Markov Switching Regression Model Research Articles

Endogenous Markov Switching Regression Models for High-Frequency Data Under Microstructure Noise

We present a novel method in analyzing microstructure noise of high-frequency data as a measurement error problem within an endogenous Markov-switching regression model. In this model, the regression disturbance and the latent state variable controlling the regime are correlated. We show that under endogeneity the popular realized variance estimator is biased and no longer converges to the integrated regime dependent volatility. Exploring intraday return data on foreign exchange rates, we find significant endogeneity at high frequencies. Similar to the popular volatility signature plot suggested by Andersen, Bollerslev, Diebold, and Labys (2000b), we propose an endogeneity plot, which indicates as to which sampling frequency the assumption of exogeneity of the state variable controlling the regime remains valid.

인플레이션 불확실성의 기업 설비투자에 대한 비대칭적 효과 분석

Inflation uncertainty is known to have deleterious effects on facilities investment by disturbing the corporate decision on the opportunity cost of investment. In this paper, we test the validity of this hypothesis in Korea by estimating the inflation uncertainty with both a time-varing parameter model with GARCH disturbances and the relative price volatility and then, estimate the facilities investment equation which includes those uncertainty indicators. The uncertainty indexes estimated by the above-mentioned methods continue to fluctuate even after the inflation rate has dropped dramatically reflecting the structural changes of Korea’s economy since the financial crisis in 1997. As a result of estimation of the investment equation by both OLS and GMM, we find the inflation uncertainty has a negative effect on facilities investment with a statistical significance. Moreover, by means of Markov-switching regression model utilized to verify the non-linearity of this relationship, we draw a conclusion that this negative effect of inflation uncertainty heightens asymmetrically during the downturn periods of business cycle.

Dating the Business Cycle in South Africa by Using a Markov-Switching Model

This paper applies a Markov-switching dynamic regression model to the real quarterly GDP time series from 1981 to 2010 in order to detect turning points in the South African business cycle. The model comprises several explicative variables. These include short- and long- term interest rates, monetary aggregates as well as the difference between long- and short-term interest rates. For all these variables, the possibility of dynamic lags was also considered. A chronology for the South African classical and growth cycles, using a quarterly algorithm is established. Application of this non-parametric procedure yields six complete cycles over the period 1960-2011.

Improving prediction of exchange rates using Differential EMD

Volatility is a key parameter when measuring the size of errors made in modelling returns and other financial variables such as exchanged rates. The autoregressive moving-average (ARMA) model is a linear process in time series; whilst in the nonlinear system, the generalised autoregressive conditional heteroskedasticity (GARCH) and Markov switching GARCH (MS-GARCH) have been widely applied. In statistical learning theory, support vector regression (SVR) plays an important role in predicting nonlinear and nonstationary time series variables. In this paper, we propose a new algorithm, differential Empirical Mode Decomposition (EMD) for improving prediction of exchange rates under support vector regression (SVR). The new algorithm of Differential EMD has the capability of smoothing and reducing the noise, whereas the SVR model with the filtered dataset improves predicting the exchange rates. Simulations results consisting of the Differential EMD and SVR model show that our model outperforms simulations by a state-of-the-art MS-GARCH and Markov switching regression (MSR) models.

Cyclical Bid Adjustments in Search-Engine Advertising

Keyword advertising, or sponsored search, is one of the most successful advertising models on the Internet. One distinctive feature of keyword auctions is that they enable advertisers to adjust their bids and rankings dynamically, and the payoffs are realized in real time. We capture this unique feature with a dynamic model and identify an equilibrium bidding strategy. We find that under certain conditions, advertisers may engage in cyclical bid adjustments, and equilibrium bidding prices may follow a cyclical pattern: price-escalating phases interrupted by price-collapsing phases, similar to an “Edgeworth cycle” in the context of dynamic price competitions. Such cyclical bidding patterns can take place in both first- and second-price auctions. We obtain two data sets containing detailed bidding records of all advertisers for a sample of keywords in two leading search engines. Our empirical framework, based on a Markov switching regression model, suggests the existence of such cyclical bidding strategies. The cyclical bid-updating behavior we find cannot be easily explained with static models. This paper emphasizes the importance of adopting a dynamic perspective in studying equilibrium outcomes of keyword auctions. This paper was accepted by Pradeep Chintagunta and Preyas Desai, special issue editors. This paper was accepted by Pradeep Chintagunta and Preyas Desai, special issue editors.

The Relation between Expected Returns and Volatility in the Brazilian Stock Market

This paper applies the Markov switching regression model of stock returns with volatility feedback of Turner, Startz and Nelson (1989), suitably extended to incorporate endogenous regime shifts, as in Kim, Piger and Startz (2008), to examine the intertemporal relationship between the risk premium and volatility in the Brazilian stock market over the period 1995-2011. The results suggest that there is a positive relationship between the risk premium and the expected volatility once the volatility feedback effect is taken into account. Unanticipated increases in volatility, in contrast, have a negative impact on the risk premium. This negative impact increasesby 50% when I account for endogeneity of regime shifts.

Gasoline Price Cycles Under Discrete Time Pricing

We characterise petrol pricing dynamics in an unusual policy environment. A timing restriction in the Western Australian market imposes discrete time pricing on petrol retailers, enabling us to observe the exact timing of price changes. We employ a Markov switching regression model, finding the existence of Edgeworth price cycles of a similar nature to those recently observed in some other retail petrol markets. Cycles are frequent, asymmetric, and of substantial amplitude. Importantly, firms change prices almost every period, limiting the relevance of the leading theory of Edgeworth cycles due to Maskin and Tirole (1988). We also discuss episodes of disruption and evolution of the price cycle.

Markov-switching models with endogenous explanatory variables II: A two-step MLE procedure

This paper proposes a two-step maximum likelihood estimation (MLE) procedure to deal with the problem of endogeneity in Markov-switching regression models. A joint estimation procedure provides us with an asymptotically most efficient estimator, but it is not always feasible, due to the ‘curse of dimensionality’ in the matrix of transition probabilities. A two-step estimation procedure, which ignores potential correlation between the latent state variables, suffers less from the ‘curse of dimensionality’, and it provides a reasonable alternative to the joint estimation procedure. In addition, our Monte Carlo experiments show that the two-step estimation procedure can be more efficient than the joint estimation procedure in finite samples, when there is zero or low correlation between the latent state variables.

Markov-switching model selection using Kullback–Leibler divergence

In Markov-switching regression models, we use Kullback-Leibler (KL) divergence between the true and candidate models to select the number of states and variables simultaneously. In applying Akaike information criterion (AIC), which is an estimate of KL divergence, we find that AIC retains too many states and variables in the model. Hence, we derive a new information criterion, Markov switching criterion (MSC), which yields a marked improvement in state determination and variable selection because it imposes an approriate penalty to mitigate the over-retention of states in the Markov chain. MSC performs well in Monte Carlo studies with single and multiple states, small and large samples, and low and high noise. Furthermore, it not only applies to Markov-switching regression models, but also performs well in Markov-switching autoregression models. Finally, the usefulness of MSC is illustrated via applications to the U.S. business cycle and the effectiveness of media advertising.

Markov-Switching Model Selection Using Kullback-Leibler Divergence

In Markov-switching regression models, we use Kullback-Leibler (KL) divergence between the true and candidate models to select the number of states and variables simultaneously. In applying Akaike information criterion (AIC), which is an estimate of KL divergence, we find that AIC retains too many states and variables in the model. Hence, we derive a new information criterion, Markov switching criterion (MSC), which yields a marked improvement in state determination and variable selection because it imposes an appropriate penalty to mitigate the over-retention of states in the Markov chain. MSC performs well in Monte Carlo studies with single and multiple states, small and large samples, and low and high noise. Furthermore, it not only applies to Markov-switching regression models, but also performs well in Markov-switching autoregression models. Finally, the usefulness of MSC is illustrated via applications to the U.S. business cycle and the effectiveness of media advertising.

Markov-Switching Models with Endogenous Explanatory Variables II: A Two-Step MLE Procedure with Standard-Error Correction

This paper provides a unified framework for a two-step MLE procedure to deal with the problem of endogeneity in Markov-switching regression models. Two important issues are considered. First, a consistent estimation of the Markov-switching regression equation of interest is considered. Second, obtaining correct standard errors of the coefficients estimates in the second step is considered, in light of Pagan's (1984) 'generated regressors.' Our Monte Carlo experiments provide the validity of the proposed methods in small samples. The model and the proposed methods are applied to Campbell and Mankiw's (1989) consumption function, by allowing for possibilities of structural breaks in the sensitivity of consumption growth to the predictable component of income growth. Empirical results suggest that during the 1970's and 1980's, when uncertainty in future income growth was highest, the measure of sensitivity was high and statistically significant, while it was not significant in the rest of the sample.

Markov-switching models with endogenous explanatory variables

The maximum likelihood estimation of a Markov-switching regression model based on the Hamilton filter is not valid in the presence of endogenous explanatory variables. However, we show that there exists an appropriate transformation of the model that allows us to directly employ the Hamilton filter. The transformed model explicitly allows for a vector of bias correction terms as additional regressors, and the new disturbance term is uncorrelated with all the regressors in the transformed model. Within this framework, a quasi maximum likelihood estimation procedure is presented. A procedure to test for endogeneity based on the Wald statistic or the likelihood ratio statistic is also presented.

Fundamentals and asset price dynamics

The relation between fundamentals and asset returns is analyzed by means of Markov-switching regression models with time-varying transition probabilities. By referring to the Italian Stock Exchange over the 1973-2002 period, we find that (i) returns ‘switch’ between a zero-expected return/low volatility state and a high expected return/high volatility state; (ii) states are persistent and hence state changes can be forecast to some extent; (iii) the probability of state changes can be explained in terms of changes in the fundamentals; (iv) fundamentals do not have a direct impact on the expected returns but they only affect the transition probability matrix. Overall, our results show that a non-linear relation between market price changes and market fundamentals can be caught within the framework of (Markov) switching regession models.

Finite-sample properties of the bootstrap estimator in a Markov-switching model

The size distortion problem is clearly indicative of the small-sample approximation in the Markov-switching regression model. This paper shows that the bootstrap procedure can relieve the effects that this problem has. Our Monte Carlo simulation results reveal that the bootstrap maximum likelihood asymptotic approximations to the distribution can often be good when the sample size is small.

Social interactions and fluctuations in birth rates

Fluctuations in birth rates in developed countries have been considerably less regular than many explanatory theories suggest. This paper argues that social interaction, i.e., the dependence of individuals' fertility decisions on the fertility behaviour of other population members, is relevant even in developed countries. A formal model for investigating the static and dynamic consequences of social interaction for fertility is developed, and its aggregate implications are tested using a Markov switching regression model. The findings show that social interaction can lead to fluctuations in birth rates that are swift and difficult to foresee, and that these fluctuations are likely to be asymmetric: spells of low fertility have a considerably higher persistence than spells of high fertility. The paper suggests that high birth rates are likely to be followed by spells of low fertility. Transitions from low to high fertility occur at a substantially lower rate than transitions in the opposite direction.

A dynamic programming approach to the estimation of markov switching regression models

This paper suggests an alternative two-stage estimation method for Markov Switching Regression models. The procedure, based on the Maximum A Posteriori (MAP) decision rule, is essentially related to Bellman's dynamic programming algorithm. Monte Carlo results indicate that this procedure is a good alternative to Hamilton's method. The empirical application shows that the dating of the U.S. business cycles by the MAP procedure is closer to the dating by NBER than that given by Hamilton's method.