The Credibility of Hong Kong's Currency Board System: Looking Through the Prism of MS‐VAR Models with Time‐Varying Transition Probabilities

This paper employs a Markov regime‐switching VAR model to describe and analyse the time‐varying credibility of Hong Kong's currency board system. The endogenously estimated discrete regime shifts are made dependent on macroeconomic fundamentals. This enables us to determine which changes in macroeconomic variables can trigger switches between the low and high credibility regimes. We carry out extensive testing to search for the most appropriate specification of the Markov regime‐switching model. We find strong evidence of regime switching behaviour that portrays the time‐varying nature of credibility in the historical data.     

Forecasting with vector autoregressive (VAR) models subject to business cycle restrictions

In the last decade VAR models have become a widely-used tool for forecasting macroeconomic time series. To improve the out-of-sample forecasting accuracy of these models, Bayesian random-walk prior restrictions are often imposed on VAR model parameters. This paper focuses on whether placing an alternative type of restriction on the parameters of unrestricted VAR models improves the out-of-sample forecasting performance of these models. The type of restriction analyzed here is based on the business cycle characteristics of U.S. macroeconomic data, and in particular, requires that the dynamic behavior of the restricted VAR model mimic the business cycle characteristics of historical data. The question posed in this paper is: would a VAR model, estimated subject to the restriction that the cyclical characteristics of simulated data from the model “match up” with the business cycle characteristics of U.S. data, generate more accurate out-of-sample forecasts than unrestricted or Bayesian VAR models?     

Forecasting macroeconomic variables using disaggregate survey data

We construct factor models based on disaggregate survey data for forecasting national aggregate macroeconomic variables. Our methodology applies regional and sectoral factor models to Norges Bank’s regional survey and to the Swedish Business Tendency Survey. The analysis identifies which of the pieces of information extracted from the individual regions in Norges Bank’s survey and the sectors for the two surveys perform particularly well at forecasting different variables at various horizons. The results show that several factor models beat an autoregressive benchmark in forecasting inflation and the unemployment rate. However, the factor models are most successful at forecasting GDP growth. Forecast combinations using the past performances of regional and sectoral factor models yield the most accurate forecasts in the majority of the cases.     

Using low frequency information for predicting high frequency variables

We analyze ways of incorporating low frequency information into models for the prediction of high frequency variables. In doing so, we consider the two existing versions of the mixed frequency VAR, with a focus on the forecasts for the high frequency variables. Furthermore, we introduce new models, namely the reverse unrestricted MIDAS (RU-MIDAS) and reverse MIDAS (R-MIDAS), which can be used for producing forecasts of high frequency variables that also incorporate low frequency information. We then conduct several empirical applications for assessing the relevance of quarterly survey data for forecasting a set of monthly macroeconomic indicators. Overall, it turns out that low frequency information is important, particularly when it has just been released.     

Financial information and macroeconomic forecasts

We study the forecasting power of financial variables for macroeconomic variables in 62 countries between 1980 and 2013. We find that financial variables such as credit growth, stock prices, and house prices have considerable predictive power for macroeconomic variables at the one- to four-quarter horizons. A forecasting model that includes financial variables outperforms the World Economic Outlook (WEO) forecasts in up to 85% of our sample countries at the four-quarter horizon. We also find that cross-country panel models produce more accurate out-of-sample forecasts than individual country models.     

Macroeconomic forecasting using structural factor analysis

The use of a small number of underlying factors to summarize the information from a much larger set of information variables is one of the new frontiers in forecasting. In prior work, the estimated factors have not usually had a structural interpretation and the factors have not been chosen on a theoretical basis. In this paper we propose several variants of a general structural factor forecasting model, and use these to forecast certain key macroeconomic variables. We make the choice of factors more structurally meaningful by estimating factors from subsets of information variables, where these variables can be assigned to subsets on the basis of economic theory. We compare the forecasting performance of the structural factor forecasting model with that of a univariate AR model, a standard VAR model, and some non-structural factor forecasting models. The results suggest that our structural factor forecasting model performs significantly better in forecasting real activity variables, especially at short horizons.     

Forecasting macroeconomic time series: LASSO-based approaches and their forecast combinations with dynamic factor models

In a data-rich environment, forecasting economic variables amounts to extracting and organizing useful information from a large number of predictors. So far, the dynamic factor model and its variants have been the most successful models for such exercises. In this paper, we investigate a category of LASSO-based approaches and evaluate their predictive abilities for forecasting twenty important macroeconomic variables. These alternative models can handle hundreds of data series simultaneously, and extract useful information for forecasting. We also show, both analytically and empirically, that combing forecasts from LASSO-based models with those from dynamic factor models can reduce the mean square forecast error (MSFE) further. Our three main findings can be summarized as follows. First, for most of the variables under investigation, all of the LASSO-based models outperform dynamic factor models in the out-of-sample forecast evaluations. Second, by extracting information and formulating predictors at economically meaningful block levels, the new methods greatly enhance the interpretability of the models. Third, once forecasts from a LASSO-based approach are combined with those from a dynamic factor model by forecast combination techniques, the combined forecasts are significantly better than either dynamic factor model forecasts or the naïve random walk benchmark.     

Financial nowcasts and their usefulness in macroeconomic forecasting

Financial data often contain information that is helpful for macroeconomic forecasting, while multi-step forecast accuracy benefits from incorporating good nowcasts of macroeconomic variables. This paper considers the usefulness of financial nowcasts for making conditional forecasts of macroeconomic variables with quarterly Bayesian vector autoregressions (BVARs). When nowcasting quarterly financial variables’ values, we find that taking the average of the available daily data and a daily random walk forecast to complete the quarter typically outperforms other nowcasting approaches. Using real-time data, we find gains in out-of-sample forecast accuracy from the inclusion of financial nowcasts relative to unconditional forecasts, with further gains from the incorporation of nowcasts of macroeconomic variables. Conditional forecasts from quarterly BVARs augmented with financial nowcasts rival the forecast accuracy of mixed-frequency dynamic factor models and mixed-data sampling (MIDAS) models.     

Forecasts of US short-term interest rates: A flexible forecast combination approach

This paper develops a flexible approach to combine forecasts of future spot rates with forecasts from time-series models or macroeconomic variables. We find empirical evidence that, accounting for both regimes in interest rate dynamics, and combining forecasts from different models, helps improve the out-of-sample forecasting performance for US short-term rates. Imposing restrictions from the expectations hypothesis on the forecasting model are found to help at long forecasting horizons.     

Forecasting crude oil price volatility

We use high-frequency intra-day realized volatility data to evaluate the relative forecasting performances of various models that are used commonly for forecasting the volatility of crude oil daily spot returns at multiple horizons. These models include the RiskMetrics, GARCH, asymmetric GARCH, fractional integrated GARCH and Markov switching GARCH models. We begin by implementing Carrasco, Hu, and Ploberger’s (2014) test for regime switching in the mean and variance of the GARCH(1, 1), and find overwhelming support for regime switching. We then perform a comprehensive out-of-sample forecasting performance evaluation using a battery of tests. We find that, under the MSE and QLIKE loss functions: (i) models with a Student’s t innovation are favored over those with a normal innovation; (ii) RiskMetrics and GARCH(1, 1) have good predictive accuracies at short forecast horizons, whereas EGARCH(1, 1) yields the most accurate forecasts at medium horizons; and (iii) the Markov switching GARCH shows a superior predictive accuracy at long horizons. These results are established by computing the equal predictive ability test of Diebold and Mariano (1995) and West (1996) and the model confidence set of Hansen, Lunde, and Nason (2011) over the entire evaluation sample. In addition, a comparison of the MSPE ratios computed using a rolling window suggests that the Markov switching GARCH model is better at predicting the volatility during periods of turmoil.     

Bayesian stochastic search for VAR model restrictions

We propose a Bayesian stochastic search approach to selecting restrictions for vector autoregressive (VAR) models. For this purpose, we develop a Markov chain Monte Carlo (MCMC) algorithm that visits high posterior probability restrictions on the elements of both the VAR regression coefficients and the error variance matrix. Numerical simulations show that stochastic search based on this algorithm can be effective at both selecting a satisfactory model and improving forecasting performance. To illustrate the potential of our approach, we apply our stochastic search to VAR modeling of inflation transmission from producer price index (PPI) components to the consumer price index (CPI).     

Macroeconomic forecasting and structural change

The aim of this paper is to assess whether modeling structural change can help improving the accuracy of macroeconomic forecasts. We conduct a simulated real‐time out‐of‐sample exercise using a time‐varying coefficients vector autoregression (VAR) with stochastic volatility to predict the inflation rate, unemployment rate and interest rate in the USA. The model generates accurate predictions for the three variables. In particular, the forecasts of inflation are much more accurate than those obtained with any other competing model, including fixed coefficients VARs, time‐varying autoregressions and the naïve random walk model. The results hold true also after the mid 1980s, a period in which forecasting inflation was particularly hard. Copyright © 2011 John Wiley & Sons, Ltd.     

FRED-SD: A real-time database for state-level data with forecasting applications

We construct a real-time dataset (FRED-SD) with vintage data for the U.S. states that can be used to forecast both state-level and national-level variables. Our dataset includes approximately 28 variables per state, including labor-market, production, and housing variables. We conduct two sets of real-time forecasting exercises. The first forecasts state-level labor-market variables using five different models and different levels of industrially disaggregated data. The second forecasts a national-level variable exploiting the cross-section of state data. The state-forecasting experiments suggest that large models with industrially disaggregated data tend to have higher predictive ability for industrially diversified states. For national-level data, we find that forecasting and aggregating state-level data can outperform a random walk but not an autoregression. We compare these real-time data experiments with forecasting experiments using final-vintage data and find very different results. Because these final-vintage results are obtained with revised data that would not have been available at the time the forecasts would have been made, we conclude that the use of real-time data is essential for drawing proper conclusions about state-level forecasting models.     

A large factor model for forecasting macroeconomic variables in South Africa

This paper uses large Factor Models (FMs), which accommodate a large cross-section of macroeconomic time series for forecasting the per capita growth rate, inflation, and the nominal short-term interest rate for the South African economy. The FMs used in this study contain 267 quarterly series observed over the period 1980Q1-2006Q4. The results, based on the RMSEs of one- to four-quarter-ahead out-of-sample forecasts from 2001Q1 to 2006Q4, indicate that the FMs tend to outperform alternative models such as an unrestricted VAR, Bayesian VARs (BVARs) and a typical New Keynesian Dynamic Stochastic General Equilibrium (NKDSGE) model in forecasting the three variables under consideration, hence indicating the blessings of dimensionality.     

On the forecasting performance of a small-scale DSGE model

Dynamic stochastic general equilibrium (DSGE) models have recently become standard tools for policy analysis. Nevertheless, their forecasting properties have still barely been explored. In this article, we address this problem by examining the quality of forecasts of the key U.S. economic variables: the three-month Treasury bill yield, the GDP growth rate and GDP price index inflation, from a small-size DSGE model, trivariate vector autoregression (VAR) models and the Philadelphia Fed Survey of Professional Forecasters (SPF). The ex post forecast errors are evaluated on the basis of the data from the period 1994–2006. We apply the Philadelphia Fed “Real-Time Data Set for Macroeconomists” to ensure that the data used in estimating the DSGE and VAR models was comparable to the information available to the SPF.Overall, the results are mixed. When comparing the root mean squared errors for some forecast horizons, it appears that the DSGE model outperforms the other methods in forecasting the GDP growth rate. However, this characteristic turned out to be statistically insignificant. Most of the SPF's forecasts of GDP price index inflation and the short-term interest rate are better than those from the DSGE and VAR models.     

Forecasting with Medium and Large Bayesian VARS

This paper is motivated by the recent interest in the use of Bayesian VARs for forecasting, even in cases where the number of dependent variables is large. In such cases factor methods have been traditionally used, but recent work using a particular prior suggests that Bayesian VAR methods can forecast better. In this paper, we consider a range of alternative priors which have been used with small VARs, discuss the issues which arise when they are used with medium and large VARs and examine their forecast performance using a US macroeconomic dataset containing 168 variables. We find that Bayesian VARs do tend to forecast better than factor methods and provide an extensive comparison of the strengths and weaknesses of various approaches. Typically, we find that the simple Minnesota prior forecasts well in medium and large VARs, which makes this prior attractive relative to computationally more demanding alternatives. Our empirical results show the importance of using forecast metrics based on the entire predictive density, instead of relying solely on those based on point forecasts. Copyright © 2011 John Wiley & Sons, Ltd.     

Probabilistic forecasting of industrial electricity load with regime switching behavior

This paper suggests a novel inhomogeneous Markov switching approach for the probabilistic forecasting of industrial companies’ electricity loads, for which the load switches at random times between production and standby regimes. The model that we propose describes the transitions between the regimes using a hidden Markov chain with time-varying transition probabilities that depend on calendar variables. We model the demand during the production regime using an autoregressive moving-average (ARMA) process with seasonal patterns, whereas we use a much simpler model for the standby regime in order to reduce the complexity. The maximum likelihood estimation of the parameters is implemented using a differential evolution algorithm. Using the continuous ranked probability score (CRPS) to evaluate the goodness-of-fit of our model for probabilistic forecasting, it is shown that this model often outperforms classical additive time series models, as well as homogeneous Markov switching models. We also propose a simple procedure for classifying load profiles into those with and without regime-switching behaviors.     

How to Identify and Forecast Bull and Bear Markets?

Because the state of the equity market is latent, several methods have been proposed to identify past and current states of the market and forecast future ones. These methods encompass semi‐parametric rule‐based methods and parametric Markov switching models. We compare the mean‐variance utilities that result when a risk‐averse agent uses the predictions of the different methods in an investment decision. Our application of this framework to the S&P 500 shows that rule‐based methods are preferable for (in‐sample) identification of the state of the market, but Markov switching models for (out‐of‐sample) forecasting. In‐sample, only the mean return of the market index matters, which rule‐based methods exactly capture. Because Markov switching models use both the mean and the variance to infer the state, they produce superior forecasts and lead to significantly better out‐of‐sample performance than rule‐based methods. We conclude that the variance is a crucial ingredient for forecasting the market state. Copyright © 2016 John Wiley & Sons, Ltd.     

Structural vector autoregressions with Markov switching: Combining conventional with statistical identification of shocks

In structural vector autoregressive (SVAR) analysis a Markov regime switching (MS) property can be exploited to identify shocks if the reduced form error covariance matrix varies across regimes. Unfortunately, these shocks may not have a meaningful structural economic interpretation. It is discussed how statistical and conventional identifying information can be combined. The discussion is based on a VAR model for the US containing oil prices, output, consumer prices and a short-term interest rate. The system has been used for studying the causes of the early millennium economic slowdown based on traditional identification with zero and long-run restrictions and using sign restrictions. We find that previously drawn conclusions are questionable in our framework.     

Forecasting the Chinese stock market volatility with international market volatilities: The role of regime switching

The purpose of this paper is to investigate the role of regime switching in the prediction of the Chinese stock market volatility with international market volatilities. Our work is based on the heterogeneous autoregressive (HAR) model and we further extend this simple benchmark model by incorporating an individual volatility measure from 27 international stock markets. The in-sample estimation results show that the transition probabilities are significant and the high volatility regime exhibits substantially higher volatility level than the low volatility regime. The out-of-sample forecasting results based on the Diebold-Mariano (DM) test suggest that the regime switching models consistently outperform their original counterparts with respect to not only the HAR and its extended models but also the five used combination approaches. In addition to point accuracy, the regime switching models also exhibit substantially higher directional accuracy. Furthermore, compared to time-varying parameter, Markov regime switching is found to be a more efficient way to process the volatility information in the changing world. Our results are also robust to alternative evaluation methods, various loss functions, alternative volatility estimators, various sample periods, and various settings of Markov regime switching. Finally, we provide an extension of forecasting aggregate market volatility on monthly frequency and observe mixed results.