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.     

Local to unity,long‐horizon forecasting thresholds for model selection in the AR(1)

This article introduces a novel framework for analysing long‐horizon forecasting of the near non‐stationary AR(1) model. Using the local to unity specification of the autoregressive parameter, I derive the asymptotic distributions of long‐horizon forecast errors both for the unrestricted AR(1), estimated using an ordinary least squares (OLS) regression, and for the random walk (RW). I then identify functions, relating local to unity ‘drift’ to forecast horizon, such that OLS and RW forecasts share the same expected square error. OLS forecasts are preferred on one side of these ‘forecasting thresholds’, while RW forecasts are preferred on the other. In addition to explaining the relative performance of forecasts from these two models, these thresholds prove useful in developing model selection criteria that help a forecaster reduce error. Copyright © 2004 John Wiley & Sons, Ltd.     

Can consumer sentiment and its components forecast Australian GDP and consumption?

This paper examines whether the disaggregation of consumer sentiment data into its sub‐components improves the real‐time capacity to forecast GDP and consumption. A Bayesian error correction approach augmented with the consumer sentiment index and permutations of the consumer sentiment sub‐indices is used to evaluate forecasting power. The forecasts are benchmarked against both composite forecasts and forecasts from standard error correction models. Using Australian data, we find that consumer sentiment data increase the accuracy of GDP and consumption forecasts, with certain components of consumer sentiment consistently providing better forecasts than aggregate consumer sentiment data. Copyright © 2009 John Wiley & Sons, Ltd.     

Beating the VAR: Improving Swedish GDP Forecasts Using Error and Intercept Corrections

This paper examines the forecast accuracy of an unrestricted vector autoregressive (VAR) model for GDP, relative to a comparable vector error correction model (VECM) that recognizes that the data are characterized by co‐integration. In addition, an alternative forecast method, intercept correction, is considered for further comparison. Recursive out‐of‐sample forecasts are generated for both models and forecast techniques. The generated forecasts for each model are objectively evaluated by a selection of evaluation measures and equal accuracy tests. The result shows that the VECM consistently outperforms the VAR models. Further, intercept correction enhances the forecast accuracy when applied to the VECM, whereas there is no such indication when applied to the VAR model. For certain forecast horizons there is a significant difference in forecast ability between the intercept corrected VECM compared to the VAR model. Copyright © 2015 John Wiley & Sons, Ltd.     

Multivariate Forecasting with BVARs and DSGE Models

In this paper I assess the ability of Bayesian vector autoregressions (BVARs) and dynamic stochastic general equilibrium (DSGE) models of different size to forecast comovements of major macroeconomic series in the euro area. Both approaches are compared to unrestricted VARs in terms of multivariate point and density forecast accuracy measures as well as event probabilities. The evidence suggests that BVARs and DSGE models produce accurate multivariate forecasts even for larger datasets. I also detect that BVARs are well calibrated for most events, while DSGE models are poorly calibrated for some. In sum, I conclude that both are useful tools to achieve parameter dimension reduction. Copyright © 2016 John Wiley & Sons, Ltd.     

Bootstrap prediction bands for forecast paths from vector autoregressive models

The problem of forecasting from vector autoregressive models has attracted considerable attention in the literature. The most popular non‐Bayesian approaches use either asymptotic approximations or bootstrapping to evaluate the uncertainty associated with the forecast. The practice in the empirical literature has been to assess the uncertainty of multi‐step forecasts by connecting the intervals constructed for individual forecast periods. This paper proposes a bootstrap method of constructing prediction bands for forecast paths. The bands are constructed from forecast paths obtained in bootstrap replications using an optimization procedure to find the envelope of the most concentrated paths. From extensive Monte Carlo study, it is found that the proposed method provides more accurate assessment of predictive uncertainty from the vector autoregressive model than its competitors. Copyright © 2010 John Wiley & Sons, Ltd.     

Forecasting regional house price inflation: a comparison between dynamic factor models and vector autoregressive models

This paper uses the dynamic factor model framework, which accommodates a large cross‐section of macroeconomic time series, for forecasting regional house price inflation. In this study, we forecast house price inflation for five metropolitan areas of South Africa using principal components obtained from 282 quarterly macroeconomic time series in the period 1980:1 to 2006:4. The results, based on the root mean square errors of one to four quarters ahead out‐of‐sample forecasts over the period 2001:1 to 2006:4 indicate that, in the majority of the cases, the Dynamic Factor Model statistically outperforms the vector autoregressive models, using both the classical and the Bayesian treatments. We also consider spatial and non‐spatial specifications. Our results indicate that macroeconomic fundamentals in forecasting house price inflation are important. Copyright © 2010 John Wiley & Sons, Ltd.     

A high–low model of daily stock price ranges

We observe that daily highs and lows of stock prices do not diverge over time and, hence, adopt the cointegration concept and the related vector error correction model (VECM) to model the daily high, the daily low, and the associated daily range data. The in‐sample results attest to the importance of incorporating high–low interactions in modeling the range variable. In evaluating the out‐of‐sample forecast performance using both mean‐squared forecast error and direction of change criteria, it is found that the VECM‐based low and high forecasts offer some advantages over alternative forecasts. The VECM‐based range forecasts, on the other hand, do not always dominate—the forecast rankings depend on the choice of evaluation criterion and the variables being forecast. Copyright © 2008 John Wiley & Sons, Ltd.     

A hybrid forecasting approach for piece‐wise stationary time series

We consider the problem of forecasting a stationary time series when there is an unknown mean break close to the forecast origin. Based on the intercept‐correction methods suggested by Clements and Hendry (1998) and Bewley (2003), a hybrid approach is introduced, where the break and break point are treated in a Bayesian fashion. The hyperparameters of the priors are determined by maximizing the marginal density of the data. The distributions of the proposed forecasts are derived. Different intercept‐correction methods are compared using simulation experiments. Our hybrid approach compares favorably with both the uncorrected and the intercept‐corrected forecasts. Copyright © 2006 John Wiley & Sons, Ltd.     

Covariance estimation for multivariate conditionally Gaussian dynamic linear models

In multivariate time series, estimation of the covariance matrix of observation innovations plays an important role in forecasting as it enables computation of standardized forecast error vectors as well as the computation of confidence bounds of forecasts. We develop an online, non‐iterative Bayesian algorithm for estimation and forecasting. It is empirically found that, for a range of simulated time series, the proposed covariance estimator has good performance converging to the true values of the unknown observation covariance matrix. Over a simulated time series, the new method approximates the correct estimates, produced by a non‐sequential Monte Carlo simulation procedure, which is used here as the gold standard. The special, but important, vector autoregressive (VAR) and time‐varying VAR models are illustrated by considering London metal exchange data consisting of spot prices of aluminium, copper, lead and zinc. Copyright © 2007 John Wiley & Sons, Ltd.     

A monetary real‐time conditional forecast of euro area inflation

Based on a vector error correction model we produce conditional euro area inflation forecasts. We use real‐time data on M3 and HICP, and include real GPD, the 3‐month EURIBOR and the 10‐year government bond yield as control variables. Real money growth and the term spread enter the system as stationary linear combinations. Missing and outlying values are substituted by model‐based estimates using all available data information. In general, the conditional inflation forecasts are consistent with the European Central Bank's assessment of liquidity conditions for future inflation prospects. The evaluation of inflation forecasts under different monetary scenarios reveals the importance of keeping track of money growth rate in particular at the end of 2005. Copyright © 2009 John Wiley & Sons, Ltd.     

Short‐term salmon price forecasting

This study establishes a benchmark for short‐term salmon price forecasting. The weekly spot price of Norwegian farmed Atlantic salmon is predicted 1–5 weeks ahead using data from 2007 to 2014. Sixteen alternative forecasting methods are considered, ranging from classical time series models to customized machine learning techniques to salmon futures prices. The best predictions are delivered by k‐nearest neighbors method for 1 week ahead; vector error correction model estimated using elastic net regularization for 2 and 3 weeks ahead; and futures prices for 4 and 5 weeks ahead. While the nominal gains in forecast accuracy over a naïve benchmark are small, the economic value of the forecasts is considerable. Using a simple trading strategy for timing the sales based on price forecasts could increase the net profit of a salmon farmer by around 7%.     

A New‐Keynesian DSGE model for forecasting the South African economy

This paper develops a New‐Keynesian Dynamic Stochastic General Equilibrium (NKDSGE) model for forecasting the growth rate of output, inflation, and the nominal short‐term interest rate (91 days Treasury Bill rate) for the South African economy. The model is estimated via maximum likelihood technique for quarterly data over the period of 1970:1–2000:4. Based on a recursive estimation using the Kalman filter algorithm, out‐of‐sample forecasts from the NKDSGE model are compared with forecasts generated from the classical and Bayesian variants of vector autoregression (VAR) models for the period 2001:1–2006:4. The results indicate that in terms of out‐of‐sample forecasting, the NKDSGE model outperforms both the classical and Bayesian VARs for inflation, but not for output growth and nominal short‐term interest rate. However, differences in RMSEs are not significant across the models. Copyright © 2008 John Wiley & Sons, Ltd.     

Lead-lag relationship between spot index and futures price of the nikkei stock average

This paper examines the lead-lag relationship between the spot index and futures price of the Nikkei Stock Average. Using daily data in the post-crash period we investigate the interaction between the spot and futures series through the error correction model. Two versions of error correction models are considered, depending on the postulated long-run equilibrium relationship. It is found that lagged changes in the futures price affect the short-term adjustment in the spot index, but not vice versa. Forecasting models for the spot index are also constructed using the univariate time series approach and the vector autoregressive method. For the post-sample forecast comparison the error correction models produce the best results. The vector autoregressive method performs better than the martingale model, while the univariate time series method gives the poorest forecasts.     

Efficient Multistep Forecast Procedures for Multivariate Time Series

Upon the evidence that infinite‐order vector autoregression setting is more realistic in time series models, we propose new model selection procedures for producing efficient multistep forecasts. They consist of order selection criteria involving the sample analog of the asymptotic approximation of the h‐step‐ahead forecast mean squared error matrix, where h is the forecast horizon. These criteria are minimized over a truncation order n_T under the assumption that an infinite‐order vector autoregression can be approximated, under suitable conditions, with a sequence of truncated models, where n_T is increasing with sample size. Using finite‐order vector autoregressive models with various persistent levels and realistic sample sizes, Monte Carlo simulations show that, overall, our criteria outperform conventional competitors. Specifically, they tend to yield better small‐sample distribution of the lag‐order estimates around the true value, while estimating it with relatively satisfactory probabilities. They also produce more efficient multistep (and even stepwise) forecasts since they yield the lowest h‐step‐ahead forecast mean squared errors for the individual components of the holding pseudo‐data to forecast. Thus estimating the actual autoregressive order as well as the best forecasting model can be achieved with the same selection procedure. Such results stand in sharp contrast to the belief that parsimony is a virtue in itself, and state that the relative accuracy of strongly consistent criteria such as the Schwarz information criterion, as claimed in the literature, is overstated. Our criteria are new tools extending those previously existing in the literature and hence can suitably be used for various practical situations when necessary. Copyright © 2015 John Wiley & Sons, Ltd.     

The Role of Financial Variables in predicting economic activity

Previous research found that the US business cycle leads the European one by a few quarters, and can therefore be useful in predicting euro area gross domestic product (GDP). In this paper we investigate whether additional predictive power can be gained by adding selected financial variables belonging to either the USA or the euro area. We use vector autoregressions (VARs) that include the US and euro area GDPs as well as growth in the Rest of the World and selected combinations of financial variables. Out‐of‐sample root mean square forecast errors (RMSEs) evidence that adding financial variables produces a slightly smaller error in forecasting US economic activity. This weak macro‐financial linkage is even weaker in the euro area, where financial indicators do not improve short‐ and medium‐term GDP forecasts even when their timely availability relative to GDP is exploited. It can be conjectured that neither US nor European financial variables help predict euro area GDP as the US GDP has already embodied this information. However, we show that the finding that financial variables have no predictive power for future activity in the euro area relates to the unconditional nature of the RMSE metric. When forecasting ability is assessed as if in real time (i.e. conditionally on the information available at the time when forecasts are made), we find that models using financial variables would have been preferred in several episodes and in particular between 1999 and 2002. Copyright 2011 John Wiley & Sons, Ltd.     

Forecasting the Term Structure of Interest Rates Using Integrated Nested Laplace Approximations

This article discusses the use of Bayesian methods for inference and forecasting in dynamic term structure models through integrated nested Laplace approximations (INLA). This method of analytical approximation allows accurate inferences for latent factors, parameters and forecasts in dynamic models with reduced computational cost. In the estimation of dynamic term structure models it also avoids some simplifications in the inference procedures, such as the inefficient two‐step ordinary least squares (OLS) estimation. The results obtained in the estimation of the dynamic Nelson–Siegel model indicate that this method performs more accurate out‐of‐sample forecasts compared to the methods of two‐stage estimation by OLS and also Bayesian estimation methods using Markov chain Monte Carlo (MCMC). These analytical approaches also allow efficient calculation of measures of model selection such as generalized cross‐validation and marginal likelihood, which may be computationally prohibitive in MCMC estimations. Copyright © 2014 John Wiley & Sons, Ltd.     

Do Long‐Run Theory Restrictions Help in Forecasting?

Do long‐run equilibrium relations suggested by economic theory help to improve the forecasting performance of a cointegrated vector error correction model (VECM)? In this paper we try to answer this question in the context of a two‐country model developed for the Canadian and US economies. We compare the forecasting performance of the exactly identified cointegrated VECMs to the performance of the over‐identified VECMs with the long‐run theory restrictions imposed. We allow for model uncertainty and conduct this comparison for every possible combination of the cointegration ranks of the Canadian and US models. We show that the over‐identified structural cointegrated models generally outperform the exactly identified models in forecasting Canadian macroeconomic variables. We also show that the pooled forecasts generated from the over‐identified models beat most of the individual exactly identified and over‐identified models as well as the VARs in levels and in differences. Copyright © 2011 John Wiley & Sons, Ltd.     

The accuracy of IMF and OECD forecasts for G7 countries

This paper analyses the size and nature of the errors in GDP forecasts in the G7 countries from 1971 to 1995. These GDP short‐term forecasts are produced by the Organization for Economic Cooperation and Development and by the International Monetary Fund, and published twice a year in the Economic Outlook and in the World Economic Outlook, respectively. The evaluation of the accuracy of the forecasts is based on the properties of the difference between the realization and the forecast. A forecast is considered to be accurate if it is unbiased and efficient. A forecast is unbiased if its average deviation from the outcome is zero, and it is efficient if it reflects all the information that is available at the time the forecast is made. Finally, we also examine tests of directional accuracy and offer a non‐parametric method of assessment. Copyright © 2000 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.