Markov-Switching Models with State-Dependent Time-Varying Transition Probabilities

Markov switching models are a family of models that introduces time variation in the parameters in the form of their state, or regime-specific values. This time variation is governed by a latent discrete-valued stochastic process with limited memory. More specifically, the current value of the state indicator is determined by the value of the state indicator from the previous period only implying the Markov property. A transition matrix characterizes the properties of the Markov process by determining with what probability each of the states can be visited next period conditionally on the state in the current period. This setup decides on the two main advantages of the Markov switching models: the estimation of the probability of state occurrences in each of the sample periods by using filtering and smoothing methods and the estimation of the state-specific parameters. These two features open the possibility for interpretations of the parameters associated with specific regimes combined with the corresponding regime probabilities. The most commonly applied models from this family are those that presume a finite number of regimes and the exogeneity of the Markov process, which is defined as its independence from the model’s unpredictable innovations. In many such applications, the desired properties of the Markov switching model have been obtained either by imposing appropriate restrictions on transition probabilities or by introducing the time dependence of these probabilities determined by explanatory variables or functions of the state indicator. One of the extensions of this basic specification includes infinite hidden Markov models that provide great flexibility and excellent forecasting performance by allowing the number of states to go to infinity. Another extension, the endogenous Markov switching model, explicitly relates the state indicator to the model’s innovations, making it more interpretable and offering promising avenues for development.

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Moments of Markov-Switching Models

Tatra Mountains Mathematical Publications ◽

10.2478/tmmp-2014-0032 ◽

2014 ◽

Vol 61 (1) ◽

pp. 131-140

Author(s):

Anna Petričková

Keyword(s):

Time Series ◽

Regime Switching ◽

Switching Time ◽

Markov Switching ◽

Central Moment ◽

Time Series Models ◽

Markov Switching Models ◽

State Dependent ◽

Switching Models ◽

Dependent Model

Abstract In this paper we have focused on the class of regime-switching time series models with regimes determined by unobservable variables, concretely Markov-switching models. We have derived 2nd central moment of the MSW models for two cases-state-independent and state-dependent model

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Re-examining covariance risk dynamics in international stock markets using quantile regression analysis

Acta Oeconomica ◽

10.1556/aoecon.61.2011.1.3 ◽

2011 ◽

Vol 61 (1) ◽

pp. 33-59 ◽

Cited By ~ 3

Author(s):

M. Li ◽

S. Yen

Keyword(s):

Quantile Regression ◽

Stock Markets ◽

Markov Switching ◽

Garch Models ◽

Time Varying ◽

Bear Market ◽

Markov Switching Models ◽

International Stock Markets ◽

Switching Models ◽

Risk Dynamics

This investigation is one of the first to adopt quantile regression (QR) technique to examine covariance risk dynamics in international stock markets. Feasibility of the proposed model is demonstrated in G7 stock markets. Additionally, two conventional random-coefficient frameworks, including time-varying betas derived from GARCH models and state-varying betas implied by Markov-switching models, are employed and subjected to comparative analysis. The empirical findings of this work are consistent with the following notions. First, the beta smile (beta skew) curve for the Italian, U.S. and U.K. (Canadian, French and German) markets. That is, covariance risk among global stock markets in extremely bull and/or bear market states is significantly higher than in stable periods. Additionally, the Japanese market provides a special case, and its beta estimate at extremely bust state is significantly lower, not higher than that at the middle region. Second, the quantile-varying betas are identified as possessing two key advantages. Specifically, the comparison of the system with quantile-varying betas against that with time-varying betas implied by GARCH models provides meaningful implications for correlation-volatility relationship among international stock markets. Furthermore, the quantile-varying beta design in this study relaxes a simple dual beta setting implied by Markov-switching models of Ramchand — Susmel (1998) and can identify dynamics of asymmetry in betas.

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

SSRN Electronic Journal ◽

10.2139/ssrn.516683 ◽

2004 ◽

Cited By ~ 1

Author(s):

Chang-Jin Kim

Keyword(s):

Error Correction ◽

Standard Error ◽

Markov Switching ◽

Explanatory Variables ◽

Markov Switching Models ◽

Switching Models

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A Markov-Switching VSTOXX Trading Algorithm for Enhancing EUR Stock Portfolio Performance

Mathematics ◽

10.3390/math9091030 ◽

2021 ◽

Vol 9 (9) ◽

pp. 1030

Author(s):

Oscar V. De la Torre-Torres ◽

Evaristo Galeana-Figueroa ◽

José Álvarez-García

Keyword(s):

Markov Switching ◽

Stock Index ◽

Portfolio Performance ◽

Trading Costs ◽

Weighting Method ◽

Treasury Bills ◽

Markov Switching Models ◽

Switching Models ◽

Asset Portfolio ◽

Stock Portfolio

In the present paper, we test the benefit of using Markov-Switching models and volatility futures diversification in a Euro-based stock portfolio. With weekly data of the Eurostoxx 50 (ESTOXX50) stock index, we forecasted the smoothed regime-specific probabilities at T + 1 and used them as the weighting method of a diversified portfolio in ESTOXX50 and ESTOSS50 volatility index (VSTOXX) futures. With the estimated smoothed probabilities from 9 July 2009 to 29 September 2020, we simulated the performance of three theoretical investors who paid different trading costs and invested in ESTOXX50 during calm periods (low volatility regime) or VSTOXX futures and the three-month German treasury bills in distressed or highly distressed periods (high and extreme volatility regimes). Our results suggest that diversification benefits hold in the short-term, but if a given investor manages a two-asset portfolio with ESTOXX50 and our simulated portfolios, the stock portfolio’s performance is enhanced significantly, in the long term, with the presence of trading costs. These results are of use to practitioners for algorithmic and active trading applications in ESTOXX50 ETFs and VSTOXX futures.

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Modeling and forecasting of rainfall reoccurrence changes using Markov Switching in Iran

SN Applied Sciences ◽

10.1007/s42452-021-04728-9 ◽

2021 ◽

Vol 3 (8) ◽

Author(s):

Majid Javari

Keyword(s):

Environmental Planning ◽

Rainfall Variability ◽

Markov Switching ◽

Daily Rainfall ◽

First Order ◽

Markov Switching Models ◽

Markov Transition Matrix ◽

Switching Models ◽

Markov Transition ◽

Modeling And Forecasting

AbstractThis paper represents the recurrence (reoccurrence) changes in the rainfall series using Markov Switching models (MSM). The switching employs a dynamic pattern that allows a linear model to be combined with nonlinearity models a discrete structure. The result is the Markov Switching models (MSM) reoccurrence predicting technique. Markov Switching models (MSM) were employed to analyze rainfall reoccurrence with spatiotemporal regime probabilities. In this study, Markov Switching models (MSM) were used based on the simple exogenous probability frame by identifying a first-order Markov process for the regime probabilities. The Markov transition matrix and regime probabilities were used to analyze the rainfall reoccurrence in 167 synoptic and climatology stations. The analysis results show a low distribution from 0.0 to 0.2 (0–20%) per day spatially from selecting stations, probability mean of daily rainfall recurrence is 0.84, and a different distribution based on the second regime was found to be more remarkable to the rainfall variability. The rainfall reoccurrence in daily rainfall was estimated with relatively low variability and strong reoccurrence daily with ranged from 0.851 to 0.995 (85.1–99.5%) per day based on the spatial distribution. The variability analysis of rainfall in the intermediate and long variability and irregular variability patterns would be helpful for the rainfall variability for environmental planning.

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