A Nonlinear Approach for Modeling and Forecasting US Business Cycles

The purpose of this paper is to provide a complete evaluation of four regime-switching models by checking their performance in detecting US business cycle turning points, in replicating US business cycle features and in forecasting US GDP growth rate. Both individual and combined forecasts are considered. Results indicate that while the Markov-switching model succeeded in replicating all the NBER peak and trough dates without an extra-cycle detection, it seems to be outperformed by the Bounce-back model in term of the delay time to a correct alarm. Concerning business cycle features characterization, none of the competing models dominates over all the features. The performance of the Markov-switching and bounce back models in detecting turning points was not translated into an improved business cycle feature characterization since they are outperformed by the Floor and Ceiling model. The forecast performance of the considered models varies across regimes and across forecast horizons. That is, the model performing best in an expansion period is not necessarily the same in a recession period and similarly for the forecast horizons. Finally, combining such individual forecasts generally leads to increased forecast accuracy especially for h=1.     

Anticipating business-cycle turning points in real time using density forecasts from a VAR

For the timely detection of business-cycle turning points we suggest to use medium-sized linear systems (subset VARs with automated zero restrictions) to forecast monthly industrial production index publications one to several steps ahead, and to derive the probability of the turning point from the bootstrapped forecast density as the probability mass below (or above) a suitable threshold value. We show how this approach can be used in real time in the presence of data publication lags and how it can capture the part of the data revision process that is systematic. Out-of-sample evaluation exercises show that the method is competitive especially in the case of the US, while turning-point forecasts are in general more difficult in Germany.     

The out-of-sample forecasting performance of nonlinear models of regional housing prices in the US

This article provides out-of-sample forecasts of linear and nonlinear models of US and four Census subregions’ housing prices. The forecasts include the traditional point forecasts, but also include interval and density forecasts, of the housing price distributions. The nonlinear smooth-transition autoregressive model outperforms the linear autoregressive model in point forecasts at longer horizons, but the linear autoregressive and nonlinear smooth-transition autoregressive models perform equally at short horizons. In addition, we generally do not find major differences in performance for the interval and density forecasts between the linear and nonlinear models. Finally, in a dynamic 25-step ex-ante and interval forecasting design, we, once again, do not find major differences between the linear and nonlinear models. In sum, we conclude that when forecasting regional housing prices in the United States, generally the additional costs associated with nonlinear forecasts outweigh the benefits for forecasts only a few months into the future.     

Combination forecasts of tourism demand with machine learning models

The main objective of this study is to analyse whether the combination of regional predictions generated with machine learning (ML) models leads to improved forecast accuracy. With this aim, we construct one set of forecasts by estimating models on the aggregate series, another set by using the same models to forecast the individual series prior to aggregation, and then we compare the accuracy of both approaches. We use three ML techniques: support vector regression, Gaussian process regression and neural network models. We use an autoregressive moving average model as a benchmark. We find that ML methods improve their forecasting performance with respect to the benchmark as forecast horizons increase, suggesting the suitability of these techniques for mid- and long-term forecasting. In spite of the fact that the disaggregated approach yields more accurate predictions, the improvement over the benchmark occurs for shorter forecast horizons with the direct approach.     

Do we need a global VAR model to forecast inflation and output in South Africa?

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.     

Evaluating FOMC forecast ranges: an interval data approach

The Federal Open Market Committee (FOMC) of the U.S. Federal Reserve publishes the range of members’ forecasts for key macroeconomic variables, but not the distribution of forecasts within this range. To evaluate these projections, previous papers compare the midpoint of the range with the realized outcome. This paper proposes an alternative approach to forecast evaluation that takes account of the interval nature of projections. It is shown that using the conventional Mincer–Zarnowitz approach to evaluate FOMC forecasts misses important information contained in the width of the forecast interval. This additional information plays a minor role at short forecast horizons but turns out to be of sometimes crucial importance for longer-horizon forecasts. For 18-month-ahead forecasts, the variation of members’ projections contains information that is more relevant for explaining future inflation than information embodied in the midpoint. Likewise, when longer-range forecasts for real GDP growth and the unemployment rate are considered, the width of the forecast interval comprises information over and above the one given by the midpoint alone.     

Forecasting the price of gold

This article seeks to evaluate the appropriateness of a variety of existing forecasting techniques (17 methods) at providing accurate and statistically significant forecasts for gold price. We report the results from the nine most competitive techniques. Special consideration is given to the ability of these techniques to provide forecasts which outperforms the random walk (RW) as we noticed that certain multivariate models (which included prices of silver, platinum, palladium and rhodium, besides gold) were also unable to outperform the RW in this case. Interestingly, the results show that none of the forecasting techniques are able to outperform the RW at horizons of 1 and 9 steps ahead, and on average, the exponential smoothing model is seen providing the best forecasts in terms of the lowest root mean squared error over the 24-month forecasting horizons. Moreover, we find that the univariate models used in this article are able to outperform the Bayesian autoregression and Bayesian vector autoregressive models, with exponential smoothing reporting statistically significant results in comparison with the former models, and classical autoregressive and the vector autoregressive models in most cases.     

FORECASTING GLOBAL EQUITY INDICES USING LARGE BAYESIAN VARS

This paper proposes a large Bayesian Vector Autoregressive (BVAR) model with common stochastic volatility to forecast global equity indices. Using a monthly dataset on global stock indices, the BVAR model controls for co‐movement commonly observed in global stock markets. Moreover, the time‐varying specification of the covariance structure accounts for sudden shifts in the level of volatility. In an out‐of‐sample forecasting application we show that the BVAR model with stochastic volatility significantly outperforms the random walk both in terms of point as well as density predictions. The BVAR model without stochastic volatility, on the other hand, shows some merits relative to the random walk for forecast horizons greater than six months ahead. In a portfolio allocation exercise we moreover provide evidence that it is possible to use the forecasts obtained from our model with common stochastic volatility to set up simple investment strategies. Our results indicate that these simple investment schemes outperform a naive buy‐and‐hold strategy.     

THE FORECASTING PERFORMANCE OF SETAR MODELS: AN EMPIRICAL APPLICATION

The aim of this paper is to evaluate the forecasting performance of SETAR models with an application to the Industrial Production Index (IPI) of four major European countries over a period which includes the last Great Recession. Both point and interval forecasts are considered at different horizons against those obtained from two linear models. We follow the approach suggested by Teräsvirta et al. (2005) according to which a dynamic specification may improve the forecast performance of the nonlinear models with respect to the linear models. We re‐specify the models every twelve months and we find that the advantages of this procedure are particularly evident in the forecast rounds immediately following the re‐specification.     

Predictive ability of asymmetric volatility models at medium-term horizons

Using realized volatility to estimate conditional variance of financial returns, we compare forecasts of volatility from linear GARCH models with asymmetric ones. We consider horizons extending to 30 days. Forecasts are compared using three different evaluation tests. With data from an equity index and two foreign exchange returns, we show that asymmetric models provide statistically significant forecast improvements upon the GARCH model for two of the datasets and improve forecasts for all datasets by means of forecasts combinations. These results extend to about 10 days in the future, beyond which the forecasts are statistically inseparable from each other.     

Was the recent downturn in US real GDP predictable?

This article uses a small set of variables – real GDP, the inflation rate and the short-term interest rate – and a rich set of models – atheoretical (time series) and theoretical (structural), linear and nonlinear, as well as classical and Bayesian models – to consider whether we could have predicted the recent downturn of the US real GDP. Comparing the performance of the models to the benchmark random-walk model by root mean-square errors, the two structural (theoretical) models, especially the nonlinear model, perform well on average across all forecast horizons in our ex post, out-of-sample forecasts, although at specific forecast horizons certain nonlinear atheoretical models perform the best. The nonlinear theoretical model also dominates in our ex ante, out-of-sample forecast of the Great Recession, suggesting that developing forward-looking, microfounded, nonlinear, dynamic stochastic general equilibrium models of the economy may prove crucial in forecasting turning points.     

Forecast content and content horizons for some important macroeconomic time series

Abstract.  The information content of statistical forecasts of approximately stationary quantities tends to decline as the forecast horizon increases, and there exists a maximum horizon beyond which forecasts cannot provide discernibly more information about the variable than is present in the unconditional mean (the content horizon ). The pattern of decay of forecast content (or skill) with increasing horizon is well known for many types of meteorological forecasts; by contrast, little generally accepted information about these patterns or content horizons is available for economic variables. In this paper we estimate content horizons for a variety of macroeconomic quantities; more generally, we characterize the pattern of decay of forecast content as we project farther into the future. We find a wide variety of results for the different macroeconomic quantities, with models for some quantities providing useful content several years into the future, for other quantities providing negligible content beyond one or two months or quarters.     

Modeling the behaviour of inflation deviations from the target

This study tests for and models non-linearities in inflation deviations from the target in five OECD countries that adopted inflation targeting over the 1990s. Our tests reject the linearity hypothesis and we show that the exponential smooth transition autoregressive (ESTAR) model is capable of capturing the non-linear behavior of inflation misalignments. The extent of inflation deviations from the target varies across the OECD countries, with countries that consistently undershoot the target having a rapid adjustment process, whereas countries that overshoot the target have a slower revision back to equilibrium. Out-of-sample forecasts from the ESTAR model outperform the Markov regime-switching model.     

Analyst earnings forecast revisions and the persistence of antidumping relief

Panel corrected standard errors with instrumental variables and effects are invoked to assess the significance of earnings forecast revisions around critical dates in non-steel AD petitions filed in 1985–1987. These petitions were filed between two important US trade law revisions (1984 and 1988), and the period encompasses significant stock market advances and declines. Event studies have been invoked to assess the value of AD petitions. However, they do not estimate the temporal distribution of any abnormal returns. Because analysts make quarterly earnings forecast revisions over several horizons, we can assess the short and long run value of petitions. We find that AD petitions tend to depress earnings forecasts in the year of the petition. However, second year earnings forecasts tend to be revised upwards. There is no effect on five year (long term) earnings growth forecasts. Hence any benefits of protection do not persist. There is evidence that analysts anticipate the filing by revising forecasts in the three months in advance of the filing. We also find that AD petitions do not affect the accuracy of forecasts.     

What can we learn from revisions to the Greenbook forecasts?

Although there have been many evaluations of the Federal Reserve’s Greenbook forecasts, we analyze them in a different dimension. We examine the revisions of these forecasts in the context of fixed event predictions to determine how new information is incorporated in the forecasting process. This analysis permits us to determine if there was an inefficient use of information in the sense that the forecast revision has predictive power for the forecast error. Research on forecast smoothing suggests that we might find a positive relationship between the forecast error and the forecast revision. Although we do find for some variables and horizons the Fed’s forecast errors are predictable from its forecast revisions, there is no evidence of forecast smoothing. Instead the revisions sometimes have a negative relationship with the forecast error, suggesting in these cases that the Fed may be over-responsive to new information.     

Forecasting unemployment across countries: The ins and outs

This paper evaluates the flow approach to unemployment forecasting proposed by Barnichon and Nekarda (2012) for a set of OECD countries characterized by very different labor markets. We find that the flow approach yields substantial improvements in forecast accuracy over professional forecasts for all countries, with especially large improvements at longer horizons (one-year ahead forecasts) for European countries. Moreover, the flow approach has the highest predictive ability during recessions and turning points, when unemployment forecasts are most valuable.     

Forecast combination for discrete choice models: predicting FOMC monetary policy decisions

This paper provides a methodology for combining forecasts based on several discrete choice models. This is achieved primarily by combining one-step-ahead probability forecasts associated with each model. The paper applies well-established scoring rules for qualitative response models in the context of forecast combination. Log scores, quadratic scores and Epstein scores are used to evaluate the forecasting accuracy of each model and to combine the probability forecasts. In addition to producing point forecasts, the effect of sampling variation is also assessed. This methodology is applied to forecast US Federal Open Market Committee (FOMC) decisions regarding changes in the federal funds target rate. Several of the economic fundamentals influencing the FOMC’s decisions are integrated, or I(1), and are modeled in a similar fashion to Hu and Phillips (J Appl Econom 19(7):851– 867, 2004). The empirical results show that combining forecasted probabilities using scores generally outperforms both equal weight combination and forecasts based on multivariate models.     

Forecasting the US real house price index: Structural and non-structural models with and without fundamentals

We employ a 10-variable dynamic structural general equilibrium model to forecast the US real house price index as well as its downturn in 2006:Q2. We also examine various Bayesian and classical time-series models in our forecasting exercise to compare to the dynamic stochastic general equilibrium model, estimated using Bayesian methods. In addition to standard vector-autoregressive and Bayesian vector autoregressive models, we also include the information content of either 10 or 120 quarterly series in some models to capture the influence of fundamentals. We consider two approaches for including information from large data sets — extracting common factors (principle components) in factor-augmented vector autoregressive or Bayesian factor-augmented vector autoregressive models as well as Bayesian shrinkage in a large-scale Bayesian vector autoregressive model. We compare the out-of-sample forecast performance of the alternative models, using the average root mean squared error for the forecasts. We find that the small-scale Bayesian-shrinkage model (10 variables) outperforms the other models, including the large-scale Bayesian-shrinkage model (120 variables). In addition, when we use simple average forecast combinations, the combination forecast using the 10 best atheoretical models produces the minimum RMSEs compared to each of the individual models, followed closely by the combination forecast using the 10 atheoretical models and the DSGE model. Finally, we use each model to forecast the downturn point in 2006:Q2, using the estimated model through 2005:Q2. Only the dynamic stochastic general equilibrium model actually forecasts a downturn with any accuracy, suggesting that forward-looking microfounded dynamic stochastic general equilibrium models of the housing market may prove crucial in forecasting turning points.     

Do corporate executives have accurate predictions for the economy? A directional analysis

Although many studies on the directional accuracy of forecasts by international organizations and professional forecasters have been scrutinized, little attention has been paid to forecasts by business leaders. In order to address this gap, we use directional tests to investigate whether forecasts of Gross Domestic Product by corporate executives are valuable to their users. Our findings indicate that all the forecasts with forecast horizons from 1 to 14 months are valuable, whereas established literature indicates that longer-term forecasts tend not to be valuable. This suggests that corporate executives are concerned with and focus on longer-term economic environments and can therefore serve as an important resource for policymakers. However, some of the useful forecasts with real-time data, in particular those in the Tankan survey, are not useful with historical data.     

Model uncertainty and asset return predictability: an application of Bayesian model averaging

We investigate model uncertainty associated with predictive regressions employed in asset return forecasting research. We use simple combination and Bayesian model averaging (BMA) techniques to compare the performance of these forecasting approaches in short-vs. long-run horizons of S&P500 monthly excess returns. Simple averaging involves an equally-weighted averaging of the forecasts from alternative combinations of factors used in the predictive regressions, whereas BMA involves computing the predictive probability that each model is the true model and uses these predictive probabilities as weights in combing the forecasts from different models. From a given set of multiple factors, we evaluate all possible pricing models to the extent, which they describe the data as dictated by the posterior model probabilities. We find that, while simple averaging compares quite favorably to forecasts derived from a random walk model with drift (using a 10-year out-of-sample iterative period), BMA outperforms simple averaging in longer compared to shorter forecast horizons. Moreover, we find further evidence of the latter when the predictive Bayesian model includes shorter, rather than longer lags of the predictive factors. An interesting outcome of this study tends to illustrate the power of BMA in suppressing model uncertainty through model as well as parameter shrinkage, especially when applied to longer predictive horizons.