Testing Markov switching models

In this article, we propose a new test for Markov switching models. Unlike the tests in the existing literature (e.g. Hansen, 1992; Garcia, 1998; Cho and White, 2007), we focus on testing the null of two regimes, instead of one single regime, in a switching framework. To implement our test, we propose a Markov switching model with absorbing states and examine whether the absorption probabilities are close to the boundary of the parameter space. We exploit recent advances by Andrews (2001) and conduct inference in the proposed model.     

Testing nonlinearities in economic growth in the OECD countries: an evidence from SETAR and STAR models

This study estimates the Self Exciting Threshold Autoregressive (SETAR) and Smooth Transition Autoregressive (STAR) models and examines the nonlinear and regime switching dynamics of economic growth for a set of 10 OECD countries. The null of linearity in SETAR model is tested using the recursive polynomial F test of Tsay and the bootstrap based supremum, average and exponential average Lagrange Multiplier (LM) tests of Hansen. The F test of Tsay rejects the null of linearity for all the countries, except Spain and Switzerland. The SETAR model of Hansen reinforces the evidence and suggests the rejection of linear model. The STAR model rejects the null of linearity against STAR nonlinearity for all the countries, except Denmark and Switzerland. The sequential F tests for the conditional nulls suggest the LSTAR nonlinearity for Australia, Belgium, France, Sweden and UK, and the ESTAR nonlinearity for Canada, Spain and the USA.     

Modified Quasi‐Likelihood Ratio Test for Regime Switching

In this paper we propose a modified quasi‐likelihood ratio test of the null hypothesis of one regime against the alternative of two regimes in Markov regime‐switching models. The asymptotic distribution of the proposed test statistic is a simple function of Gaussian random variables, and the inference is no more complicated than in the standard case. Our simulations show that the proposed test has good finite sample size and power that are comparable to the quasi‐likelihood ratio test of Cho and White. We apply our test to stock returns and Japanese policy functions.     

Does purchasing power parity hold sometimes? Regime switching in real exchange rates

Standard unit root tests are not very powerful in drawing conclusions regarding the validity of Purchasing Power Parity (PPP). Rather than asking whether PPP holds throughout the whole sample period, we examine, in this study, if PPP holds sometimes by employing Hamilton-type (1989) Markov regime switching models. When at least one of multiple regimes is stationary, PPP holds locally within the regime. There are indeed various reasons that we should expect that the persistence of real exchange rates changes over time. Employing five real exchange rates spanning more than 100 years, we find herein strong evidence that the strength of PPP varies during the sample periods and that there exist stationary regimes in which PPP holds. Throughout the article, we also make comparisons to previous Markov regime switching estimation results by Kanas (2006) on the same data series. The new Markov switching model selection criterion of Smith et al. (2006), which is devised especially for discriminating Markov regime switching models, unambiguously indicates a preference for the Hamilton-type Markov regime switching model employed in this study. We also find that the evidence for PPP is not much different across different nominal exchange rate arrangements.     

Regime changes and fiscal sustainability in Kenya

Kenya's fiscal policy landscape is characterized by primary deficit spending forcing the government to rely on debt to meet its objectives. The justification often being that as a developing economy, annual growth rates and future prospects may in the short run justify the uptake of debt to finance infrastructural development. However, given potential fiscal limits, fiscal cycles usually alternates between sustainable and unsustainable regimes and this has a bearing on long run sustainability. This study therefore sought to investigate the nature of fiscal policy regime in Kenya and the extent to which fiscal policy is sustainable in the long run taking into account periodic regime shifts. Markov switching models were used to endogenously determine fiscal policy regimes. Regime switching tests were used to test whether No-Ponzi game condition and debt stabilizing condition were met. The results established that regime switching model was suitable in explaining regime sustainable and unsustainable cycles. An investigation of fiscal policy regimes established that both sustainable and unsustainable regimes were dominant, and each lasted for an average of four years. There was evidence to imply the existence of procyclical fiscal policy in Kenya. Regime switching tests for long run sustainability suggested that the No-Ponzi game condition weakly holds in the Kenyan economy. Regime-based sensitivity analysis indicated that persistence of unsustainability regime for more than 4 years could threaten long-run fiscal sustainability.     

Volatility forecasting: long memory,regime switching and heteroscedasticity

In this article, we account for the first time for long memory, regime switching and the conditional time-varying volatility of volatility (heteroscedasticity) to model and forecast market volatility using the heterogeneous autoregressive model of realized volatility (HAR-RV) and its extensions. We present several interesting and notable findings. First, existing models exhibit significant nonlinearity and clustering, which provide empirical evidence on the benefit of introducing regime switching and heteroscedasticity. Second, out-of-sample results indicate that combining regime switching and heteroscedasticity can substantially improve predictive power from a statistical viewpoint. More specifically, our proposed models generally exhibit higher forecasting accuracy. Third, these results are widely consistent across a variety of robustness tests such as different forecasting windows, forecasting models, realized measures, and stock markets. Consequently, this study sheds new light on forecasting future volatility.     

Fads or bubbles?

This paper tests between fads and bubbles using a switching regression to distinguish between competing models. Two main features of the bubbles model distinguish it from the fads model. First, the bubbles model implies that returns are drawn from regimes which differ in the way returns vary with deviations from fundamental prices. Second, the bubbles model implies that deviations from fundamental price will help predict regime switches. Using US data for 1926–89, we find evidence which is consistent with the fads model even when we allow for variation in expected dividend growth rates and expected discount rates. However, the restrictions which the fads model implies for a more general switching-regression specification are rejected. The rejections point in the direction of the bubbles model, although not all of the implications of the bubbles model are supported by the data. First Version Received: October 2000/Final Version Received: October 2001     

Conditional Markov regime switching model applied to economic modelling

In this paper we discuss the calibration issues of regime switching models built on mean-reverting and local volatility processes combined with two Markov regime switching processes. In fact, the volatility structure of these models depends on a first exogenous Markov chain whereas the drift structure depends on a conditional Markov chain with respect to the first one. The structure is also assumed to be Markovian and both structure and regime are unobserved. Regarding this construction, we extend the classical Expectation–Maximization (EM) algorithm to be applied to our regime switching model. We apply it to economic data (Euro/Dollar (USD) foreign exchange rate and Brent oil price) to show that such modelling clearly identifies both mean reverting and volatility regime switches. Moreover, it allows us to make economic interpretations of this regime classification as in some financial crises or some economic policies.     

Testing volatility persistence on Markov switching stochastic volatility models

In the literature, some researchers found that the high persistence of the volatility can be caused by Markov regime switching. This concern can be reflected as a unit root problem on the basis of Markov switching models. In this paper, our main purpose is to provide a Bayesian unit root testing approach for Markov switching stochastic volatility (MSSV) models. We illustrate the developed approach using S&P 500 daily return covering the subprime crisis started in 2008.     

Tests for cointegration allowing for an unknown number of breaks

This paper introduces cointegration tests allowing for an unknown number of breaks. The introduced tests assume that the unspecified number of breaks is smaller than or equal to the maximum number of breaks set a priori. Monte Carlo simulations provide two main results. First, the proposed tests perform as well as the tests of Gregory and Hansen (1996a) and Hatemi-J (2008), which assume one or two breaks a priori, when the cointegration relationship has one or two breaks. Second, the proposed tests perform better than the tests of Gregory and Hansen (1996a) and Hatemi-J (2008) when the cointegration relationship has more than three breaks or persistent Markov switching shifts. We also provide empirical applications for the money demand of the U.S. The empirical results show that the proposed tests reject the null hypothesis of no cointegration as compared to other tests.     

Do macroeconomic variables have regime-dependent effects on stock return dynamics? Evidence from the Markov regime switching model

The predictability of stock return dynamics is a topic discussed most frequently in empirical studies; however, no unanimous conclusion has yet been reached due to the ignorance of structural changes in stock price dynamics. This study applies various regime switching GJR-GARCH models to analyze the effects of macroeconomic variables (interest rate, dividend yield, and default premium) on stock return movements (including conditional mean, conditional variance, and transition probabilities) in the U.S. stock market, so as to clearly compare the predictive validity of stable and volatile states, as well as compare the in-sample and out-of-sample portfolio performance of regime switching models. The empirical results show that macro factors can affect the stock return dynamics through two different channels, and that the magnitude of their influences on returns and volatility is not constant. The effects of the three economic variables on returns are not time-invariant, but are closely related to stock market fluctuations, and the strength of predictability in a volatile regime is far greater than that in a stable regime. It is found that interest rate and dividend yield seem to play an important role in predicting conditional variance, and out-of-sample performance is largely eroded when the effects of these two factors on volatility are ignored. In addition, the three macro factors do not play any role in predicting transition probabilities.     

A regime-switching approach to the study of speculative attacks: A focus on EMS crises

This paper implements a regime-switching framework to study speculative attacks against EMS currencies during 1979–1993. To identify speculative episodes, we model exchange rates, reserves, and interest rates as time series subject to discrete regime shifts between two possible states: “tranquil” and “speculative”. We allow the probabilities of switching between states to be a function of fundamentals and expectations. The regime-switching framework improves the ability to identify speculative attacks vis-à-vis the indices of speculative pressure used in the literature. The results also indicate that fundamentals (particularly budget deficits) and expectations drive the probability of switching to a speculative state. First Version Received: October 2000/Final Version Received: June 2001     

Four centuries of British economic growth: the roles of technology and population

Using long historical data for Britain over the period 1620–2006, this paper seeks to explain the importance of innovative activity, population growth and other factors in inducing the transition from the Malthusian trap to the post-Malthusian growth regime. Furthermore, the paper tests the ability of two competing second-generation endogenous growth models to account for the British growth experience. The results suggest that innovative activity was an important force in shaping the Industrial Revolution and that the British growth experience is consistent with Schumpeterian growth theory.     

Asymmetric expectation effects of regime shifts in monetary policy

This paper addresses two substantive issues: (1) Does the magnitude of the expectation effect of regime switching in monetary policy depend on a particular policy regime? (2) Under which regime is the expectation effect quantitatively important? Using two canonical DSGE models, we show that there exists asymmetry in the expectation effect across regimes. The expectation effect under the dovish policy regime is quantitatively more important than that under the hawkish regime. These results suggest that the possibility of regime shifts in monetary policy can have important effects on rational agents' expectation formation and on equilibrium dynamics. They offer a theoretical explanation for the empirical possibility that a policy shift from the dovish regime to the hawkish regime may not be the main source of substantial reductions in the volatilities of inflation and output.     

Non-parametric tests of real exchange rates in the post-Bretton Woods era

This paper examines the mean-reverting property of real exchange rates. Earlier studies have generally not been able to reject the null hypothesis of a unit-root in real exchange rates, especially for the post-Bretton Woods floating period. The results imply that long-run purchasing power parity does not hold. More recent studies, especially those using panel unit-root tests or nonlinear time series models, have found more favorable results, however. But the results from these recent studies are far from conclusive. Consistent individual country time series evidence that supports long-run purchasing power parity continues to be scarce. In this paper, we test for long memory using (Lo’s in Econometrica 59:1279–1313, 1991) the modified rescaled range test, and the rescaled variance test of Giraitis et al. (J Econ 112:265–294, 2003a). Our testing procedure provides a non-parametric alternative to the parametric tests commonly used in this literature. Our data set consists of monthly observations from April 1973 to April 2001 of the G-6 countries (excluding the US) in the OECD. Using the modified rescaled range test, we find only 2 cases out of 15 where the null hypothesis of a unit-root with short-term dependence could be rejected in favor of the alternative hypothesis of long-term dependence and none using the rescaled variance test. Our results therefore do not provide strong empirical support for the stationarity of real exchange rates.     

The asymmetric effects of oil shocks on output growth: A Markov–Switching analysis for the G-7 countries

Oil shocks are generally acknowledged to have important effects on both economic activity and macroeconomic policy. The aim of this paper is to investigate how oil price shocks affect the growth rate of output of a subset of developed countries by comparing alternative regime switching models. Different Markov–Switching (MS) regime autoregressive models are, therefore, specified and estimated. In a successive step, univariate MS models are extended in order to verify if the inclusion of asymmetric oil shocks as an exogenous variable improves the ability of each specification to identify the different phases of the business cycle for each country under scrutiny. Following the wide literature on this topic, seven different definitions of oil shocks which are able to describe oil price changes, asymmetric transformations of oil price changes, oil price volatility, and oil supply conditions are considered.     

A test for the presence of central bank intervention in the foreign exchange market with an application to the Bank of Canada

In this article, a general nonlinear simultaneous equations framework for the econometric analysis of models of intervention in foreign exchange markets by central banks in response to deviations of exchange rates from target levels is proposed. The instrumental variables estimation of possibly nonlinear response functions and tests of intervention, when the functional form may be nonlinear, asymmetric, and may contain unknown shape parameters, is considered. The methodology applies techniques developed for testing in the presence of nuisance parameters unidentified under a null hypothesis to a nonlinear simultaneous equations model. The results of an empirical analysis of stabilization activity of the Bank of Canada, for the period from 1953 to 2009, with regard to the Canada–U.S exchange rate are reported here. A nonlinear specification is found necessary to capture activity after 1998.     

Do bubbles have an explosive signature in markov switching models?

We investigate nine data series previously identified as containing bubbles using Bayesian Markov switching models.  Nearly all series appear to display strong regime switching that could possibly be induced by ‘bubble’ processes, but in each case the type of model that best describes each price differs substantively.  We pay particular attention to whether these series contain transient explosive roots, a feature which has been suggested to exist in several bubble formulations.  Bayesian model averaging is employed which allows us to average across a range of submodels, so that our empirical findings are not based on only one well performing model.  We show that explosive regimes may exist in many submodels, but only when the flexibility of the model is limited in other important respects.  In particular, when Markov switching models allow for switching levels of error variance, explosive root regimes occur in only a minority of the series.     

OPTIMAL FORECAST COMBINATION UNDER REGIME SWITCHING*

This article proposes a new forecast combination method that lets the combination weights be driven by regime switching in a latent state variable. An empirical application that combines forecasts from survey data and time series models finds that the proposed regime switching combination scheme performs well for a variety of macroeconomic variables. Monte Carlo simulations shed light on the type of data‐generating processes for which the proposed combination method can be expected to perform better than a range of alternative combination schemes. Finally, we show how time variations in the combination weights arise when the target variable and the predictors share a common factor structure driven by a hidden Markov process.     

CREDIBILITY, MACROECONOMIC FUNDAMENTALS AND MARKOV REGIME SWITCHES IN THE EMS

The main objective of this paper is to use the Markov regime‐switching modelling framework to describe and analyse the credibility of a number of countries participating in the European Monetary System during 1980–1998. Our credibility indicator, based on Hughes Hallet et al.'s (1997) methodology, is subject to discrete regime shifts and is made dependent on macroeconomic fundamentals. We carry out extensive testing to assess the specification of the Markov regime‐switching model and the potential existence of permanent breaks. A contribution of our paper is the specification of a multivariate Markov switching model that allows us to examine whether macroeconomic variables have asymmetric effects on credibility. Another contribution is the specification of a regime‐switching model with time‐varying transition probabilities, which enables us to determine whether changes in macroeconomic variables can trigger switches between the low and high credibility regimes. We find strong evidence of regime switching behaviour in all countries. Both the level of credibility and the transition probabilities display an asymmetric response to changes in macroeconomic variables, with the stance of fiscal policy exerting the most systematic influence in all countries.