M*-BVAR: Bayesian Vector Autoregression with Macroeconomic Stars

This study determines whether the global vector autoregressive (GVAR) approach provides better forecasts of key South African variables than a vector error correction model (VECM) and a Bayesian vector autoregressive (BVAR) model augmented with foreign variables. The article considers both a small GVAR model and a large GVAR model in determining the most appropriate model for forecasting South African variables. We compare the recursive out-of-sample forecasts for South African GDP and inflation from six types of models: a general 33 country (large) GVAR, a customized small GVAR for South Africa, a VECM for South Africa with weakly exogenous foreign variables, a BVAR model, autoregressive (AR) models and random walk models. The results show that the forecast performance of the large GVAR is generally superior to the performance of the customized small GVAR for South Africa. The forecasts of both the GVAR models tend to be better than the forecasts of the augmented VECM, especially at longer forecast horizons. Importantly, however, on average, the BVAR model performs the best when it comes to forecasting output, while the AR(1) model outperforms all the other models in predicting inflation. We also conduct ex ante forecasts from the BVAR and AR(1) models over 2010:Q1–2013:Q4 to highlight their ability to track turning points in output and inflation, respectively.

A Bayesian vector error correction model for forecasting exchange rates

This paper evaluates the performance of 11 vector autoregressive models in forecasting 15 macroeconomic variables for the Indian economy over the 2007:01 to 2011:10 out-of-sample period. We consider 3 classical VARs, 4 Bayesian VARs and 4 Bayesian Factor Augmented VARs. Comparing the performance by minimum average RMSEs of the models to the benchmark random walk model, we find that in general, the 11 models outperform the random walk model. Although, there is no specific model that outperforms others at all horizons for any of the variables, the Bayesian VARs and Bayesian Factor Augmented VAR models on average outperform the classical VARs. We also provide an ex ante forecast using the selected `best' models and find that these models do not perfectly capture the turning points in each of the series pointing to the importance of conducting future research in a non-linear framework.

This paper evaluates the forecast performance of Bayesian vector autoregressions (BVARs) on Russian data. We estimate BVARs of different sizes and compare the accuracy of their out-of-sample forecasts with those obtained with unrestricted vector autoregressions and random walk with drift. We show that many Russian macroeconomic indicators can be forecast by BVARs more accurately than by competing models. However, contrary to several other studies, we do not confirm that the relative forecast error monotonically decreases with increasing the cross-sectional dimension of the sample. In half of those cases where a BVAR appears to be the most accurate model, a small-dimensional BVAR outperforms its high-dimensional counterpart.

This paper develops univariate (ARIMA and ARCH/GARCH) and multivariate models (VAR, VECM and Bayesian VAR) to forecast short- and long-term rates, viz., call money rate, 15–91 days Treasury Bill rates and interest rates on Government securities with (residual) maturities of one year, five years and 10 years. Multivariate models consider factors such as liquidity, repo rate, yield spread, inflation rate, foreign interest rates and forward premium. The paper finds that multivariate models generally outperform univariate ones over longer forecast horizons. Overall, the paper concludes that the forecasting performance of Bayesian VAR models is satisfactory for most interest rates and their superiority in performance is marked at longer forecast horizons.

PurposeThe paper compares multi-period forecasting performances by direct and iterated method using Bayesian vector autoregressive (VAR) models.Design/methodology/approachThe paper adopts Bayesian VAR models with three different priors – independent Normal-Wishart prior, the Minnesota prior and the stochastic search variable selection (SSVS). Monte Carlo simulations are conducted to compare forecasting performances. An empirical study using US macroeconomic data are shown as an illustration.FindingsIn theory direct forecasts are more efficient asymptotically and more robust to model misspecification than iterated forecasts, and iterated forecasts tend to bias but more efficient if the one-period ahead model is correctly specified. From the results of the Monte Carlo simulations, iterated forecasts tend to outperform direct forecasts, particularly with longer lag model and with longer forecast horizons. Implementing SSVS prior generally improves forecasting performance over unrestricted VAR model for either nonstationary or stationary data.Originality/valueThe paper finds that iterated forecasts using model with the SSVS prior generally best outperform, suggesting that the SSVS restrictions on insignificant parameters alleviates over-parameterized problem of VAR in one-step ahead forecast and thus offers an appreciable improvement in forecast performance of iterated forecasts.

I estimate a model for earnings containing a cyclical (stationary) component, in addition to a random walk trend modeled in extant studies, and investigate the extent to which the earnings cycle is capitalized in stock price. I estimate the cyclical component utilizing the Kalman filter. I find that the cyclical component of earnings is priced in addition to the trend component at a multiple of approximately one-half. I further decompose the stock price series into trend and cyclical components and find that the cyclical component of stock prices is related to that of earnings. Further tests reveal that cyclical swings in GNP and interest rates do appear to explain a portion, but not all, of the association between cyclical components of earnings and stock prices. The pricing of the cyclical component of earnings appears to capture a different phenomenon from those previously hypothesized as contributors to mean reversion in stock prices. Finally, I form hedge portfolios of firms at cyclical peaks (troughs) in earnings and report positive market adjusted returns similar to those reported in extant studies. Further tests indicate that these excess returns are not a function of firm size or betas.

The difficulty in predicting exchange rates has been a long-standing problem in international finance as most standard econometric methods are unable to produce significantly better forecasts than the random walk model. Recent studies provide some evidence for the ability of multivariate time-series models to generate better forecasts. At the same time, artificial neural network models have been emerging as alternatives to predict exchange rates. In this paper we propose a nonlinear forecast model combining the neural network with the multivariate econometric framework. This hybrid model contains two forecasting stages. A time series approach based on Bayesian Vector Autoregression (BVAR) models is applied to the first stage of forecasting. The estimates from BVAR are then used by the nonparametric General Regression Neural Network (GRNN) to generate enhanced forecasts. To evaluate the economic impact of forecasts, we develop a set of currency trading rules guided by these models. The optimal conditions implied by the investment rules maximize the expected profits given the expected changes in exchange rates and the interest rate differentials between domestic and foreign countries. Both empirical and simulation experiments suggest that the proposed nonlinear adaptive forecasting model not only produces better forecasts but also results in higher investment returns than other types of models. The effect of risk aversion is also considered in the investment simulation.

Bayesian vector autoregressions (BVARs) are standard multivariate autoregressive models routinely used in empirical macroeconomics and finance for structural analysis, forecasting, and scenario analysis in an ever-growing number of applications. A preeminent field of application of BVARs is forecasting. BVARs with informative priors have often proved to be superior tools compared to standard frequentist/flat-prior VARs. In fact, VARs are highly parametrized autoregressive models, whose number of parameters grows with the square of the number of variables times the number of lags included. Prior information, in the form of prior distributions on the model parameters, helps in forming sharper posterior distributions of parameters, conditional on an observed sample. Hence, BVARs can be effective in reducing parameters uncertainty and improving forecast accuracy compared to standard frequentist/flat-prior VARs. This feature in particular has favored the use of Bayesian techniques to address “big data” problems, in what is arguably one of the most active frontiers in the BVAR literature. Large-information BVARs have in fact proven to be valuable tools to handle empirical analysis in data-rich environments. BVARs are also routinely employed to produce conditional forecasts and scenario analysis. Of particular interest for policy institutions, these applications permit evaluating “counterfactual” time evolution of the variables of interests conditional on a pre-determined path for some other variables, such as the path of interest rates over a certain horizon. The “structural interpretation” of estimated VARs as the data generating process of the observed data requires the adoption of strict “identifying restrictions.” From a Bayesian perspective, such restrictions can be seen as dogmatic prior beliefs about some regions of the parameter space that determine the contemporaneous interactions among variables and for which the data are uninformative. More generally, Bayesian techniques offer a framework for structural analysis through priors that incorporate uncertainty about the identifying assumptions themselves.

Category management—a relatively new function in marketing—involves large‐scale, real‐time forecasting of multiple data series in complex environments. In this paper, we illustrate how Bayesian Vector Auto regression (BVAR) fulfils the category manager's decision‐support requirements by providing accurate forecasts of a category's state variables (prices, volumes and advertising levels), incorporating management interventions (merchandising events such as end‐aisle displays), and revealing competitive dynamics through impulse response analyses. Using 124 weeks of point‐of‐sale scanner data comprising 31 variables for four brands, we compare the out‐of‐sample forecasts from BVAR to forecasts from exponential smoothing, univariate and multivariate Box‐Jenkins transfer function analyses, and multivariate ARMA models. TheilU'sindicate that BVAR forecasts are superior to those from alternate approaches. In large‐scale forecasting applications, BVAR's ease of identification and parsimonious use of degrees of freedom are particularly valuable.

A framework for developing marketing category management decision support systems (DSS) based upon the Bayesian Vector Autoregressive (BVAR) model is extended. Since the BVAR model is vulnerable to permanent and temporary shifts in purchasing patterns over time, a form that can correct for the shifts and still provide the other advantages of the BVAR is a Bayesian Vector Error-Correction Model (BVECM). We present the mechanics of extending the DSS to move from a BVAR model to the BVECM model for the category management problem. Several additional iterative steps are required in the DSS to allow the decision maker to arrive at the best forecast possible. The revised marketing DSS framework and model fitting procedures are described. Validation is conducted on a sample problem.

When studying a time series, it is traditionally customary to use a generalized mathematical model where a trend component, a cyclic component that describes the repeatability of a cyclic process over time intervals and a random component or noise – this component is responsible for factors hidden from the observer. It is assumed that the main trend and the cyclical component can be accurately described because they are formed by known factors that can be taken into account within the framework of models. The discrete wavelet transform is traditionally used to decompose BP into additive components. The first discrete wavelet transform was invented by the Hungarian mathematician Alfred Haar (1910-1920). In parallel with this method, in the 70s and 80s, the idea of a time series analysis method called SSA (Singular Spectrum Analysis) arose in Russia, the method was called "Caterpillar". During the existence of the method, it has received an extension of its application – automation of the allocation of trend and cyclic components of BP has been developed. Using the example of a study of the real time series of TRAFFAT, two methods of decomposition time series into additive components are considered. The complexity of determining the initial parameters is compared, the applicability to the decomposition of real time series is tested, and the quality of decomposition by both methods of one reference time series is compared. An assessment of the quality of the decomposition of the time series into components was made, as well as a comparison of the two methods in terms of the complexity of the analyst's application and the possibility of automating the selection of parameters.

This article compares the accuracy of vector autoregressive (VAR), restricted vector autoregressive (RVAR), Bayesian vector autoregressive (BVAR), vector error correction (VEC) and Bayesian vector error correction (BVEC) models in forecasting the exchange rates for five Central and Eastern European currencies (Czech Koruna, Hungarian Forint, Polish Zloty, Slovak Koruna and Slovenian Tolar) against the Euro and the US dollar. Among the specifications composing this battery of multivariate time series models, those with the smallest prediction error still fail to reject the test of equality of forecasting accuracy against the random walk model in short-term predictions, with the exception of the Slovenian Tolar/Euro exchange rate.

Multiple cointegrating vectors, error correction, and forecasting with Litterman's model

In various fields of macroeconomic modelling, researchers often face the problem of decomposing time series into trend component and cycle fluctuations. While there are several potentially useful methods to perform the task in question, Hodrick-Prescott (HP) fi lter seems to have remained (despite some serious criticism) the most popular approach over the past decade. In this article I propose a straightforward and easy-to-implement bootstrap procedure for building pointwise and simultaneous confidence intervals around point estimates produced by HP filter. The principle of proposed method can be described as follows: first, we use maximum entropy bootstrap (Vinod, 2004, 2006) to approximate ensemble from which original time series is drawn and then apply the HP filter directly to each bootstrap replication. If necessary, the proposed method can be adapted to allow for uncertainty in the smoothing parameter. Practical usefulness of our approach is demonstrated with an application to the GDP data. Results are encouraging - obtained confi dence intervals for the trend and cyclical component are overall plausible thus supplying a researcher with some measure of uncertainty related to HP filtering. Finally, we demonstrate that a former approach to build confidence intervals for HP filter (Gallego and Johnson, 2005) leads to erratic inference for cycle due to the shape-destroying block bootstrap sampling.