Robust optimization of forecast combinations

We develop a methodology for constructing robust combinations of time series forecast models which improve upon a given benchmark specification for all symmetric and convex loss functions. Under standard regularity conditions, the optimal forecast combination asymptotically almost surely dominates the benchmark, and also optimizes the chosen goal function. The optimum in a given sample can be found by solving a convex optimization problem. An application to the forecasting of changes in the S&P 500 volatility index shows that robust optimized combinations improve significantly upon the out-of-sample forecasting accuracy of both simple averaging and unrestricted optimization.     

New perspectives on forecasting inflation in emerging market economies: An empirical assessment

We use a broad-range set of inflation models and pseudo out-of-sample forecasts to assess their predictive ability among 14 emerging market economies (EMEs) at different horizons (1–12 quarters ahead) with quarterly data over the period 1980Q1-2016Q4. We find, in general, that a simple arithmetic average of the current and three previous observations (the RW-AO model) consistently outperforms its standard competitors—based on the root mean squared prediction error (RMSPE) and on the accuracy in predicting the direction of change. These include conventional models based on domestic factors, existing open-economy Phillips curve-based specifications, factor-augmented models, and time-varying parameter models. Often, the RMSPE and directional accuracy gains of the RW-AO model are shown to be statistically significant. Our results are robust to forecast combinations, intercept corrections, alternative transformations of the target variable, different lag structures, and additional tests of (conditional) predictability. We argue that the RW-AO model is successful among EMEs because it is a straightforward method to downweight later data, which is a useful strategy when there are unknown structural breaks and model misspecification.     

Forecasting macroeconomic time series: LASSO-based approaches and their forecast combinations with dynamic factor models

In a data-rich environment, forecasting economic variables amounts to extracting and organizing useful information from a large number of predictors. So far, the dynamic factor model and its variants have been the most successful models for such exercises. In this paper, we investigate a category of LASSO-based approaches and evaluate their predictive abilities for forecasting twenty important macroeconomic variables. These alternative models can handle hundreds of data series simultaneously, and extract useful information for forecasting. We also show, both analytically and empirically, that combing forecasts from LASSO-based models with those from dynamic factor models can reduce the mean square forecast error (MSFE) further. Our three main findings can be summarized as follows. First, for most of the variables under investigation, all of the LASSO-based models outperform dynamic factor models in the out-of-sample forecast evaluations. Second, by extracting information and formulating predictors at economically meaningful block levels, the new methods greatly enhance the interpretability of the models. Third, once forecasts from a LASSO-based approach are combined with those from a dynamic factor model by forecast combination techniques, the combined forecasts are significantly better than either dynamic factor model forecasts or the naïve random walk benchmark.     

Optimal probabilistic forecasts: When do they work?

Proper scoring rules are used to assess the out-of-sample accuracy of probabilistic forecasts, with different scoring rules rewarding distinct aspects of forecast performance. Herein, we re-investigate the practice of using proper scoring rules to produce probabilistic forecasts that are ‘optimal’ according to a given score and assess when their out-of-sample accuracy is superior to alternative forecasts, according to that score. Particular attention is paid to relative predictive performance under misspecification of the predictive model. Using numerical illustrations, we document several novel findings within this paradigm that highlight the important interplay between the true data generating process, the assumed predictive model and the scoring rule. Notably, we show that only when a predictive model is sufficiently compatible with the true process to allow a particular score criterion to reward what it is designed to reward, will this approach to forecasting reap benefits. Subject to this compatibility, however, the superiority of the optimal forecast will be greater, the greater is the degree of misspecification. We explore these issues under a range of different scenarios and using both artificially simulated and empirical data.     

Theory-coherent forecasting

We consider a method for producing multivariate density forecasts that satisfy moment restrictions implied by economic theory, such as Euler conditions. The method starts from a base forecast that might not satisfy the theoretical restrictions and forces it to satisfy the moment conditions using exponential tilting. Although exponential tilting has been considered before in a Bayesian context (Robertson et al. 2005), our main contributions are: (1) to adapt the method to a classical inferential context with out-of-sample evaluation objectives and parameter estimation uncertainty; and (2) to formally discuss the conditions under which the method delivers improvements in forecast accuracy. An empirical illustration which incorporates Euler conditions into forecasts produced by Bayesian vector autoregressions shows that the improvements in accuracy can be sizable and significant.     

Predictive regressions under asymmetric loss: Factor augmentation and model selection

This paper discusses the specifics of forecasting using factor-augmented predictive regressions under general loss functions. In line with the literature, we employ principal component analysis to extract factors from the set of predictors. In addition, we also extract information on the volatility of the series to be predicted, since the volatility is forecast-relevant under non-quadratic loss functions. We ensure asymptotic unbiasedness of the forecasts under the relevant loss by estimating the predictive regression through the minimization of the in-sample average loss. Finally, we select the most promising predictors for the series to be forecast by employing an information criterion that is tailored to the relevant loss. Using a large monthly data set for the US economy, we assess the proposed adjustments in a pseudo out-of-sample forecasting exercise for various variables. As expected, the use of estimation under the relevant loss is found to be effective. Using an additional volatility proxy as the predictor and conducting model selection that is tailored to the relevant loss function enhances the forecast performance significantly.     

Moving average stochastic volatility models with application to inflation forecast

We introduce a new class of models that has both stochastic volatility and moving average errors, where the conditional mean has a state space representation. Having a moving average component, however, means that the errors in the measurement equation are no longer serially independent, and estimation becomes more difficult. We develop a posterior simulator that builds upon recent advances in precision-based algorithms for estimating these new models. In an empirical application involving US inflation we find that these moving average stochastic volatility models provide better in-sample fitness and out-of-sample forecast performance than the standard variants with only stochastic volatility.     

Bayesian forecasting and portfolio decisions using dynamic dependent sparse factor models

We extend the recently introduced latent threshold dynamic models to include dependencies among the dynamic latent factors which underlie multivariate volatility. With an ability to induce time-varying sparsity in factor loadings, these models now also allow time-varying correlations among factors, which may be exploited in order to improve volatility forecasts. We couple multi-period, out-of-sample forecasting with portfolio analysis using standard and novel benchmark neutral portfolios. Detailed studies of stock index and FX time series include: multi-period, out-of-sample forecasting, statistical model comparisons, and portfolio performance testing using raw returns, risk-adjusted returns and portfolio volatility. We find uniform improvements on all measures relative to standard dynamic factor models. This is due to the parsimony of latent threshold models and their ability to exploit between-factor correlations so as to improve the characterization and prediction of volatility. These advances will be of interest to financial analysts, investors and practitioners, as well as to modeling researchers.     

MULTI-STEP ESTIMATION FOR FORECASTING

We delineate conditions which favour multi-step, or dynamic, estimation for multi-step forecasting. An analytical example shows how dynamic estimation (DE) may accommodate incorrectly-specified models as the forecast lead alters, improving forecast performance for some misspecifications. However, in correctly-specified models, reducing finite-sample biases does not justify DE. In a Monte Carlo forecasting study for integrated processes, estimating a unit root in the presence of a neglected negative moving-average error may favour DE, though other solutions exist to that scenario. A second Monte Carlo study obtains the estimator biases and explains these using asymptotic approximations.     

Forecasts of market shares from VAR and BVAR models: a comparison of their accuracy

This paper develops a Bayesian vector autoregressive model (BVAR) for the leader of the Portuguese car market to forecast the market share. The model includes five marketing decision variables. The Bayesian prior is selected on the basis of the accuracy of the out-of-sample forecasts. We find that BVAR models generally produce more accurate forecasts. The out-of-sample accuracy of the BVAR forecasts is also compared with that of forecasts from an unrestricted VAR model and of benchmark forecasts produced from three univariate models. Additionally, competitive dynamics are revealed through variance decompositions and impulse response analyses.     

An empirical analysis of neural network memory structures for basin water quality forecasting

This research investigates the cumulative multi-period forecast accuracy of a diverse set of potential forecasting models for basin water quality management. The models are characterized by their short-term (memory by delay or memory by feedback) and long-term (linear or nonlinear) memory structures. The experiments are conducted as a series of forecast cycles, with a rolling origin of a constant fit size. The models are recalibrated with each cycle, and out-of-sample forecasts are generated for a five-period forecast horizon. The results confirm that the JENN and GMNN neural network models are generally more accurate than competitors for cumulative multi-period basin water quality prediction. For example, the JENN and GMNN models reduce the cumulative five-period forecast errors by as much as 50%, relative to exponential smoothing and ARIMA models. These findings are significant in view of the increasing social and economic consequences of basin water quality management, and have the potential for extention to other scientific, medical, and business applications where multi-period predictions of nonlinear time series are critical.     

The power of tests of predictive ability in the presence of structural breaks

This paper presents analytical, Monte Carlo, and empirical evidence on the effects of structural breaks on tests for equal forecast accuracy and encompassing. We show that out-of-sample predictive content can be hard to find because out-of-sample tests are highly dependent on the timing of the predictive ability. Moreover, predictive content is harder to find with some tests than others: in power, F-type tests of equal forecast accuracy and encompassing often dominate t-type alternatives. Based on these results and evidence from an empirical application, we conclude that structural breaks under the alternative may explain why researchers often find evidence of in-sample, but not out-of-sample, predictive content.     

Forecasting realized volatility of agricultural commodities

We forecast the realized and median realized volatility of agricultural commodities using variants of the heterogeneous autoregressive (HAR) model. We obtain tick-by-tick data on five widely-traded agricultural commodities (corn, rough rice, soybeans, sugar, and wheat) from the CME/ICE. Real out-of-sample forecasts are produced for between 1 and 66 days ahead. Our in-sample analysis shows that the variants of the HAR model which decompose volatility measures into their continuous path and jump components and incorporate leverage effects offer better fitting in the predictive regressions. However, we demonstrate convincingly that such HAR extensions do not offer any superior predictive ability in their out-of-sample results, since none of these extensions produce significantly better forecasts than the simple HAR model. Our results remain robust even when we evaluate them in a Value-at-Risk framework. Thus, there is no benefit from including more complexity, related to the volatility decomposition or relative transformations of the volatility, in the forecasting models.     

Equity premium prediction and optimal portfolio decision with Bagging

We propose using the statistical method of Bagging to forecast the equity premium out-of-sample for multivariate regression models. Bagging allows for the flexible and efficient extraction of valuable informational content from a large set of predictors, leading to statistically and economically significant gains relative to not only the historical mean, but also other soft-threshold methods such as forecast combinations and shrinkage estimators in our empirical results. Furthermore, we find that the source of economic gains for Bagging primarily comes from the fact that it encourages the investor to actively manage portfolio by flexibly utilizing short selling or leveraging to better time the market following correctly prognosticated trends. However, other strategies such as forecast combinations keep the equity shares nearly fixed regardless of the predicted market prospect.     

Dynamic functional time-series forecasts of foreign exchange implied volatility surfaces

This paper presents static and dynamic versions of univariate, multivariate, and multilevel functional time-series methods to forecast implied volatility surfaces in foreign exchange markets. We find that dynamic functional principal component analysis generally improves out-of-sample forecast accuracy. Specifically, the dynamic univariate functional time-series method shows the greatest improvement. Our models lead to multiple instances of statistically significant improvements in forecast accuracy for daily EUR–USD, EUR–GBP, and EUR–JPY implied volatility surfaces across various maturities, when benchmarked against established methods. A stylised trading strategy is also employed to demonstrate the potential economic benefits of our proposed approach.     

Multivariate volatility forecasts for stock market indices

Volatility forecasts aim to measure future risk and they are key inputs for financial analysis. In this study, we forecast the realized variance as an observable measure of volatility for several major international stock market indices and accounted for the different predictive information present in jump, continuous, and option-implied variance components. We allowed for volatility spillovers in different stock markets by using a multivariate modeling approach. We used heterogeneous autoregressive (HAR)-type models to obtain the forecasts. Based an out-of-sample forecast study, we show that: (i) including option-implied variances in the HAR model substantially improves the forecast accuracy, (ii) lasso-based lag selection methods do not outperform the parsimonious day-week-month lag structure of the HAR model, and (iii) cross-market spillover effects embedded in the multivariate HAR model have long-term forecasting power.     

Volatility forecasting in the Bitcoin market: A new proposed measure based on the VS-ACARR approach

This paper proposes a new volatility-spillover-asymmetric conditional autoregressive range (VS-ACARR) approach that takes into account the intraday information, the volatility spillover from crude oil as well as the volatility asymmetry (leverage effect) to model/forecast Bitcoin volatility (price range). An empirical application to Bitcoin and crude oil (WTI) price ranges shows the existence of strong volatility spillover from crude oil to the Bitcoin market and a weak leverage effect in the Bitcoin market. The VS-ACARR model yields higher forecasting accuracy than the GARCH, CARR, and VS-CARR models regarding out-of-sample forecast performance, suggesting that accounting for the volatility spillover and asymmetry can significantly improve the forecasting accuracy of Bitcoin volatility. The superior forecast performance of the VS-ACARR model is robust to alternative out-of-sample forecast windows. Our findings highlight the importance of accommodating intraday information, spillover from crude oil, and volatility asymmetry in forecasting Bitcoin volatility.     

Conformal prediction interval estimation and applications to day-ahead and intraday power markets

In this study, we investigated the application of the conformal prediction (CP) concept in the context of short-term electricity price forecasting. In particular, we determined the most important aspects related to the utility of CP, as well as explaining why this simple but highly effective idea has proved useful in other application areas and why its characteristics make it promising for short-term power applications. We compared the performance of CP with various state-of-the-art electricity price forecasting models, such as quantile regression averaging, in an empirical out-of-sample study of three short-term electricity time series. We combined CP with various underlying point forecast models to demonstrate its versatility and behavior under changing conditions. Our findings suggest that CP yields sharp and reliable prediction intervals in short-term power markets. We also inspected the effects of each of the model components to provide path-based guideline regarding how to find the best CP model for each market.     

Takeover prediction using forecast combinations

The ability to identify likely takeover targets at an early stage should provide investors with valuable information, enabling them to profit by investing in potential target firms. In this paper we contribute to the takeover forecasting literature by suggesting the combination of probability forecasts as an alternative method of improving the forecast accuracy in takeover prediction and realizing improved economic returns from portfolios made up of predicted targets. Forecasts from several non-linear forecasting models, such as logistic and neural network models and a combination of them, are used to determine the methodology that best reduces the out-of-sample misclassification error. We draw two general conclusions from our results. First, the forecast combination method outperforms the single models, and should therefore be used to improve the accuracy of takeover target predictions. Second, we demonstrate that an investment in a portfolio of the combined predicted targets results in significant abnormal returns being made by an investor, in the order of up to double the market benchmark return when using a portfolio of manageable size.     

Forecasting value at risk and expected shortfall with mixed data sampling

I propose applying the Mixed Data Sampling (MIDAS) framework to forecast Value at Risk (VaR) and Expected shortfall (ES). The new methods exploit the serial dependence on short-horizon returns to directly forecast the tail dynamics of the desired horizon. I perform a comprehensive comparison of out-of-sample VaR and ES forecasts with established models for a wide range of financial assets and backtests. The MIDAS-based models significantly outperform traditional GARCH-based forecasts and alternative conditional quantile specifications, especially in terms of multi-day forecast horizons. My analysis advocates models that feature asymmetric conditional quantiles and the use of the Asymmetric Laplace density to jointly estimate VaR and ES.