Predicting crypto‐currencies using sparse non‐Gaussian state space models

In this paper we forecast daily returns of crypto‐currencies using a wide variety of different econometric models. To capture salient features commonly observed in financial time series like rapid changes in the conditional variance, non‐normality of the measurement errors and sharply increasing trends, we develop a time‐varying parameter VAR with t‐distributed measurement errors and stochastic volatility. To control for overparametrization, we rely on the Bayesian literature on shrinkage priors, which enables us to shrink coefficients associated with irrelevant predictors and/or perform model specification in a flexible manner. Using around one year of daily data, we perform a real‐time forecasting exercise and investigate whether any of the proposed models is able to outperform the naive random walk benchmark. To assess the economic relevance of the forecasting gains produced by the proposed models we, moreover, run a simple trading exercise.     

Forecasting and nowcasting emerging market GDP growth rates: The role of latent global economic policy uncertainty and macroeconomic data surprise factors

In this paper, we assess the predictive content of latent economic policy uncertainty and data surprise factors for forecasting and nowcasting gross domestic product (GDP) using factor-type econometric models. Our analysis focuses on five emerging market economies: Brazil, Indonesia, Mexico, South Africa, and Turkey; and we carry out a forecasting horse race in which predictions from various different models are compared. These models may (or may not) contain latent uncertainty and surprise factors constructed using both local and global economic datasets. The set of models that we examine in our experiments includes both simple benchmark linear econometric models as well as dynamic factor models that are estimated using a variety of frequentist and Bayesian data shrinkage methods based on the least absolute shrinkage operator (LASSO). We find that the inclusion of our new uncertainty and surprise factors leads to superior predictions of GDP growth, particularly when these latent factors are constructed using Bayesian variants of the LASSO. Overall, our findings point to the importance of spillover effects from global uncertainty and data surprises, when predicting GDP growth in emerging market economies.     

Time‐Varying Parameter Realized Volatility Models

In this paper, we introduce the functional coefficient to heterogeneous autoregressive realized volatility (HAR‐RV) models to make the parameters change over time. A nonparametric statistic is developed to perform a specification test. The simulation results show that our test displays reliable size and good power. Using the proposed test, we find a significant time variation property of coefficients to the HAR‐RV models. Time‐varying parameter (TVP) models can significantly outperform their constant‐coefficient counterparts for longer forecasting horizons. The predictive ability of TVP models can be improved by accounting for VIX information. Copyright © 2016 John Wiley & Sons, Ltd.     

What can we learn from the return predictability over the business cycle?

In this paper, we forecast stock returns using time‐varying parameter (TVP) models with parameters driven by economic conditions. An in‐sample specification test shows significant variation in the parameters. Out‐of‐sample results suggest that the TVP models outperform their constant coefficient counterparts. We also find significant return predictability from both statistical and economic perspectives with the application of TVP models. The out‐of‐sample R² of an equal‐weighted combination of TVP models is as high as 2.672%, and the gains in the certainty equivalent return are 214.7 basis points. Further analysis indicates that the improvement in predictability comes from the use of information on economic conditions rather than simply from allowing the coefficients to vary with time.     

Neural network versus econometric models in forecasting inflation

Artificial neural network modelling has recently attracted much attention as a new technique for estimation and forecasting in economics and finance. The chief advantages of this new approach are that such models can usually find a solution for very complex problems, and that they are free from the assumption of linearity that is often adopted to make the traditional methods tractable. In this paper we compare the performance of Back‐Propagation Artificial Neural Network (BPN) models with the traditional econometric approaches to forecasting the inflation rate. Of the traditional econometric models we use a structural reduced‐form model, an ARIMA model, a vector autoregressive model, and a Bayesian vector autoregression model. We compare each econometric model with a hybrid BPN model which uses the same set of variables. Dynamic forecasts are compared for three different horizons: one, three and twelve months ahead. Root mean squared errors and mean absolute errors are used to compare quality of forecasts. The results show the hybrid BPN models are able to forecast as well as all the traditional econometric methods, and to outperform them in some cases. Copyright © 2000 John Wiley & Sons, Ltd.     

The Informational Content of the Term Spread in Forecasting the US Inflation Rate: A Nonlinear Approach

The difficulty in modelling inflation and the significance in discovering the underlying data‐generating process of inflation is expressed in an extensive literature regarding inflation forecasting. In this paper we evaluate nonlinear machine learning and econometric methodologies in forecasting US inflation based on autoregressive and structural models of the term structure. We employ two nonlinear methodologies: the econometric least absolute shrinkage and selection operator (LASSO) and the machine‐learning support vector regression (SVR) method. The SVR has never been used before in inflation forecasting considering the term spread as a regressor. In doing so, we use a long monthly dataset spanning the period 1871:1–2015:3 that covers the entire history of inflation in the US economy. For comparison purposes we also use ordinary least squares regression models as a benchmark. In order to evaluate the contribution of the term spread in inflation forecasting in different time periods, we measure the out‐of‐sample forecasting performance of all models using rolling window regressions. Considering various forecasting horizons, the empirical evidence suggests that the structural models do not outperform the autoregressive ones, regardless of the model's method. Thus we conclude that the term spread models are not more accurate than autoregressive models in inflation forecasting. Copyright © 2016 John Wiley & Sons, Ltd.     

Forecasting output growth rates and median output growth rates: a hierarchical Bayesian approach

This paper describes procedures for forecasting countries' output growth rates and medians of a set of output growth rates using Hierarchical Bayesian (HB) models. The purpose of this paper is to show how the γ‐shrinkage forecast of Zellner and Hong ( 1989 ) emerges from a hierarchical Bayesian model and to describe how the Gibbs sampler can be used to fit this model to yield possibly improved output growth rate and median output growth rate forecasts. The procedures described in this paper offer two primary methodological contributions to previous work on this topic: (1) the weights associated with widely‐used shrinkage forecasts are determined endogenously, and (2) the posterior predictive density of the future median output growth rate is obtained numerically from which optimal point and interval forecasts are calculated. Using IMF data, we find that the HB median output growth rate forecasts outperform forecasts obtained from variety of benchmark models. Copyright © 2001 John Wiley & Sons, Ltd.     

Smooth transition exponential smoothing

Adaptive exponential smoothing methods allow a smoothing parameter to change over time, in order to adapt to changes in the characteristics of the time series. However, these methods have tended to produce unstable forecasts and have performed poorly in empirical studies. This paper presents a new adaptive method, which enables a smoothing parameter to be modelled as a logistic function of a user‐specified variable. The approach is analogous to that used to model the time‐varying parameter in smooth transition models. Using simulated data, we show that the new approach has the potential to outperform existing adaptive methods and constant parameter methods when the estimation and evaluation samples both contain a level shift or both contain an outlier. An empirical study, using the monthly time series from the M3‐Competition, gave encouraging results for the new approach. Copyright © 2004 John Wiley & Sons, Ltd.     

Time series forecasting using functional partial least square regression with stochastic volatility,GARCH, and exponential smoothing

We propose a method for improving the predictive ability of standard forecasting models used in financial economics. Our approach is based on the functional partial least squares (FPLS) model, which is capable of avoiding multicollinearity in regression by efficiently extracting information from the high‐dimensional market data. By using its well‐known ability, we can incorporate auxiliary variables that improve the predictive accuracy. We provide an empirical application of our proposed methodology in terms of its ability to predict the conditional average log return and the volatility of crude oil prices via exponential smoothing, Bayesian stochastic volatility, and GARCH (generalized autoregressive conditional heteroskedasticity) models, respectively. In particular, what we call functional data analysis (FDA) traces in this article are obtained via the FPLS regression from both the crude oil returns and auxiliary variables of the exchange rates of major currencies. For forecast performance evaluation, we compare out‐of‐sample forecasting accuracy of the standard models with FDA traces to the accuracy of the same forecasting models with the observed crude oil returns, principal component regression (PCR), and least absolute shrinkage and selection operator (LASSO) models. We find evidence that the standard models with FDA traces significantly outperform our competing models. Finally, they are also compared with the test for superior predictive ability and the reality check for data snooping. Our empirical results show that our new methodology significantly improves predictive ability of standard models in forecasting the latent average log return and the volatility of financial time series.     

Incorporating higher moments into value‐at‐risk forecasting

Value‐at‐risk (VaR) forecasting generally relies on a parametric density function of portfolio returns that ignores higher moments or assumes them constant. In this paper, we propose a simple approach to forecasting of a portfolio VaR. We employ the Gram‐Charlier expansion (GCE) augmenting the standard normal distribution with the first four moments, which are allowed to vary over time. In an extensive empirical study, we compare the GCE approach to other models of VaR forecasting and conclude that it provides accurate and robust estimates of the realized VaR. In spite of its simplicity, on our dataset GCE outperforms other estimates that are generated by both constant and time‐varying higher‐moments models. Copyright © 2009 John Wiley & Sons, Ltd.     

Forecasting US GNP growth: The role of uncertainty

A large number of models have been developed in the literature to analyze and forecast changes in output dynamics. The objective of this paper was to compare the predictive ability of univariate and bivariate models, in terms of forecasting US gross national product (GNP) growth at different forecasting horizons, with the bivariate models containing information on a measure of economic uncertainty. Based on point and density forecast accuracy measures, as well as on equal predictive ability (EPA) and superior predictive ability (SPA) tests, we evaluate the relative forecasting performance of different model specifications over the quarterly period of 1919:Q2 until 2014:Q4. We find that the economic policy uncertainty (EPU) index should improve the accuracy of US GNP growth forecasts in bivariate models. We also find that the EPU exhibits similar forecasting ability to the term spread and outperforms other uncertainty measures such as the volatility index and geopolitical risk in predicting US recessions. While the Markov switching time‐varying parameter vector autoregressive model yields the lowest values for the root mean squared error in most cases, we observe relatively low values for the log predictive density score, when using the Bayesian vector regression model with stochastic volatility. More importantly, our results highlight the importance of uncertainty in forecasting US GNP growth rates.     

Forecasting with Specification‐Switching VARs

The specification choices of vector autoregressions (VARs) in forecasting are often not straightforward, as they are complicated by various factors. To deal with model uncertainty and better utilize multiple VARs, this paper adopts the dynamic model averaging/selection (DMA/DMS) algorithm, in which forecasting models are updated and switch over time in a Bayesian manner. In an empirical application to a pool of Bayesian VAR (BVAR) models whose specifications include level and difference, along with differing lag lengths, we demonstrate that specification‐switching VARs are flexible and powerful forecast tools that yield good performance. In particular, they beat the overall best BVAR in most cases and are comparable to or better than the individual best models (for each combination of variable, forecast horizon, and evaluation metrics) for medium‐ and long‐horizon forecasts. We also examine several extensions in which forecast model pools consist of additional individual models in partial differences as well as all level/difference models, and/or time variations in VAR innovations are allowed, and discuss the potential advantages and disadvantages of such specification choices. Copyright © 2016 John Wiley & Sons, Ltd.     

Last Night a Shrinkage Saved My Life: Economic Growth,Model Uncertainty and Correlated Regressors

We compare the predictive ability of Bayesian methods which deal simultaneously with model uncertainty and correlated regressors in the framework of cross‐country growth regressions. In particular, we assess methods with spike and slab priors combined with different prior specifications for the slope parameters in the slab. Our results indicate that moving away from Gaussian g‐priors towards Bayesian ridge, LASSO or elastic net specifications has clear advantages for prediction when dealing with datasets of (potentially highly) correlated regressors, a pervasive characteristic of the data used hitherto in the econometric literature. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive learning from model space

Dynamic model averaging (DMA) is used extensively for the purpose of economic forecasting. This study extends the framework of DMA by introducing adaptive learning from model space. In the conventional DMA framework all models are estimated independently and hence the information of the other models is left unexploited. In order to exploit the information in the estimation of the individual time‐varying parameter models, this paper proposes not only to average over the forecasts but, in addition, also to dynamically average over the time‐varying parameters. This is done by approximating the mixture of individual posteriors with a single posterior, which is then used in the upcoming period as the prior for each of the individual models. The relevance of this extension is illustrated in three empirical examples involving forecasting US inflation, US consumption expenditures, and forecasting of five major US exchange rate returns. In all applications adaptive learning from model space delivers improvements in out‐of‐sample forecasting performance.     

Moment tests for density forecast evaluation in the presence of parameter estimation uncertainty

Density forecast (DF) possesses appealing properties when it is correctly specified for the true conditional distribution. Although a number of parametric specification tests have been introduced for the DF evaluation (DFE) in the parameter‐free context, econometric DF models are typically parameter‐dependent. In this paper, we first use a generalized probability integral transformation‐based moment test to unify these existing tests, and then apply the Newey–Tauchen method (the West–McCracken method) to correct this unified test as a generalized full‐sample (out‐of‐sample) test in the parameter‐dependent context. Unlike the corrected tests, the uncorrected tests could be substantially undersized (oversized) when they are directly applied to the full‐sample (out‐of‐sample) DFE in the presence of parameter estimation uncertainty. We also use a simulation to show the usefulness of the corrected tests in rectifying the size distortion problem, and apply the corrected tests to an empirical study of stock index returns. Copyright © 2010 John Wiley & Sons, Ltd.     

A Bayesian analysis of periodic integration

Recent empirical research into the seasonal and trend properties of macroeconomic time series using periodic models has resulted in strong evidence in favour of periodic integration (PI). PI implies that the differencing filter necessary to remove a stochastic trend varies across seasons and, hence, that seasonal fluctuations are related to the stochastic trend. Previous studies finding evidence of PI have used classical econometric techniques. In this paper, we investigate the possible sensitivity of this empirical result by using Bayesian techniques. An application of posterior odds analysis and highest posterior density interval tests to several quarterly UK macroeconomic series suggests strong evidence for PI, even when we allow for structural breaks in the deterministic seasonals. A predictive exercise indicates that PI usually outperforms other competing models in terms of out-of-sample forecasting. © 1997 John Wiley & Sons, Ltd.     

A large Bayesian VAR with a block-specific shrinkage: A forecasting application for Italian industrial production

This paper proposes a Bayesian vector autoregression (BVAR) model with the Kalman filter to forecast the Italian industrial production index in a pseudo real-time experiment. Minnesota priors are adopted as a general framework, but a different shrinkage pattern is imposed for both the VAR coefficients and the Kalman gain, depending on the informative contribution of each variable investigated at frequency level. Both a time-varying and a constant selection for the shrinkage are proposed. Overall, the new BVAR models significantly improve the forecasting performance in comparison with the more traditional versions based on standard Minnesota priors with a single shrinkage, equal for all the variables, and selected on the basis of some optimal criteria. Very promising results come out in terms of density forecasting as well.     

Long Memory of Financial Time Series and Hidden Markov Models with Time‐Varying Parameters

Hidden Markov models are often used to model daily returns and to infer the hidden state of financial markets. Previous studies have found that the estimated models change over time, but the implications of the time‐varying behavior have not been thoroughly examined. This paper presents an adaptive estimation approach that allows for the parameters of the estimated models to be time varying. It is shown that a two‐state Gaussian hidden Markov model with time‐varying parameters is able to reproduce the long memory of squared daily returns that was previously believed to be the most difficult fact to reproduce with a hidden Markov model. Capturing the time‐varying behavior of the parameters also leads to improved one‐step density forecasts. Finally, it is shown that the forecasting performance of the estimated models can be further improved using local smoothing to forecast the parameter variations. Copyright © 2016 John Wiley & Sons, Ltd.     

Forecasting with many predictors using Bayesian additive regression trees

Forecasting with many predictors provides the opportunity to exploit a much richer base of information. However, macroeconomic time series are typically rather short, raising problems for conventional econometric models. This paper explores the use of Bayesian additive regression trees (Bart) from the machine learning literature to forecast macroeconomic time series in a predictor‐rich environment. The interest lies in forecasting nine key macroeconomic variables of interest for government budget planning, central bank policy making and business decisions. It turns out that Bart is a valuable addition to existing methods for handling high dimensional data sets in a macroeconomic context.