Forecasting economic activity by Bayesian bridge model averaging

This paper proposes the use of Bayesian model averaging (BMA) as an alternative tool to forecast GDP relative to simple bridge models and factor models. BMA is a computationally feasible method that allows us to explore the model space even in the presence of a large set of candidate predictors. We test the performance of BMA in now-casting by means of a recursive experiment for the euro area and the three largest countries. This method allows flexibility in selecting the information set month by month. We find that BMA-based forecasts produce smaller forecast errors than standard bridge model when forecasting GDP in Germany, France and Italy. At the same time, it also performs as well as medium-scale factor models when forecasting Eurozone GDP.     

UK macroeconomic forecasting with many predictors: Which models forecast best and when do they do so?

Block factor methods offer an attractive approach to forecasting with many predictors. These extract the information in these predictors into factors reflecting different blocks of variables (e.g. a price block, a housing block, a financial block, etc.). However, a forecasting model which simply includes all blocks as predictors risks being over-parameterized. Thus, it is desirable to use a methodology which allows for different parsimonious forecasting models to hold at different points in time. In this paper, we use dynamic model averaging and dynamic model selection to achieve this goal. These methods automatically alter the weights attached to different forecasting models as evidence comes in about which has forecast well in the recent past. In an empirical study involving forecasting output growth and inflation using 139 UK monthly time series variables, we find that the set of predictors changes substantially over time. Furthermore, our results show that dynamic model averaging and model selection can greatly improve forecast performance relative to traditional forecasting methods.     

MONTHLY GDP FORECASTING USING BRIDGE MODELS: APPLICATION FOR THE FRENCH ECONOMY

This paper presents a model to predict French gross domestic product (GDP) quarterly growth rate. The model is designed to be used on a monthly basis by integrating monthly economic information through bridge models, for both supply and demand sides, allowing thus economic interpretations. For each GDP component, bridge equations are specified by using a general‐to‐specific approach implemented in an automated way by Hoover and Perez and improved by Krolzig and Hendry. This approach allows to select explanatory variables among a large data set of hard and soft data. A rolling forecast study is carried out to assess the forecasting performance in the prediction of aggregated GDP, by taking publication lags into account in order to run pseudo real‐time forecasts. It turns out that the model outperforms benchmark models. The results show that changing the set of equations over the quarter is superior to keeping the same equations over time. In addition, GDP growth seems to be more precisely predicted from a supply‐side approach rather than a demand‐side approach.     

基于ARIMA与GARCH模型的国际油价预测比较分析

在分析影响油价波动因素的基础上,利用1986年1月至2010年12月的WTI国际原油价格月度数据,分别建立ARIMA和GARCH模型对油价进行预测。并通过对2011年1月至2012年4月WTI原油价格进行外推预测,检验模型的预测效果。比较分析发现,在短期预测中,ARIMA和GARCH模型对油价的预测均比较准确,但当油价由于受到重大事件的影响而有较大波动时,模型的预测精度下降;在长期预测中,GARCH模型的预测效果优于ARIMA模型;整体来看,GARCH模型预测的精度高于ARIMA模型。因此,在国际油价预测中,用GARCH模型是比较合适的。     

Forecasting South African inflation using non-linearmodels: a weighted loss-based evaluation

The conduct of inflation targeting is heavily dependent on accurate inflation forecasts. Non-linear models have increasingly featured, along with linear counterparts, in the forecasting literature. In this study, we focus on forecasting South African inflation by means of non-linear models and using a long historical dataset of seasonally adjusted monthly inflation rates spanning from 1921:02 to 2013:01. For an emerging market economy such as South Africa, non-linearities can be a salient feature of such long data, hence the relevance of evaluating non-linear models’ forecast performance. In the same vein, given the fact that 1969:10 marks the beginning of a protracted rising trend in South African inflation data, we estimate the models for an in-sample period of 1921:02–1966:09 and evaluate 1, 4, 12, and 24 step-ahead forecasts over an out-of-sample period of 1966:10–2013:01. In addition, using a weighted loss function specification, we evaluate the forecast performance of different non-linear models across various extreme economic environments and forecast horizons. In general, we find that no competing model consistently and significantly beats the LoLiMoT’s performance in forecasting South African inflation.     

Forecasting China's GDP growth using dynamic factors and mixed-frequency data

Forecasting GDP growth is important and necessary for Chinese government to set GDP growth target. To fully and efficiently utilize macroeconomic and financial information, this paper attempts to forecast China's GDP growth using dynamic predictors and mixed-frequency data. The dynamic factor model is first applied to select dynamic predictors among large amount of monthly macroeconomic and daily financial data and then the mixed data sampling regression is applied to forecast quarterly GDP growth based on the selected monthly and daily predictors. Empirical results show that forecasts using dynamic predictors and mixed-frequency data have better accuracy comparing to traditional forecasting methods. Moreover, forecasts with leads and forecast combination can further improve forecast performance.     

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.     

Forecasting the S&P 500 index volatility

This study introduces a new pre-differencing transformation for the AR1MA model for forecasting S&P 500 index volatility. The out of sample forecasting performance of the ARIMA model using the new pre-differencing transformation is compared with the out of sample forecasting performance of the mean reversion model and the GARCH model. The ARIMA model using the new pre-differencing transformation introduced in this study is found to be superior to both the mean reversion model and the GARCH model in forecasting monthly S&P 500 index volatility for the forecast comparison periods used in this study.     

Time-series model forecasts and structural breaks: evidence from Spanish pre-EMU interest rates

Analysis of the future behaviour of economic variables can be biased if structural breaks are not considered. When these structural breaks are present, the in-sample fit of a model gives us a poor guide to ex ante forecast performance. This problem is true for both univariate and multivariate analysis and can be extremely important when co-integration relationships are analysed. The main goal of this article is to analyse the impact of structural breaks on forecast accuracy evaluation. We focus on forecasting several interest rates from the Spanish interbank money market. In order to carry out the analysis, we perform two forecasting exercises: (a) without structural breaks and (b) when structural breaks are explicitly considered. We use new sequential methods in order to estimate change-points in an endogenous way. This method allows us to detect structural breaks in all four rates in May 1993. However, the effects of these breaks are not very strong, since we found scarce gains in forecasting accuracy when the structural breaks are included in the models.     

Dissecting models' forecasting performance

The fact that the predictive performance of models used in forecasting stock returns, exchange rates, and macroeconomic variables is not stable and varies over time has been widely documented in the forecasting literature. Under these circumstances excessive reliance on forecast evaluation metrics that ignores this instability in forecasting accuracy, like squared errors averaged over the whole forecast evaluation sample, masks important information regarding the temporal evolution of relative forecasting performance of competing models. In this paper we suggest an approach based on the combination of the Cumulated Sum of Squared Forecast Error Differential (CSSFED) of Welch and Goyal (2008) and the Bayesian change point analysis of Barry and Hartigan (1993) that tracks the contribution of forecast errors to the aggregate measures of forecast accuracy observation by observation. In doing so, it allows one to track the evolution of the relative forecasting performance over time. We illustrate the suggested approach by using forecasts of the GDP growth rate in Switzerland.     

Forecasting house prices using dynamic model averaging approach: Evidence from China

Forecasting house price has been of great interests for macroeconomists, policy makers and investors in recent years. To improve the forecasting accuracy, this paper introduces a dynamic model averaging (DMA) method to forecast the growth rate of house prices in 30 major Chinese cities. The advantage of DMA is that this method allows both the sets of predictors (forecasting models) as well as their coefficients to change over time. Both recursive and rolling forecasting modes are applied to compare the performance of DMA with other traditional forecasting models. Furthermore, a model confidence set (MCS) test is used to statistically evaluate the forecasting efficiency of different models. The empirical results reveal that DMA generally outperforms other models, such as Bayesian model averaging (BMA), information-theoretic model averaging (ITMA) and equal-weighted averaging (EW), in both recursive and rolling forecasting modes. In addition, in recent years it is found that the Google search index, instead of fundamental macroeconomic or monetary indicators, has developed greater predictive power for house price in China.     

Out-of-sample forecasting of the Canadian unemployment rates using univariate models

This article investigates the out-of-sample forecasting performance of some linear and nonlinear univariate time series models on the monthly seasonally adjusted Canadian unemployment rates during the 1980–2013 period. The findings reveal that nonlinear time series models better capture the asymmetry present in the unemployment rate series at short and long forecast horizons.     

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.     

Does the vector error correction model perform better than others in forecasting stock price? An application of residual income valuation theory

This paper employs a multi-equation model approach to consider three statistic problems (heteroskedasticity, endogeneity and persistency), which are sources of bias and inefficiency in the predictive regression models. This paper applied the residual income valuation model (RIM) proposed by Ohlson (1995) to forecast stock prices for Taiwan three sectors. We compare relative forecasting accuracy of vector error correction model (VECM) with the vector autoregressive model (VAR) as well as OLS and RW models used in the prior studies. We conduct out-of-sample forecasting and employ two instruments to assess forecasting performance. Our empirical results suggest that the VECM statistically outperforms other three models in forecasting stock prices. When forecasting horizons extend longer, VECM produces smaller forecasting errors and performs substantially better than VAR, suggesting that the ability of VECM to improve VAR forecast accuracy is stronger with longer horizons. These findings imply that an error correction term (ECT) of the VECM contributes to improving forecast accuracy of stock prices. Our economic significance analyses and robustness tests for different data frequency are in favor of the superiority of VECM estimator.     

Forecasting Dutch GDP and inflation using alternative factor model specifications based on large and small datasets

We compare the factor forecasting performance of nested specifications of the generalized factor model based on various configurations of a large macroeconomic data set. The forecast simulation design involves in-sample model selection, factor estimation, parameter estimation and, finally, generating factor forecasts and factor augmented autoregressive forecasts. To empirically determine the importance of the size and the structure of the data set, we run the forecast simulation design for different configurations of the data set. We compare the factor model diagnostics of each specification and data configuration with the corresponding forecast performance. The results favour the factor structure as the specification that imposes the factor structure to the least extent and, hence, is allowed most flexibility to adapt to the data, is significantly being outperformed. Moreover, the results show that size matters as though smaller macroeconomic data sets exhibit stronger coherence, the factors being well fit, however, generally do not show improved forecasting performance.     

Forecasting and combining competing models of exchange rate determination

This article investigates the out-of-sample forecast performance of a set of competing models of exchange rate determination. We compare standard linear models with models that characterize the relationship between exchange rate and the underlying fundamentals by nonlinear dynamics. Linear models tend to outperform at short forecast horizons especially when deviations from long-term equilibrium are small. In contrast, nonlinear models with more elaborate mean-reverting components dominate at longer horizons especially when deviations from long-term equilibrium are large. The results also suggest that combining different forecasting procedures generally produces more accurate forecasts than can be attained from a single model.     

FORECASTING THE YIELD CURVE USING PRIORS FROM NO‐ARBITRAGE AFFINE TERM STRUCTURE MODELS*

I propose a strategy for forecasting the term structure of interest rates that may produce significant gains in predictive accuracy. The key idea is to use the restrictions implied by Gaussian, no‐arbitrage, affine term structure models on a vector autoregression as prior information instead of imposing the restrictions dogmatically. This allows us to account for possible model misspecification. We use the proposed method to forecast a system of five U.S. yields up to 12 months ahead, and we find it provides significant gains in forecast accuracy.     

FORECASTING US INFLATION USING DYNAMIC GENERAL‐TO‐SPECIFIC MODEL SELECTION

We forecast US inflation using a standard set of macroeconomic predictors and a dynamic model selection and averaging methodology that allows the forecasting model to change over time. Pseudo out‐of‐sample forecasts are generated from models identified from a multipath general‐to‐specific algorithm that is applied dynamically using rolling regressions. Our results indicate that the inflation forecasts that we obtain employing a short rolling window substantially outperform those from a well‐established univariate benchmark, and contrary to previous evidence, are considerably robust to alternative forecast periods.     

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.