Forecasting cryptocurrencies under model and parameter instability

This paper studies the predictability of cryptocurrency time series. We compare several alternative univariate and multivariate models for point and density forecasting of four of the most capitalized series: Bitcoin, Litecoin, Ripple and Ethereum. We apply a set of crypto-predictors and rely on dynamic model averaging to combine a large set of univariate dynamic linear models and several multivariate vector autoregressive models with different forms of time variation. We find statistically significant improvements in point forecasting when using combinations of univariate models, and in density forecasting when relying on the selection of multivariate models. Both schemes deliver sizable directional predictability.     

Macroeconomic Forecasting Performance under Alternative Specifications of Time‐Varying Volatility

This paper compares alternative models of time‐varying volatility on the basis of the accuracy of real‐time point and density forecasts of key macroeconomic time series for the USA. We consider Bayesian autoregressive and vector autoregressive models that incorporate some form of time‐varying volatility, precisely random walk stochastic volatility, stochastic volatility following a stationary AR process, stochastic volatility coupled with fat tails, GARCH and mixture of innovation models. The results show that the AR and VAR specifications with conventional stochastic volatility dominate other volatility specifications, in terms of point forecasting to some degree and density forecasting to a greater degree. Copyright © 2014 John Wiley & Sons, Ltd.     

Order-invariant tests for proper calibration of multivariate density forecasts

Established tests for proper calibration of multivariate density forecasts based on Rosenblatt probability integral transforms can be manipulated by changing the order of variables in the forecasting model. We derive order-invariant tests. The new tests are applicable to densities of arbitrary dimensions and can deal with parameter estimation uncertainty and dynamic misspecification. Monte Carlo simulations show that they often have superior power relative to established approaches. We use the tests to evaluate generalized autoregressive conditional heteroskedasticity-based multivariate density forecasts for a vector of stock market returns and macroeconomic forecasts from a Bayesian vector autoregression with time-varying parameters.     

Forecasting electricity prices with expert,linear, and nonlinear models

This paper compares several models for forecasting regional hourly day-ahead electricity prices, while accounting for fundamental drivers. Forecasts of demand, in-feed from renewable energy sources, fossil fuel prices, and physical flows are all included in linear and nonlinear specifications, ranging in the class of ARFIMA-GARCH models—hence including parsimonious autoregressive specifications (known as expert-type models). The results support the adoption of a simple structure that is able to adapt to market conditions. Indeed, we include forecasted demand, wind and solar power, actual generation from hydro, biomass, and waste, weighted imports, and traditional fossil fuels. The inclusion of these exogenous regressors, in both the conditional mean and variance equations, outperforms in point and, especially, in density forecasting when the superior set of models is considered. Indeed, using the model confidence set and considering northern Italian prices, predictions indicate the strong predictive power of regressors, in particular in an expert model augmented for GARCH-type time-varying volatility. Finally, we find that using professional and more timely predictions of consumption and renewable energy sources improves the forecast accuracy of electricity prices more than using predictions publicly available to researchers.     

Forecasting with Global Vector Autoregressive Models: a Bayesian Approach

This paper develops a Bayesian variant of global vector autoregressive (B‐GVAR) models to forecast an international set of macroeconomic and financial variables. We propose a set of hierarchical priors and compare the predictive performance of B‐GVAR models in terms of point and density forecasts for one‐quarter‐ahead and four‐quarter‐ahead forecast horizons. We find that forecasts can be improved by employing a global framework and hierarchical priors which induce country‐specific degrees of shrinkage on the coefficients of the GVAR model. Forecasts from various B‐GVAR specifications tend to outperform forecasts from a naive univariate model, a global model without shrinkage on the parameters and country‐specific vector autoregressions. Copyright © 2016 John Wiley & Sons, Ltd.     

A forecasting comparison of some var techniques

Higher dimensional multivariate time series models suffer from the problem of over-parametrisation which impairs their forecasting performance. Starting from such unrestricted vector autoregressive models the paper discusses two ways to cope with this difficulty. The first approach reduces the number of free parameters by applying a subset modelling strategy. The second approach takes a Bayesian point of view by formulating ‘priors’ which are then combined with sample information, but leaving the original specification unaltered. Using Austrian quarterly macroeconomic time series a comparative study is undertaken by running alternative forecasting exercises. Both methods improve out-of-sample forecasting performance substantially at the cost of some bias in ex-post simulations. Comparing the ex-ante predictions of the two approaches, the former does better at short horizons whereas the latter gains as the forecast horizon lengthens.     

Bayesian median autoregression for robust time series forecasting

We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to the widely used mean-based methods. Motivated by a working Laplace likelihood approach in Bayesian quantile regression, BayesMAR adopts a parametric model bearing the same structure as autoregressive models by altering the Gaussian error to Laplace, leading to a simple, robust, and interpretable modeling strategy for time series forecasting. We estimate model parameters by Markov chain Monte Carlo. Bayesian model averaging is used to account for model uncertainty, including the uncertainty in the autoregressive order, in addition to a Bayesian model selection approach. The proposed methods are illustrated using simulations and real data applications. An application to U.S. macroeconomic data forecasting shows that BayesMAR leads to favorable and often superior predictive performance compared to the selected mean-based alternatives under various loss functions that encompass both point and probabilistic forecasts. The proposed methods are generic and can be used to complement a rich class of methods that build on autoregressive models.     

BAYESIAN MODEL SELECTION AND FORECASTING IN NONCAUSAL AUTOREGRESSIVE MODELS

In this paper, we propose a Bayesian estimation and forecasting procedure for noncausal autoregressive (AR) models. Specifically, we derive the joint posterior density of the past and future errors and the parameters, yielding predictive densities as a by‐product. We show that the posterior model probabilities provide a convenient model selection criterion in discriminating between alternative causal and noncausal specifications. As an empirical application, we consider US inflation. The posterior probability of noncausality is found to be high—over 98%. Furthermore, the purely noncausal specifications yield more accurate inflation forecasts than alternative causal and noncausal AR models. Copyright © 2010 John Wiley & Sons, Ltd.     

Ordinal-response GARCH models for transaction data: A forecasting exercise

We use numerous high-frequency transaction data sets to evaluate the forecasting performances of several dynamic ordinal-response time series models with generalized autoregressive conditional heteroscedasticity (GARCH). The specifications account for three components: leverage effects, in-mean effects and moving average error terms. We estimate the model parameters by developing Markov chain Monte Carlo algorithms. Our empirical analysis shows that the proposed ordinal-response GARCH models achieve better point and density forecasts than standard benchmarks.     

Forecasting realized volatility: a Bayesian model‐averaging approach

How to measure and model volatility is an important issue in finance. Recent research uses high‐frequency intraday data to construct ex post measures of daily volatility. This paper uses a Bayesian model‐averaging approach to forecast realized volatility. Candidate models include autoregressive and heterogeneous autoregressive specifications based on the logarithm of realized volatility, realized power variation, realized bipower variation, a jump and an asymmetric term. Applied to equity and exchange rate volatility over several forecast horizons, Bayesian model averaging provides very competitive density forecasts and modest improvements in point forecasts compared to benchmark models. We discuss the reasons for this, including the importance of using realized power variation as a predictor. Bayesian model averaging provides further improvements to density forecasts when we move away from linear models and average over specifications that allow for GARCH effects in the innovations to log‐volatility. Copyright © 2009 John Wiley & Sons, Ltd.     

Forecasting correlated time series with exponential smoothing models

This paper presents the Bayesian analysis of a general multivariate exponential smoothing model that allows us to forecast time series jointly, subject to correlated random disturbances. The general multivariate model, which can be formulated as a seemingly unrelated regression model, includes the previously studied homogeneous multivariate Holt-Winters’ model as a special case when all of the univariate series share a common structure. MCMC simulation techniques are required in order to approach the non-analytically tractable posterior distribution of the model parameters. The predictive distribution is then estimated using Monte Carlo integration. A Bayesian model selection criterion is introduced into the forecasting scheme for selecting the most adequate multivariate model for describing the behaviour of the time series under study. The forecasting performance of this procedure is tested using some real examples.     

Time series estimation of the bond default risk premium

The bond default risk premium, measured by the spread between higher and lower grade bond returns, is often estimated with univariate time series procedures and used as an input in financial models. In this paper, time series properties of the historical default risk premium are analyzed and forecasting results from univariate time series models are compared. An autoregressive model with an overreaction component provides the best statistical fit for the bond default risk premium series. A random walk model exhibits the worst fit. The findings are robust over a variety of model specifications and measurement choices. For all forms of the time series process the univariate time series models explain a small percentage of the variation in the default risk premium, raising questions about traditional approaches to estimating the expected default risk premium.     

Modelling and forecasting stock returns: exploiting the futures market,regime shifts and international spillovers

This paper proposes a vector equilibrium correction model of stock returns that exploits the information in the futures market, while allowing for both regime‐switching behaviour and international spillovers across stock market indices. Using data for three major stock market indices since 1989, we find that: (i) in sample, our model outperforms several alternative models on the basis of standard statistical criteria; (ii) in out‐of‐sample forecasting, our model does not produce significant gains in terms of point forecasts relative to more parsimonious alternative specifications, but it does so both in terms of market timing ability and in density forecasting performance. The economic value of the density forecasts is illustrated with an application to a simple risk management exercise. Copyright © 2005 John Wiley & Sons, Ltd.     

REAL‐TIME FORECASTING OF INFLATION AND OUTPUT GROWTH WITH AUTOREGRESSIVE MODELS IN THE PRESENCE OF DATA REVISIONS

We examine how the accuracy of real‐time forecasts from models that include autoregressive terms can be improved by estimating the models on ‘lightly revised’ data instead of using data from the latest‐available vintage. The benefits of estimating autoregressive models on lightly revised data are related to the nature of the data revision process and the underlying process for the true values. Empirically, we find improvements in root mean square forecasting error of 2–4% when forecasting output growth and inflation with univariate models, and of 8% with multivariate models. We show that multiple‐vintage models, which explicitly model data revisions, require large estimation samples to deliver competitive forecasts. Copyright © 2012 John Wiley & Sons, Ltd.     

Efficient estimation of Bayesian VARMAs with time‐varying coefficients

Empirical work in macroeconometrics has been mostly restricted to using vector autoregressions (VARs), even though there are strong theoretical reasons to consider general vector autoregressive moving averages (VARMAs). A number of articles in the last two decades have conjectured that this is because estimation of VARMAs is perceived to be challenging and proposed various ways to simplify it. Nevertheless, VARMAs continue to be largely dominated by VARs, particularly in terms of developing useful extensions. We address these computational challenges with a Bayesian approach. Specifically, we develop a Gibbs sampler for the basic VARMA, and demonstrate how it can be extended to models with time‐varying vector moving average (VMA) coefficients and stochastic volatility. We illustrate the methodology through a macroeconomic forecasting exercise. We show that in a class of models with stochastic volatility, VARMAs produce better density forecasts than VARs, particularly for short forecast horizons.     

Evaluating factor forecasts for the UK: The role of asset prices

This paper applies a large data set, consisting of 167 monthly time series for the UK, both economic and financial, to simulate out-of-sample predictions of industrial production, inflation, 3-month Treasury Bills, and other variables. Fifteen dynamic factor models that allow forecasting based on large panels of time series are considered. The performances of these factor models are then compared to the following competing models: a simple univariate autoregressive, a vector autoregressive, a leading indicator, and a Phillips curve models. The results show that the best dynamic factor models outperform the competing models in forecasting at 6-, 12-, and 24-month horizons. Thus, the financial markets may have predictive power for the economic activity. This can be a useful tool for central banks and financial institutions, which may use the factor models to construct leading indicators of the economic conditions. In addition, researchers can see a strategic application of factor models.     

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.     

Bayesian stochastic search for VAR model restrictions

We propose a Bayesian stochastic search approach to selecting restrictions for vector autoregressive (VAR) models. For this purpose, we develop a Markov chain Monte Carlo (MCMC) algorithm that visits high posterior probability restrictions on the elements of both the VAR regression coefficients and the error variance matrix. Numerical simulations show that stochastic search based on this algorithm can be effective at both selecting a satisfactory model and improving forecasting performance. To illustrate the potential of our approach, we apply our stochastic search to VAR modeling of inflation transmission from producer price index (PPI) components to the consumer price index (CPI).     

Combination schemes for turning point predictions

We propose new forecast combination schemes for predicting turning points of business cycles. The proposed combination schemes are based on the forecasting performances of a given set of models with the aim to provide better turning point predictions. In particular, we consider predictions generated by autoregressive (AR) and Markov-switching AR models, which are commonly used for business cycle analysis. In order to account for parameter uncertainty we consider a Bayesian approach for both estimation and prediction and compare, in terms of statistical accuracy, the individual models and the combined turning point predictions for the United States and the Euro area business cycles.     

A comprehensive evaluation of macroeconomic forecasting methods

We employ datasets for seven developed economies and consider four classes of multivariate forecasting models in order to extend and enhance the empirical evidence in the macroeconomic forecasting literature. The evaluation considers forecasting horizons of between one quarter and two years ahead. We find that the structural model, a medium-sized DSGE model, provides accurate long-horizon US and UK inflation forecasts. We strike a balance between being comprehensive and producing clear messages by applying meta-analysis regressions to 2,976 relative accuracy comparisons that vary with the forecasting horizon, country, model class and specification, number of predictors, and evaluation period. For point and density forecasting of GDP growth and inflation, we find that models with large numbers of predictors do not outperform models with 13–14 hand-picked predictors. Factor-augmented models and equal-weighted combinations of single-predictor mixed-data sampling regressions are a better choice for dealing with large numbers of predictors than Bayesian VARs.