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.     

Finding good predictors for inflation: a Bayesian model averaging approach

We consider a Bayesian model averaging approach for the purpose of forecasting Swedish consumer price index inflation using a large set of potential indicators, comprising some 80 quarterly time series covering a wide spectrum of Swedish economic activity. The paper demonstrates how to efficiently and systematically evaluate (almost) all possible models that these indicators in combination can give rise to. The results, in terms of out‐of‐sample performance, suggest that Bayesian model averaging is a useful alternative to other forecasting procedures, in particular recognizing the flexibility by which new information can be incorporated. Copyright © 2004 John Wiley & Sons, Ltd.     

LASSO‐Type Penalties for Covariate Selection and Forecasting in Time Series

This paper studies some forms of LASSO‐type penalties in time series to reduce the dimensionality of the parameter space as well as to improve out‐of‐sample forecasting performance. In particular, we propose a method that we call WLadaLASSO (weighted lag adaptive LASSO), which assigns not only different weights to each coefficient but also further penalizes coefficients of higher‐lagged covariates. In our Monte Carlo implementation, the WLadaLASSO is superior in terms of covariate selection, parameter estimation precision and forecasting, when compared to both LASSO and adaLASSO, especially for a higher number of candidate lags and a stronger linear dependence between predictors. Empirical studies illustrate our approach for US risk premium and US inflation forecasting with good results. Copyright © 2016 John Wiley & Sons, Ltd.     

Bayesian Forecasting for Time Series of Categorical Data

Time series of categorical data is not a widely studied research topic. Particularly, there is no available work on the Bayesian analysis of categorical time series processes. With the objective of filling that gap, in the present paper we consider the problem of Bayesian analysis including Bayesian forecasting for time series of categorical data, which is modelled by Pegram's mixing operator, applicable for both ordinal and nominal data structures. In particular, we consider Pegram's operator‐based autoregressive process for the analysis. Real datasets on infant sleep status are analysed for illustrations. We also illustrate that the Bayesian forecasting is more accurate than the corresponding frequentist's approach when we intend to forecast a large time gap ahead. Copyright © 2016 John Wiley & Sons, Ltd.     

Bayesian Model Averaging under Regime Switching with Application to Cyclical Macro Variable Forecasting

Model uncertainty and recurrent or cyclical structural changes in macroeconomic time series dynamics are substantial challenges to macroeconomic forecasting. This paper discusses a macro variable forecasting methodology that combines model uncertainty and regime switching simultaneously. The proposed predictive regression specification permits both regime switching of the regression parameters and uncertainty about the inclusion of forecasting variables by employing Bayesian model averaging. In an empirical exercise involving quarterly US inflation, we observed that our Bayesian model averaging with regime switching leads to substantial improvements in forecast performance, particularly in the medium horizon (two to four quarters). Copyright © 2015 John Wiley & Sons, Ltd.     

Assessing the Macroeconomic Forecasting Performance of Boosting: Evidence for the United States,the Euro Area and Germany

The use of large datasets for macroeconomic forecasting has received a great deal of interest recently. Boosting is one possible method of using high‐dimensional data for this purpose. It is a stage‐wise additive modelling procedure, which, in a linear specification, becomes a variable selection device that iteratively adds the predictors with the largest contribution to the fit. Using data for the United States, the euro area and Germany, we assess the performance of boosting when forecasting a wide range of macroeconomic variables. Moreover, we analyse to what extent its forecasting accuracy depends on the method used for determining its key regularization parameter: the number of iterations. We find that boosting mostly outperforms the autoregressive benchmark, and that K‐fold cross‐validation works much better as stopping criterion than the commonly used information criteria. Copyright © 2014 John Wiley & Sons, Ltd.     

Forecasting US inflation by Bayesian model averaging

Recent empirical work has considered the prediction of inflation by combining the information in a large number of time series. One such method that has been found to give consistently good results consists of simple equal‐weighted averaging of the forecasts from a large number of different models, each of which is a linear regression relating inflation to a single predictor and a lagged dependent variable. In this paper, I consider using Bayesian model averaging for pseudo out‐of‐sample prediction of US inflation, and find that it generally gives more accurate forecasts than simple equal‐weighted averaging. This superior performance is consistent across subsamples and a number of inflation measures. Copyright © 2008 John Wiley & Sons, Ltd.     

Comparison of Near Neighbour and Neural Network in Travel Forecasting

In this paper we confirm the existence of nonlinear dynamics in a time series of airport arrivals. We subsequently propose alternative non‐parametric forecasting techniques to be used in a travel forecasting problem, emphasizing the difference between the reconstruction and learning approach. We compare the results achieved in point prediction versus sign prediction. The reconstruction approach offers better results in sign prediction and the learning approach in point prediction. Copyright © 2015 John Wiley & Sons, Ltd.     

Forecasting with panel data

This paper gives a brief survey of forecasting with panel data. It begins with a simple error component regression model and surveys the best linear unbiased prediction under various assumptions of the disturbance term. This includes various ARMA models as well as spatial autoregressive models. The paper also surveys how these forecasts have been used in panel data applications, running horse races between heterogeneous and homogeneous panel data models using out‐of‐sample forecasts. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting with unbalanced panel data

This paper derives the best linear unbiased prediction (BLUP) for an unbalanced panel data model. Starting with a simple error component regression model with unbalanced panel data and random effects, it generalizes the BLUP derived by Taub (Journal of Econometrics, 1979, 10, 103–108) to unbalanced panels. Next it derives the BLUP for an unequally spaced panel data model with serial correlation of the AR(1) type in the remainder disturbances considered by Baltagi and Wu (Econometric Theory, 1999, 15, 814–823). This in turn extends the BLUP for a panel data model with AR(1) type remainder disturbances derived by Baltagi and Li (Journal of Forecasting, 1992, 11, 561–567) from the balanced to the unequally spaced panel data case. The derivations are easily implemented and reduce to tractable expressions using an extension of the Fuller and Battese (Journal of Econometrics, 1974, 2, 67–78) transformation from the balanced to the unbalanced panel data case.     

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.     

Forecasting domestic liquidity during a crisis: what works best?

The 1990s were a turbulent time for Latin American and Caribbean countries. During this period, the region suffered from no less than 16 banking crises. One the most important determinants of the severity of banking a crisis is commercial bank liquidity. Banking systems that are relatively liquid are better able to deal with the large deposit withdrawals which tend to accompany bank runs. This study provides an assessment of whether behavioural models, linear time series or nonlinear time series models are better able to account for liquidity dynamics during a crisis. Copyright © 2007 John Wiley & Sons, Ltd.     

Treed Avalanche Forecasting: Mitigating Avalanche Danger Utilizing Bayesian Additive Regression Trees

Little Cottonwood Canyon Highway is a dead‐end, two‐lane road leading to Utah's Alta and Snowbird ski resorts. It is the only road access to these resorts and is heavily traveled during the ski season. Professional avalanche forecasters monitor this road throughout the ski season in order to make road closure decisions in the face of avalanche danger. Forecasters at the Utah Department of Transportation (UDOT) avalanche guard station at Alta have maintained an extensive daily winter database on explanatory variables relating to avalanche prediction. Whether or not an avalanche crosses the road is modeled in this paper via Bayesian additive tree methods. Utilizing daily winter data from 1995 to 2011, results show that using Bayesian tree analysis outperforms traditional statistical methods in terms of realized misclassification costs that take into consideration asymmetric losses arising from two types of error. Closing the road when an avalanche does not occur is an error harmful to resort owners, and not closing the road when one does may result in injury or death. Copyright © 2016 John Wiley & Sons, Ltd.     

Empirical Bayesian Density Forecasting in Iowa and Shrinkage for the Monte Carlo Era

The track record of a 20‐year history of density forecasts of state tax revenue in Iowa is studied, and potential improvements sought through a search for better‐performing ‘priors’ similar to that conducted three decades ago for point forecasts by Doan, Litterman and Sims (Econometric Reviews, 1984). Comparisons of the point and density forecasts produced under the flat prior are made to those produced by the traditional (mixed estimation) ‘Bayesian VAR’ methods of Doan, Litterman and Sims, as well as to fully Bayesian ‘Minnesota Prior’ forecasts. The actual record and, to a somewhat lesser extent, the record of the alternative procedures studied in pseudo‐real‐time forecasting experiments, share a characteristic: subsequently realized revenues are in the lower tails of the predicted distributions ‘too often’. An alternative empirically based prior is found by working directly on the probability distribution for the vector autoregression parameters—the goal being to discover a better‐performing entropically tilted prior that minimizes out‐of‐sample mean squared error subject to a Kullback–Leibler divergence constraint that the new prior not differ ‘too much’ from the original. We also study the closely related topic of robust prediction appropriate for situations of ambiguity. Robust ‘priors’ are competitive in out‐of‐sample forecasting; despite the freedom afforded the entropically tilted prior, it does not perform better than the simple alternatives. Copyright © 2014 John Wiley & Sons, Ltd.     

A new Bayesian formulation for Holt's exponential smoothing

In this paper we propose a Bayesian forecasting approach for Holt's additive exponential smoothing method. Starting from the state space formulation, a formula for the forecast is derived and reduced to a two‐dimensional integration that can be computed numerically in a straightforward way. In contrast to much of the work for exponential smoothing, this method produces the forecast density and, in addition, it considers the initial level and initial trend as part of the parameters to be evaluated. Another contribution of this paper is that we have derived a way to reduce the computation of the maximum likelihood parameter estimation procedure to that of evaluating a two‐dimensional grid, rather than applying a five‐variable optimization procedure. Simulation experiments confirm that both proposed methods give favorable performance compared to other approaches. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting euro area variables with German pre‐EMU data

It is investigated whether euro area variables can be forecast better based on synthetic time series for the pre‐euro period or by using just data from Germany for the pre‐euro period. Our forecast comparison is based on quarterly data for the period 1970Q1–2003Q4 for 10 macroeconomic variables. The years 2000–2003 are used as forecasting period. A range of different univariate forecasting methods is applied. Some of them are based on linear autoregressive models and we also use some nonlinear or time‐varying coefficient models. It turns out that most variables which have a similar level for Germany and the euro area such as prices can be better predicted based on German data, while aggregated European data are preferable for forecasting variables which need considerable adjustments in their levels when joining German and European Monetary Union (EMU) data. These results suggest that for variables which have a similar level for Germany and the euro area it may be reasonable to consider the German pre‐EMU data for studying economic problems in the euro area. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting stock prices using a hierarchical Bayesian approach

The Ohlson model is evaluated using quarterly data from stocks in the Dow Jones Index. A hierarchical Bayesian approach is developed to simultaneously estimate the unknown coefficients in the time series regression model for each company by pooling information across firms. Both estimation and prediction are carried out by the Markov chain Monte Carlo (MCMC) method. Our empirical results show that our forecast based on the hierarchical Bayes method is generally adequate for future prediction, and improves upon the classical method. Copyright © 2005 John Wiley & Sons, Ltd.     

Forecasting in long horizons using smoothed direct forecast

This paper constructs a forecast method that obtains long‐horizon forecasts with improved performance through modification of the direct forecast approach. Direct forecasts are more robust to model misspecification compared to iterated forecasts, which makes them preferable in long horizons. However, direct forecast estimates tend to have jagged shapes across horizons. Our forecast method aims to “smooth out” erratic estimates across horizons while maintaining the robust aspect of direct forecasts through ridge regression, which is a restricted regression on the first differences of regression coefficients. The forecasts are compared to the conventional iterated and direct forecasts in two empirical applications: real oil prices and US macroeconomic series. In both applications, our method shows improvement over direct forecasts.     

Forecasting stock market volatility using (non-linear) Garch models

In this paper we study the performance of the GARCH model and two of its non-linear modifications to forecast weekly stock market volatility. The models are the Quadratic GARCH (Engle and Ng, 1993) and the Glosten, Jagannathan and Runkle (1992) models which have been proposed to describe, for example, the often observed negative skewness in stock market indices. We find that the QGARCH model is best when the estimation sample does not contain extreme observations such as the 1987 stock market crash and that the GJR model cannot be recommended for forecasting.     

Forecasting with Micro Panels: The Case of Health Care Costs

Micro panels characterized by large numbers of individuals observed over a short time period provide a rich source of information, but as yet there is only limited experience in using such data for forecasting. Existing simulation evidence supports the use of a fixed‐effects approach when forecasting but it is not based on a truly micro panel set‐up. In this study, we exploit the linkage of a representative survey of more than 250,000 Australians aged 45 and over to 4 years of hospital, medical and pharmaceutical records. The availability of panel health cost data allows the use of predictors based on fixed‐effects estimates designed to guard against possible omitted variable biases associated with unobservable individual specific effects. We demonstrate the preference towards fixed‐effects‐based predictors is unlikely to hold in many practical situations, including our models of health care costs. Simulation evidence with a micro panel set‐up adds support and additional insights to the results obtained in the application. These results are supportive of the use of the ordinary least squares predictor in a wide range of circumstances. Copyright © 2016 John Wiley & Sons, Ltd.