Does the Macroeconomy Predict UK Asset Returns in a Nonlinear Fashion? Comprehensive Out‐of‐Sample Evidence

We perform a comprehensive examination of the recursive, comparative predictive performance of linear and nonlinear models for UK stock and bond returns. We estimate Markov switching, threshold autoregressive (TAR) and smooth transition autoregressive (STR) regime switching models and a range of linear specifications including models with GARCH type specifications. Results demonstrate UK asset returns require nonlinear dynamics to be modelled with strong evidence in favour of Markov switching frameworks. Our results appear robust to the choice of sample period, changes in loss functions and to the methodology employed to test for equal predictive accuracy. The key findings extend to a similar sample of US data.     

Conditional Markov chain and its application in economic time series analysis

Motivated by the great moderation in major US macroeconomic time series, we formulate the regime switching problem through a conditional Markov chain. We model the long‐run volatility change as a recurrent structure change, while short‐run changes in the mean growth rate as regime switches. Both structure and regime are unobserved. The structure is assumed to be Markovian. Conditioning on the structure, the regime is also Markovian, whose transition matrix is structure‐dependent. This formulation imposes interpretable restrictions on the Hamilton Markov switching model. Empirical studies show that this restricted model well identifies both short‐run regime switches and long‐run structure changes in the US macroeconomic data. Copyright © 2010 John Wiley & Sons, Ltd.     

Unemployment persistence: does the size of the shock matter?

One of the stylized facts of unemployment is that shifts in its mean rate between decades and half-decades account for most of its variance. In this paper, we use a statistical analysis based on Markov switching regression models to identify the dates of infrequent changes in the mean of the unemployment rate series of fifteen countries. We find that in most countries, unemployment persistence is much reduced once the (infrequently) changing mean rate, induced by large shocks to unemployment, has been removed. We conclude that the observed persistence in unemployment appears to be consistent with multiple equilibria models and models with an endogeneous natural rate. © 1998 John Wiley & Sons, Ltd.     

This is what the leading indicators lead

We propose an optimal filter to transform the Conference Board Composite Leading Index (CLI) into recession probabilities in the US economy. We also analyse the CLI's accuracy at anticipating US output growth. We compare the predictive performance of linear, VAR extensions of smooth transition regression and switching regimes, probit, non‐parametric models and conclude that a combination of the switching regimes and non‐parametric forecasts is the best strategy at predicting both the NBER business cycle schedule and GDP growth. This confirms the usefulness of CLI, even in a real‐time analysis. Copyright © 2002 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.     

Labor market entry and earnings dynamics: Bayesian inference using mixtures‐of‐experts Markov chain clustering

This paper analyzes patterns in the earnings development of young labor market entrants over their life cycle. We identify four distinctly different types of transition patterns between discrete earnings states in a large administrative dataset. Further, we investigate the effects of labor market conditions at the time of entry on the probability of belonging to each transition type. To estimate our statistical model we use a model‐based clustering approach. The statistical challenge in our application comes from the difficulty in extending distance‐based clustering approaches to the problem of identifying groups of similar time series in a panel of discrete‐valued time series. We use Markov chain clustering, which is an approach for clustering discrete‐valued time series obtained by observing a categorical variable with several states. This method is based on finite mixtures of first‐order time‐homogeneous Markov chain models. In order to analyze group membership we present an extension to this approach by formulating a probabilistic model for the latent group indicators within the Bayesian classification rule using a multinomial logit model. Copyright © 2011 John Wiley & Sons, Ltd.     

Exit problems in regime-switching models

This paper provides a general framework for pricing of perpetual American and real options in regime-switching Lévy models. In each state of the Markov chain, which determines switches from one Lévy process to another, the payoff stream is a monotone function of the Lévy process labeled by the state. This allows for additional switching within each state of the Markov chain (payoffs can be different in different regions of the real line). The pricing procedure is efficient even if the number of states is large provided the transition rates are not very large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modeled as finite-state Markov chains. As an application, we solve exit problems for a price-taking firm, and study the dependence of the exit threshold on the interest rate uncertainty.     

Interconnections Between Eurozone and US Booms and Busts Using a Bayesian Panel Markov‐Switching VAR Model

The proposed panel Markov‐switching VAR model accommodates changes in low and high data frequencies and incorporates endogenous time‐varying transition matrices of country‐specific Markov chains, allowing for interconnections. An efficient multi‐move sampling algorithm draws time‐varying Markov‐switching chains. Using industrial production growth and credit spread data, several important data features are obtained. Three regimes appear, with slow growth becoming persistent in the eurozone. Turning point analysis indicates the USA leading the eurozone cycle. Amplification effects influence recession probabilities for Eurozone countries. A credit shock results in temporary negative industrial production growth in Germany, Spain and the USA. Core and peripheral countries exist in the eurozone. Copyright © 2016 John Wiley & Sons, Ltd.     

A unified approach to nonlinearity,structural change,and outliers

This paper demonstrates that the class of conditionally linear and Gaussian state-space models offers a general and convenient framework for simultaneously handling nonlinearity, structural change and outliers in time series. Many popular nonlinear time series models, including threshold, smooth transition and Markov-switching models, can be written in state-space form. It is then straightforward to add components that capture parameter instability and intervention effects. We advocate a Bayesian approach to estimation and inference, using an efficient implementation of Markov Chain Monte Carlo sampling schemes for such linear dynamic mixture models. The general modelling framework and the Bayesian methodology are illustrated by means of several examples. An application to quarterly industrial production growth rates for the G7 countries demonstrates the empirical usefulness of the approach.     

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.     

Estimating the U.S. output gap with state‐level data

This paper develops a method to estimate the U.S. output gap by exploiting the cross‐sectional variation of state‐level output and unemployment rate data. The model assumes that there are common output and unemployment rate trend and cycle components, and that each state's output and unemployment rate are subject to idiosyncratic trend and cycle perturbations. I estimate the model with Bayesian methods using quarterly data from 2005:Q1 to 2018:Q2 for the 50 states and the District of Columbia. Results show that the U.S. output gap reached about negative 4.6% around the years of the Great Recession and was about 0.9% in 2018:Q2.     

Bayesian median autoregression for robust time series forecasting

We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to the widely used mean-based methods. Motivated by a working Laplace likelihood approach in Bayesian quantile regression, BayesMAR adopts a parametric model bearing the same structure as autoregressive models by altering the Gaussian error to Laplace, leading to a simple, robust, and interpretable modeling strategy for time series forecasting. We estimate model parameters by Markov chain Monte Carlo. Bayesian model averaging is used to account for model uncertainty, including the uncertainty in the autoregressive order, in addition to a Bayesian model selection approach. The proposed methods are illustrated using simulations and real data applications. An application to U.S. macroeconomic data forecasting shows that BayesMAR leads to favorable and often superior predictive performance compared to the selected mean-based alternatives under various loss functions that encompass both point and probabilistic forecasts. The proposed methods are generic and can be used to complement a rich class of methods that build on autoregressive models.     

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.     

Markov switching quantile autoregression

This paper considers the location‐scale quantile autoregression in which the location and scale parameters are subject to regime shifts. The regime changes in lower and upper tails are determined by the outcome of a latent, discrete‐state Markov process. The new method provides direct inference and estimate for different parts of a non‐stationary time series distribution. Bayesian inference for switching regimes within a quantile, via a three‐parameter asymmetric Laplace distribution, is adapted and designed for parameter estimation. Using the Bayesian output, the marginal likelihood is readily available for testing the presence and the number of regimes. The simulation study shows that the predictability of regimes and conditional quantiles by using asymmetric Laplace distribution as the likelihood is fairly comparable with the true model distributions. However, ignoring that autoregressive coefficients might be quantile dependent leads to substantial bias in both regime inference and quantile prediction. The potential of this new approach is illustrated in the empirical applications to the US inflation and real exchange rates for asymmetric dynamics and the S&P 500 index returns of different frequencies for financial market risk assessment.     

Testing Granger Causality in the presence of threshold effects

This paper proposes a Granger Causality test allowing for threshold effects. The proposed test can be conducted on the basis of the threshold autoregressive distributed lag model or the augmented logistic smooth transition autoregressive model. The proposed test is applied to the U.S. civilian unemployment rate, and it is shown that real investment, real GDP and real interest rate are helpful for improving the in-sample fit of unemployment.     

Money‐output Causality Revisited – A Bayesian Logistic Smooth Transition VECM Perspective*

This article proposes a Bayesian approach to examining money‐output causality within the context of a logistic smooth transition vector error correction model. Our empirical results provide substantial evidence that the postwar US money‐output relationship is nonlinear, with regime changes mainly governed by the output growth and price levels. Furthermore, we obtain strong support for nonlinear Granger causality from money to output, although there is also some evidence for models indicating that money is not Granger causal or long‐run causal to output.     

Contemporaneous threshold autoregressive models: Estimation,testing and forecasting

This paper proposes a contemporaneous smooth transition threshold autoregressive model (C-STAR) as a modification of the smooth transition threshold autoregressive model surveyed in Teräsvirta [1998. Modelling economic relationships with smooth transition regressions. In: Ullah, A., Giles, D.E.A. (Eds.), Handbook of Applied Economic Statistics. Marcel Dekker, New York, pp. 507–552.], in which the regime weights depend on the ex ante probability that a latent regime-specific variable will exceed a threshold value. We argue that the contemporaneous model is well suited to rational expectations applications (and pricing exercises), in that it does not require the initial regimes to be predetermined. We investigate the properties of the model and evaluate its finite-sample maximum likelihood performance. We also propose a method to determine the number of regimes based on a modified Hansen [1992. The likelihood ratio test under nonstandard conditions: testing the Markov switching model of GNP. Journal of Applied Econometrics 7, S61–S82.] procedure. Furthermore, we construct multiple-step ahead forecasts and evaluate the forecasting performance of the model. Finally, an empirical application of the short term interest rate yield is presented and discussed.     

Inference on Self‐Exciting Jumps in Prices and Volatility Using High‐Frequency Measures

Dynamic jumps in the price and volatility of an asset are modelled using a joint Hawkes process in conjunction with a bivariate jump diffusion. A state‐space representation is used to link observed returns, plus nonparametric measures of integrated volatility and price jumps, to the specified model components, with Bayesian inference conducted using a Markov chain Monte Carlo algorithm. An evaluation of marginal likelihoods for the proposed model relative to a large number of alternative models, including some that have featured in the literature, is provided. An extensive empirical investigation is undertaken using data on the S&P 500 market index over the 1996–2014 period, with substantial support for dynamic jump intensities—including in terms of predictive accuracy—documented. Copyright © 2016 John Wiley & Sons, Ltd.     

Testing the unbiased forward exchange rate hypothesis using a Markov switching model and instrumental variables

This paper develops a model for the forward and spot exchange rate which allows for the presence of a Markov switching risk premium in the forward market and considers the issue of testing the unbiased forward exchange rate (UFER) hypothesis. Using US/UK data, it is shown that the UFER hypothesis cannot be rejected, provided that instrumental variables are used to account for within‐regime correlation between explanatory variables and disturbances in the Markov switching model on which the test is based. Copyright © 2005 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.