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I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of Markov Switching models to fit the data, filter unknown regimes and states on the basis of the data, to allow a powerful tool to test hypotheses formulated in light of financial theories, and to their forecasting performance with reference to both point and density predictions. The review covers papers concerning a multiplicity of sub-fields in financial economics, ranging from empirical analyses of stock returns, the term structure of default-free interest rates, the dynamics of exchange rates, as well as the joint process of stock and bond returns.

This paper attempts to interpret the Bartholomew (1973) index of mobility in terms of a directional mobility index based on the one-step expected states of movement corresponding to a specific state of transition matrix. A partial ordering of directional mobility of a general state of transition matrices, referred to as “upward mobility favoring sequential averaging (UMFSA),” is proposed using the algebraic equivalent of the generalized Lorenz ordering of expected states. When the underlying mobility depends on the initial distribution of the states, using a Bayesian approach, the indices are reexamined for a general class of matrices. This enables us to interpret the Prais (1955) and Bibby (1975) mobility index in this framework.

I survey applications of Markov switching models to the asset pricing and portfolio choice literatures. In particular, I discuss the potential that Markov switching models have to fit financial time series and at the same time provide powerful tools to test hypotheses formulated in the light of financial theories, and to generate positive economic value, as measured by risk-adjusted performances, in dynamic asset allocation applications. The chapter also reviews the role of Markov switching dynamics in modern asset pricing models in which the no-arbitrage principle is used to characterize the properties of the fundamental pricing measure in the presence of regimes.

“It should also be noted that the objective of convergence and equal distribution, including across under-performing areas, can hinder efforts to generate growth. Contrariwise, the objective of competitiveness can exacerbate regional and social inequalities, by targeting efforts on zones of excellence where projects achieve greater returns (dynamic major cities, higher levels of general education, the most advanced projects, infrastructures with the heaviest traffic, and so on). If cohesion policy and the Lisbon Strategy come into conflict, it must be borne in mind that the former, for the moment, is founded on a rather more solid legal foundation than the latter” European Commission (2005, p. 9)Adaptation of Cohesion Policy to the Enlarged Europe and the Lisbon and Gothenburg Objectives.

We compare the finite sample power of short- and long-horizon tests in nonlinear predictive regression models of regime switching between bull and bear markets, allowing for time varying transition probabilities. As a point of reference, we also provide a similar comparison in a linear predictive regression model without regime switching. Overall, our results do not support the contention of higher power in longer horizon tests in either the linear or nonlinear regime switching models. Nonetheless, it is possible that other plausible nonlinear models provide stronger justification for long-horizon tests.

In scientific works on forecasting price volatility (of which the overwhelming majority, in comparison with works on price forecasting) for energy products: crude oil, natural gas, fuel oil, the authors compared the effectiveness of forecasting models of generalized autoregressive heteroscedasticity (Generalized Autoregressive Conditional Heteroscedastic model, GARCH) with regression of support vectors for futures contracts. GARCH models are a standard tool used in the literature on volatility, and the vector machine nonlinear regression model is one of the machine learning methods that has been gaining huge popularity in recent years. The authors have shown that the accuracy of volatility forecasts for energy and aluminum prices significantly depends on the volatility proxy used. The model with correctly defined parameters can lead to fewer prediction errors than GARCH models when the square of the daily yield is used as an indicator of volatility in the evaluation. In addition, it is difficult to choose the best model among GARCH models, but forecasts based on asymmetric GARCH models are often the most accurate. The work is based on a model with a representative investor who solves the problem of optimizing utility in a two-period model. The key assumption of the model is the homogeneity of energy and aluminum investor preferences, that is, preferences do not change over time. There are also works with an attempt to solve this problem in a continuous state space. A completely new theory has been put forward that allows predicting the movement of the underlying asset without using historical data, so this topic is very relevant.