariate multifractal model improves upon the volatility forecasts of multivariate GARCH over medium to long forecast horizons.     

A dynamic factor model framework for forecast combination

A panel of ex-ante forecasts of a single time series is modeled as a dynamic factor model, where the conditional expectation is the single unobserved factor. When applied to out-of-sample forecasting, this leads to combination forecasts that are based on methods other than OLS. These methods perform well in a Monte Carlo experiment. These methods are evaluated empirically in a panel of simulated real-time computer-generated univariate forecasts of U.S. macroeconomic time series.     

How do oil price forecast errors impact inflation forecast errors? An empirical analysis from US,French and UK inflation forecasts

This paper proposes an empirical investigation of the impact of oil price forecast errors on inflation forecast errors for three different sets of recent forecast data: the median of SPF inflation forecasts for the United States and the Central Bank inflation forecasts for France and the United Kingdom. Mainly two salient points emerge from our results. First, there is a significant contribution of oil price forecast errors to the explanation of inflation forecast errors, whatever the country or the period considered. Second, the pass-through of oil price forecast errors to inflation forecast errors is typically multiplied by around 2 when the oil price volatility is large.     

Forecasting stock market volatility: The role of technical variables

Accurate volatility forecasts are required by both market participants and policy makers. In this paper, we forecast stock return volatility by using a wide range of technical indicators constructed based on the past behavior of stock price, volatility and trading volume. Our out-of-sample results indicate that the incorporation of technical variables in the autoregression benchmark can produce significantly more accurate volatility forecasts. The forecasting performance of the combination of technical indicators is further compared with that of the popular economic indicators. Technical variables perform better than economic variables when the economy is an expansion, while the economic variables generate more accurate forecasts when the economy belongs a recession. These two types of variables provide complementary information over the business cycle. We obtain more reliable forecasts by combining all economic and technical information together than by combining either type of information alone.     

The Implications for Econometric Modelling of Forecast Failure

To reconcile forecast failure with building congruent empirical models, we analyze the sources of mis-prediction. This reveals that ex ante forecast failure is purely a function of forecast-period events, not determinable from in-sample information. The primary causes are unmodelled shifts in deterministic factors, rather than model mis-specification, collinearity, or a lack of parsimony. We examine the effects of deterministic breaks on equilibrium-correction mechanisms, and consider the role of causal variables. Throughout, Monte Carlo simulation and empirical models illustrate the analysis, and support a progressive research strategy based on learning from past failures.     

FORECASTING US INFLATION USING DYNAMIC GENERAL‐TO‐SPECIFIC MODEL SELECTION

We forecast US inflation using a standard set of macroeconomic predictors and a dynamic model selection and averaging methodology that allows the forecasting model to change over time. Pseudo out‐of‐sample forecasts are generated from models identified from a multipath general‐to‐specific algorithm that is applied dynamically using rolling regressions. Our results indicate that the inflation forecasts that we obtain employing a short rolling window substantially outperform those from a well‐established univariate benchmark, and contrary to previous evidence, are considerably robust to alternative forecast periods.     

Forecasting house prices using dynamic model averaging approach: Evidence from China

Forecasting house price has been of great interests for macroeconomists, policy makers and investors in recent years. To improve the forecasting accuracy, this paper introduces a dynamic model averaging (DMA) method to forecast the growth rate of house prices in 30 major Chinese cities. The advantage of DMA is that this method allows both the sets of predictors (forecasting models) as well as their coefficients to change over time. Both recursive and rolling forecasting modes are applied to compare the performance of DMA with other traditional forecasting models. Furthermore, a model confidence set (MCS) test is used to statistically evaluate the forecasting efficiency of different models. The empirical results reveal that DMA generally outperforms other models, such as Bayesian model averaging (BMA), information-theoretic model averaging (ITMA) and equal-weighted averaging (EW), in both recursive and rolling forecasting modes. In addition, in recent years it is found that the Google search index, instead of fundamental macroeconomic or monetary indicators, has developed greater predictive power for house price in China.     

Understanding forecast failure of ESTAR models of real exchange rates

The forecast performance of the empirical ESTAR model of Taylor et al. (2001) is examined for 4 bilateral real exchange rate series over an out-of-sample evaluation period of nearly 12?years. Point as well as density forecasts are constructed, considering forecast horizons of 1 to 22 steps head. The study finds that no forecast gains over a simple AR(1) specification exist at any of the forecast horizons that are considered, regardless of whether point or density forecasts are utilised in the evaluation. Non-parametric methods are used in conjunction with simulation techniques to learn about the models and their forecasts. It is shown graphically that the nonlinearity in the conditional means (or point forecasts) of the ESTAR model decreases as the forecast horizon increases. The non-parametric methods show also that the multiple steps ahead forecast densities are normal looking with no signs of bi-modality, skewness or kurtosis.     

Estimation and Testing of Forecast Rationality under Flexible Loss

In situations where a sequence of forecasts is observed, a common strategy is to examine „rationality” conditional on a given loss function. We examine this from a different perspective—supposing that we have a family of loss functions indexed by unknown shape parameters, then given the forecasts can we back out the loss function parameters consistent with the forecasts being rational even when we do not observe the underlying forecasting model? We establish identification of the parameters of a general class of loss functions that nest popular loss functions as special cases and provide estimation methods and asymptotic distributional results for these parameters. This allows us to construct new tests of forecast rationality that allow for asymmetric loss. The methods are applied in an empirical analysis of IMF and OECD forecasts of budget deficits for the G7 countries. We find that allowing for asymmetric loss can significantly change the outcome of empirical tests of forecast rationality.     

The out-of-sample performance of an exact median-unbiased estimator for the near-unity AR(1) model

We analyse the forecasting performance of several strategies when estimating the near-unity AR(1) model. We focus on the Andrews’ (1993) exact median-unbiased estimator (BC), the OLS estimator and the driftless random walk (RW). We also explore two pairwise combinations between these strategies. We do this to investigate whether BC helps in reducing forecast errors. Via simulations, we find that BC forecasts typically outperform OLS forecasts. When BC is compared to the RW we obtain mixed results, favouring the latter while the persistence of the true process increases. Interestingly, we find that the combination of BC-RW performs well in a near-unity scheme.     

Quantile forecast combination using stochastic dominance

This paper derives optimal forecast combinations based on stochastic dominance efficiency (SDE) analysis with differential forecast weights for different quantiles of forecast error distribution. For the optimal forecast combination, SDE will minimize the cumulative density functions of the levels of loss at different quantiles of the forecast error distribution by combining different time-series model-based forecasts. Using two exchange rate series on weekly data for the Japanese yen/US dollar and US dollar/Great Britain pound, we find that the optimal forecast combinations with SDE weights perform better than different forecast selection and combination methods for the majority of the cases at different quantiles of the error distribution. However, there are also some very few cases where some other forecast selection and combination model performs equally well at some quantiles of the forecast error distribution. Different forecasting period and quadratic loss function are used to obtain optimal forecast combinations, and results are robust to these choices. The out-of-sample performance of the SDE forecast combinations is also better than that of the other forecast selection and combination models we considered.     

Forecasting volatility in the Chinese stock market under model uncertainty

Volatility forecasting is an important issue in empirical finance. In this paper, the main purpose is to apply the model averaging techniques to reduce volatility model uncertainty and improve volatility forecasting. Six GARCH-type models are considered as candidate models for model averaging. As to the Chinese stock market, the largest emerging market in the world, the empirical study shows that forecast combination using model averaging can be a better approach than the individual forecasts.     

Forecasting economic activity by Bayesian bridge model averaging

This paper proposes the use of Bayesian model averaging (BMA) as an alternative tool to forecast GDP relative to simple bridge models and factor models. BMA is a computationally feasible method that allows us to explore the model space even in the presence of a large set of candidate predictors. We test the performance of BMA in now-casting by means of a recursive experiment for the euro area and the three largest countries. This method allows flexibility in selecting the information set month by month. We find that BMA-based forecasts produce smaller forecast errors than standard bridge model when forecasting GDP in Germany, France and Italy. At the same time, it also performs as well as medium-scale factor models when forecasting Eurozone GDP.     

Do equity index industry groups improve forecasts of inflation and production? A US analysis

This study develops a new financial market indicator, which may be a useful addition to analysing real activity in the US. By taking the ratio of the price return of equity industry groups of the S&P 500 over a benchmark industry group, in this case taken to be the Utilities industry group, an indicator is created which represents the price return performance specific to each individual industry. We then perform recursive pseudo out-of-sample bivariate forecasts of future changes in the Industrial Production Index (IPI) and the Consumer Price Index (CPI) at 3-month, 6-month and 12-month horizons using each of the indicators and compare results against an AR forecast. The results of the bivariate forecasts using a number of the indicators produce better forecasts of changes in the IPI and are also significant for causality, both for the full sample period and when tested recursively. Bivariate forecasts of changes to the CPI, however, do not improve upon the AR forecasts.     

A two factor model to combine US inflation forecasts

The combination of individual forecasts is often a useful tool to improve forecast accuracy. The most commonly used technique for forecast combination is the mean, and it has frequently proved hard to surpass. This study considers factor analysis to combine US inflation forecasts showing that just one factor is not enough to beat the mean and that the second one is necessary. The first factor is usually a weighted mean of the variables and it can be interpreted as a consensus forecast, while the second factor generally provides the differences among the variables and, since the observations are forecasts, it may be related with the dispersion in forecasting expectations and, in a sense, with its uncertainty. Within this approach, the study also revisits Friedman's hypothesis relating the level of inflation with expectations uncertainty at the beginning of the twenty-first century.     

Do we need a global VAR model to forecast inflation and output in South Africa?

This study determines whether the global vector autoregressive (GVAR) approach provides better forecasts of key South African variables than a vector error correction model (VECM) and a Bayesian vector autoregressive (BVAR) model augmented with foreign variables. The article considers both a small GVAR model and a large GVAR model in determining the most appropriate model for forecasting South African variables. We compare the recursive out-of-sample forecasts for South African GDP and inflation from six types of models: a general 33 country (large) GVAR, a customized small GVAR for South Africa, a VECM for South Africa with weakly exogenous foreign variables, a BVAR model, autoregressive (AR) models and random walk models. The results show that the forecast performance of the large GVAR is generally superior to the performance of the customized small GVAR for South Africa. The forecasts of both the GVAR models tend to be better than the forecasts of the augmented VECM, especially at longer forecast horizons. Importantly, however, on average, the BVAR model performs the best when it comes to forecasting output, while the AR(1) model outperforms all the other models in predicting inflation. We also conduct ex ante forecasts from the BVAR and AR(1) models over 2010:Q1–2013:Q4 to highlight their ability to track turning points in output and inflation, respectively.