Improving Markov switching models using realized variance

This paper proposes a class of models that jointly model returns and ex post variance measures under a Markov switching framework. Both univariate and multivariate return versions of the model are introduced. Estimation can be conducted under a fixed dimension state space or an infinite one. The proposed models can be seen as nonlinear common factor models subject to Markov switching and are able to exploit the information content in both returns and ex post volatility measures. Applications to equity returns compare the proposed models to existing alternatives. The empirical results show that the joint models improve density forecasts for returns and point predictions of return variance. Using the information in ex post volatility measures can increase the precision of parameter estimates, sharpen the inference on the latent state variable, and improve portfolio decisions.     

General Bayesian time-varying parameter vector autoregressions for modeling government bond yields

US yield curve dynamics are subject to time-variation, but there is ambiguity about its precise form. This paper develops a vector autoregressive (VAR) model with time-varying parameters and stochastic volatility, which treats the nature of parameter dynamics as unknown. Coefficients can evolve according to a random walk, a Markov switching process, observed predictors, or depend on a mixture of these. To decide which form is supported by the data and to carry out model selection, we adopt Bayesian shrinkage priors. Our framework is applied to model the US yield curve. We show that the model forecasts well, and focus on selected in-sample features to analyze determinants of structural breaks in US yield curve dynamics.     

Structural breaks and GARCH models of exchange rate volatility

We investigate the empirical relevance of structural breaks for GARCH models of exchange rate volatility using both in‐sample and out‐of‐sample tests. We find significant evidence of structural breaks in the unconditional variance of seven of eight US dollar exchange rate return series over the 1980–2005 period—implying unstable GARCH processes for these exchange rates—and GARCH(1,1) parameter estimates often vary substantially across the subsamples defined by the structural breaks. We also find that it almost always pays to allow for structural breaks when forecasting exchange rate return volatility in real time. Combining forecasts from different models that accommodate structural breaks in volatility in various ways appears to offer a reliable method for improving volatility forecast accuracy given the uncertainty surrounding the timing and size of the structural breaks. Copyright © 2008 John Wiley & Sons, Ltd.     

MODELLING REGIME SWITCHING AND STRUCTURAL BREAKS WITH AN INFINITE HIDDEN MARKOV MODEL

This paper proposes an infinite hidden Markov model to integrate the regime switching and structural break dynamics in a unified Bayesian framework. Two parallel hierarchical structures, one governing the transition probabilities and another governing the parameters of the conditional data density, keep the model parsimonious and improve forecasts. This flexible approach allows for regime persistence and estimates the number of states automatically. An application to US real interest rates compares the new model to existing parametric alternatives. Copyright © 2013 John Wiley & Sons, Ltd.     

Kernel-based calibration diagnostics for recession and inflation probability forecasts

A probabilistic forecast is the estimated probability with which a future event will occur. One interesting feature of such forecasts is their calibration, or the match between the predicted probabilities and the actual outcome probabilities. Calibration has been evaluated in the past by grouping probability forecasts into discrete categories. We show here that we can do this without discrete groupings; the kernel estimators that we use produce efficiency gains and smooth estimated curves relating the predicted and actual probabilities. We use such estimates to evaluate the empirical evidence on the calibration error in a number of economic applications, including the prediction of recessions and inflation, using both forecasts made and stored in real time and pseudo-forecasts made using the data vintage available at the forecast date. The outcomes are evaluated using both first-release outcome measures and subsequent revised data. We find substantial evidence of incorrect calibration in professional forecasts of recessions and inflation from the SPF, as well as in real-time inflation forecasts from a variety of output gap models.     

A Bayesian Multiple Comparison Procedure for Order-Restricted Mixed Models

A Bayesian hierarchical mixed model is developed for multiple comparisons under a simple order restriction. The model facilitates inferences on the successive differences of the population means, for which we choose independent prior distributions that are mixtures of an exponential distribution and a discrete distribution with its entire mass at zero. We employ Markov Chain Monte Carlo (MCMC) techniques to obtain parameter estimates and estimates of the posterior probabilities that any two of the means are equal. The latter estimates allow one both to determine if any two means are significantly different and to test the homogeneity of all of the means. We investigate the performance of the model-based inferences with simulated data sets, focusing on parameter estimation and successive-mean comparisons using posterior probabilities. We then illustrate the utility of the model in an application based on data from a study designed to reduce lead blood concentrations in children with elevated levels. Our results show that the proposed hierarchical model can effectively unify parameter estimation, tests of hypotheses and multiple comparisons in one setting.     

Estimating and Forecasting the Yield Curve Using A Markov Switching Dynamic Nelson and Siegel Model

We estimate versions of the Nelson–Siegel model of the yield curve of US government bonds using a Markov switching latent variable model that allows for discrete changes in the stochastic process followed by the interest rates. Our modeling approach is motivated by evidence suggesting the existence of breaks in the behavior of the US yield curve that depend, for example, on whether the economy is in a recession or a boom, or on the stance of monetary policy. Our model is parsimonious, relatively easy to estimate and flexible enough to match the changing shapes of the yield curve over time. We also derive the discrete time non‐arbitrage restrictions for the Markov switching model. We compare the forecasting performance of these models with that of the standard dynamic Nelson and Siegel model and an extension that allows the decay rate parameter to be time varying. We show that some parametrizations of our model with regime shifts outperform the single‐regime Nelson and Siegel model and other standard empirical models of the yield curve. Copyright © 2014 John Wiley & Sons, Ltd.     

Dealing with Benchmark Revisions in Real‐Time Data: The Case of German Production and Orders Statistics*

Benchmark revisions in non‐stationary real‐time data may adversely affect the results of regular revision analysis and the estimates of long‐run economic relationships. Cointegration analysis can reveal the nature of vintage heterogeneity and guide the adjustment of real‐time data for benchmark revisions. Affine vintage transformation functions estimated by cointegration regressions are a flexible tool, whereas differencing and rebasing work well only under certain circumstances. Inappropriate vintage transformation may cause observed revision statistics to be affected by nuisance parameters. Using real‐time data of German industrial production and orders, the econometric techniques are exemplified and the theoretical claims are examined empirically.     

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.     

Long-term forecasting and evaluation

Looking ahead thirty years is a difficult task, but is not impossible. In this paper we illustrate how to evaluate such long-term forecasts. Long-term forecasting is likely to be dominated by trend curves, particularly the simple linear and exponential trends. However, there will certainly be breaks in their parameter values at some unknown points, so that eventually the forecasts will be unsatisfactory. We investigate whether or not simple methods of long-run forecasting can ever be successful, after one takes into account the uncertainty level associated with the forecasts.     

Business and consumer expectations and macroeconomic forecasts

Business and consumer surveys have become an essential tool for gathering information about different economic variables. While the fast availability of the results and the wide range of variables covered have made them very useful for monitoring the current state of the economy, there is no consensus on their usefulness for forecasting macroeconomic developments.The objective of this paper is to analyse the possibility of improving forecasts for selected macroeconomic variables for the euro area using the information provided by these surveys. After analyzing the potential presence of seasonality and the issue of quantification, we tested whether these indicators provide useful information for improving forecasts of the macroeconomic variables. With this aim, different sets of models have been considered (AR, ARIMA, SETAR, Markov switching regime models and VAR) to obtain forecasts for the selected macroeconomic variables. Then, information from surveys has been considered for forecasting these variables in the context of the following models: autoregressive, VAR, Markov switching regime and leading indicator models. In all cases, the root mean square error (RMSE) has been computed for different forecast horizons.The comparison of the forecasting performance of the two sets of models permits us to conclude that, in most cases, models that include information from the surveys have lower RMSEs than the best model without survey information. However, this reduction is only significant in a limited number of cases. In this sense, the results obtained extend the results of previous research that has included information from business and consumer surveys to explain the behaviour of macroeconomic variables, but are not conclusive about its role.     

REAL‐TIME FORECASTING OF INFLATION AND OUTPUT GROWTH WITH AUTOREGRESSIVE MODELS IN THE PRESENCE OF DATA REVISIONS

We examine how the accuracy of real‐time forecasts from models that include autoregressive terms can be improved by estimating the models on ‘lightly revised’ data instead of using data from the latest‐available vintage. The benefits of estimating autoregressive models on lightly revised data are related to the nature of the data revision process and the underlying process for the true values. Empirically, we find improvements in root mean square forecasting error of 2–4% when forecasting output growth and inflation with univariate models, and of 8% with multivariate models. We show that multiple‐vintage models, which explicitly model data revisions, require large estimation samples to deliver competitive forecasts. Copyright © 2012 John Wiley & Sons, Ltd.     

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 loss given default estimation for European sovereign bonds

We develop and apply a Bayesian model for the loss rates given defaults (LGDs) of European Sovereigns. Financial institutions are in need of LGD forecasts under Pillar II of the regulatory Basel Accord and the downturn in LGD forecasts under Pillar I. Both are challenging for portfolios with a small number of observations such as sovereigns. Our approach comprises parameter risk and generates LGD forecasts under both regular and downturn conditions. With sovereign-specific rating information, we found that average LGD estimates vary between 0.46 and 0.64, while downturn estimates lay between 0.50 and 0.86.     

Inversion copulas from nonlinear state space models with an application to inflation forecasting

We propose the construction of copulas through the inversion of nonlinear state space models. These copulas allow for new time series models that have the same serial dependence structure as a state space model, but with an arbitrary marginal distribution, and flexible density forecasts. We examine the time series properties of the copulas, outline serial dependence measures, and estimate the models using likelihood-based methods. Copulas constructed from three example state space models are considered: a stochastic volatility model with an unobserved component, a Markov switching autoregression, and a Gaussian linear unobserved component model. We show that all three inversion copulas with flexible margins improve the fit and density forecasts of quarterly U.S. broad inflation and electricity inflation.     

Keeping track of global trade in real time

This paper builds an innovative composite world trade-cycle index by means of a dynamic factor model for short-term forecasts of world trade growth of both goods and (usually neglected) services. Trade indicators are selected using a multidimensional approach, including Bayesian model averaging techniques, dynamic correlations, and Granger non-causality tests in a linear vector autoregression framework. To overcome real-time forecasting challenges, the dynamic factor model is extended to account for mixed frequencies, to deal with asynchronous data publication, and to include hard and survey data along with leading indicators. Nonlinearities are addressed with a Markov switching model. Pseudo-real-time empirical simulations suggest that: (i) the global trade index is a useful tool for tracking and forecasting world trade in real time; (ii) the model is able to infer global trade cycles very precisely and better than several competing alternatives; and (iii) global trade finance conditions seem to lead the trade cycle, a conclusion that is in line with the theoretical literature.     

Can we improve the perceived quality of economic forecasts?

A number of topics are discussed concerning how economic forecasts can be improved in quality or at least in presentation. These include the following: using 50% uncertainty intervals rather than 95%; noting that even though forecasters use many different techniques, they are all occasionally incorrect in the same direction; that there is a tendency to underestimate changes; that some expectations and recently available data are used insufficiently; lagged forecasts errors can help compensate for structural breaks; series that are more forecastable could be emphasized and that present methods of evaluating forecasts do not capture the useful properties of some methods compared to alternatives.     

马尔可夫性及其检验方法研究

马尔可夫链广泛应用于信息论、自动控制、通信技术、基因遗传、计算机科学、经济管理、教育管理、市场预测等领域,马尔可夫性是其最基本特征,因此,在运用马尔可夫链进行预测时,必须对预测对象以往的统计数据资料构成的随机变量序列的马尔可夫性进行检验,只有符合马尔可夫性,才能利用马尔可夫链进行预测,才能保证预测精度。本文探讨了马氏性的概念及性质,研究了马尔可夫性的检验方法,通过实例对该检验方法进行了分析。     

The sampling distribution of forecasts from a first-order autoregression

Previous work on characterising the distribution of forecast errors in time series models by statistics such as the asymptotic mean square error has assumed that observations used in estimating parameters are statistically independent of those used to construct the forecasts themselves. This assumption is quite unrealistic in practical situations and the present paper is intended to tackle the question of how the statistical dependence between the parameter estimates and the final period observations used to generate forecasts affects the sampling distribution of the forecast errors. We concentrate on the first-order autoregression and, for this model, show that the conditional distribution of forecast errors given the final period observation is skewed towards the origin and that this skewness is accentuated in the majority of cases by the statistical dependence between the parameter estimates and the final period observation.