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Journal articles on the topic 'Markov Switching'

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Published: 4 June 2021

Last updated: 10 March 2023

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1

Guérin, Pierre, and Massimiliano Marcellino. "Markov-Switching MIDAS Models." Journal of Business & Economic Statistics 31, no. 1 (January 2013): 45–56. http://dx.doi.org/10.1080/07350015.2012.727721.

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2

Huang, Yu-Lieh. "Testing Markov switching models." Applied Economics 46, no. 17 (March 3, 2014): 2047–51. http://dx.doi.org/10.1080/00036846.2014.892201.

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3

Liu, Xiaochun. "Markov switching quantile autoregression." Statistica Neerlandica 70, no. 4 (October 12, 2016): 356–95. http://dx.doi.org/10.1111/stan.12091.

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4

Liu, Ji-Chun. "INTEGRATED MARKOV-SWITCHING GARCH PROCESS." Econometric Theory 25, no. 5 (October 2009): 1277–88. http://dx.doi.org/10.1017/s0266466608090506.

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This paper investigates stationarity of the so-called integrated Markov-switching generalized autoregressive conditionally heteroskedastic (GARCH) process, which is an important subclass of the Markov-switching GARCH process introduced by Francq, Roussignol, and Zakoïan (2001, Journal of Time Series Analysis 22,197–220) and a Markov-switching version of the integrated GARCH (IGARCH) process. We show that, like the classical IGARCH process, a stationary solution with infinite variance for the integrated Markov-switching GARCH process may exist. To this purpose, an alternative condition for the existence of a strictly stationary solution of the Markov-switching GARCH process is presented, and some results obtained in Hennion (1997, Annals of Probability 25, 1545–1587) are employed. In addition, we also discuss conditions for the existence of a strictly stationary solution of the Markov-switching GARCH process with finite variance, which is a modification of Theorem 2 in Francq et al. (2001).

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5

Nunian, Mohd Azizi Amin, Siti Meriam Zahari, and S. Sarifah Radiah Shariff. "Modelling foreign exchange rates: a comparison between markov-switching and markov-switching GARCH." Indonesian Journal of Electrical Engineering and Computer Science 20, no. 2 (November 1, 2020): 917. http://dx.doi.org/10.11591/ijeecs.v20.i2.pp917-923.

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Foreign exchange rate is important as it determines a country's economic condition. It is used to carry out transfers of purchasing power between two or more countries. Volatility in exchange rates may result in difficulty in decision making especially, in financial sectors as high volatility could increase the risk in exchange rates. Thus, Markov switching model is employed in this study as it is believed to be efficient in handling not only volatilility but also nonlinearity characteristics in exchange rates. The aims of this study are to model the foreign exchange rates using two models; Markov Switching (M-S) models and Markov Switching Generalized Autoregressive Conditional Heteroscedasticity (M-S GARCH) and to compare these two models based on log-likelihood, AIC and BIC criteria. This study used the quarterly data of foreign exchange rates for Singapore Dollar (SGD), Korean Won (KRW), China Yuan Renminbi (CNY), Japanese Yen (JPY) and the US Dollar (USD) against Malaysia Ringgit (MYR) which were collected from Quarter 4, 2006 to Quarter 1, 2018. The findings indicate that Markov Switching is the best model since it has the highest log-likelihood value, and the lowest AIC and BIC values. The results show that JPY and SGD have highly persistent trends on regime 1 with probability values 0.96 and 0.84, respectively as compared to CNY, KRW and USD, while the latter have high persistent trends on regime 2 with probability values, 0.99, 0.95, 0.82, respectively.

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6

Hou, Zhenting, Hailing Dong, and Peng Shi. "Asymptotic stability in the distribution of nonlinear stochastic systems with semi-Markovian switching." ANZIAM Journal 49, no. 2 (October 2007): 231–41. http://dx.doi.org/10.1017/s1446181100012803.

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abstractIn this paper, finite phase semi-Markov processes are introduced. By introducing variables and a simple transformation, every finite phase semi-Markov process can be transformed to a finite Markov chain which is called its associated Markov chain. A consequence of this is that every phase semi-Markovian switching system may be equivalently expressed as its associated Markovian switching system. Existing results for Markovian switching systems may then be applied to analyze phase semi-Markovian switching systems. In the following, we obtain asymptotic stability for the distribution of nonlinear stochastic systems with semi-Markovian switching. The results can also be extended to general semi-Markovian switching systems. Finally, an example is given to illustrate the feasibility and effectiveness of the theoretical results obtained.

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7

Fuh, Cheng-Der, Kwok Wah Remus Ho, Inchi Hu, and Ren-Her Wang. "Option Pricing with Markov Switching." Journal of Data Science 10, no. 3 (March 21, 2021): 483–509. http://dx.doi.org/10.6339/jds.201207_10(3).0008.

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8

Petričková, Anna. "Moments of Markov-Switching Models." Tatra Mountains Mathematical Publications 61, no. 1 (December 1, 2014): 131–40. http://dx.doi.org/10.2478/tmmp-2014-0032.

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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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9

Chiappa, Silvia. "Explicit-Duration Markov Switching Models." Foundations and Trends® in Machine Learning 7, no. 6 (2014): 803–86. http://dx.doi.org/10.1561/2200000054.

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10

Malyutov, M. B. "Offline fitting Markov switching model." Model Assisted Statistics and Applications 14, no. 3 (July 18, 2019): 193–213. http://dx.doi.org/10.3233/mas-190461.

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11

Tsionas, Efthymios G., and Subal C. Kumbhakar. "Markov switching stochastic frontier model." Econometrics Journal 7, no. 2 (November 25, 2004): 398–425. http://dx.doi.org/10.1111/j.1368-423x.2004.00137.x.

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12

Serletis, Apostolos, and Libo Xu. "Markov Switching Oil Price Uncertainty." Oxford Bulletin of Economics and Statistics 81, no. 5 (February 4, 2019): 1045–64. http://dx.doi.org/10.1111/obes.12300.

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13

Langrock, Roland, Thomas Kneib, Richard Glennie, and Théo Michelot. "Markov-switching generalized additive models." Statistics and Computing 27, no. 1 (December 28, 2015): 259–70. http://dx.doi.org/10.1007/s11222-015-9620-3.

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14

Timmermann, Allan. "Moments of Markov switching models." Journal of Econometrics 96, no. 1 (May 2000): 75–111. http://dx.doi.org/10.1016/s0304-4076(99)00051-2.

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15

ELLIOTT, ROBERT J., TAK KUEN SIU, and LEUNGLUNG CHAN. "OPTION PRICING FOR GARCH MODELS WITH MARKOV SWITCHING." International Journal of Theoretical and Applied Finance 09, no. 06 (September 2006): 825–41. http://dx.doi.org/10.1142/s0219024906003846.

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In this paper we develop a method for pricing derivatives under a Markov switching version of the Heston-Nandi GARCH (1, 1) model by using a well known tool from actuarial science, namely the Esscher transform. We suppose that the dynamics of the GARCH process switch over time according to one of the regimes described by the states of an observable Markov chain process. By augmenting the conditional Esscher transform with the observable Markov switching process, a Markov switching conditional Esscher transform (MSCET) is developed to identify a martingale measure for option valuation in the incomplete market described by our model. We provide an alternative approach for the derivation of an analytical option valuation formula under the Markov switching Heston-Nandi GARCH (1, 1) model. The use of the MSCET can be justified by considering a utility maximization problem with respect to a power utility function associated with the Markov switching risk-averse parameters.

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16

Sun, Zhongyang, Isabelle Kemajou-Brown, and Olivier Menoukeu-Pamen. "A risk-sensitive maximum principle for a Markov regime-switching jump-diffusion system and applications." ESAIM: Control, Optimisation and Calculus of Variations 24, no. 3 (2018): 985–1013. http://dx.doi.org/10.1051/cocv/2017039.

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In this paper, we derive a general stochastic maximum principle for a risk-sensitive type optimal control problem of Markov regime-switching jump-diffusion model. The results are obtained via a logarithmic transformation and the relationship between adjoint variables and the value function. We apply the results to study both a linear-quadratic optimal control problem and a risk-sensitive benchmarked asset management problem for Markov regime-switching models. In the latter case, the optimal control is of feedback form and is given in terms of solutions to a Markov regime-switching Riccatti equation and an ordinary Markov regime-switching differential equation.

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17

Yang, Haoyue, Hao Zhao, Zhuping Wang, and Xuemei Zhou. "ℋ∞ leader-following consensus of multi-agent systems with channel fading under switching topologies: a semi-Markov kernel approach." Intelligence & Robotics 2, no. 3 (2022): 223–43. http://dx.doi.org/10.20517/ir.2022.19.

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This paper focuses on the leader-following consensus problem of discrete-time multi-agent systems subject to channel fading under switching topologies. First, a topology switching-based channel fading model is established to describe the information fading of the communication channel among agents, which also considers the channel fading from leader to follower and from follower to follower. It is more general than models in the existing literature that only consider follower-to-follower fading. For discrete multi-agent systems, the existing literature usually adopts time series or Markov process to characterize topology switching while ignoring the more general semi-Markov process. Based on the advantages and properties of semi-Markov processes, discrete semi-Markov jump processes are adopted to model network topology switching. Then, the semi-Markov kernel approach for handling discrete semi-Markov jumping systems is exploited and some novel sufficient conditions to ensure the leader-following mean square consensus of closed-loop systems are derived. Furthermore, the distributed consensus protocol is proposed by means of the stochastic Lyapunov stability theory so that the underlying systems can achieve ℋ∞ consensus performance index. In addition, the proposed method is extended to the scenario where the semi-Markov kernel of semi-Markov switching topologies is not completely accessible. Finally, a simulation example is given to verify the results proposed in this paper. Compared with the existing literature, the method in this paper is more effective and general.

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18

Pan, Lijun, Jinde Cao, and Ahmed Alsaedi. "Stability of reaction–diffusion systems with stochastic switching." Nonlinear Analysis: Modelling and Control 24, no. 3 (April 23, 2019): 315–31. http://dx.doi.org/10.15388/na.2019.3.1.

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In this paper, we investigate the stability for reaction systems with stochastic switching. Two types of switched models are considered: (i) Markov switching and (ii) independent and identically distributed switching. By means of the ergodic property of Markov chain, Dynkin formula and Fubini theorem, together with the Lyapunov direct method, some sufficient conditions are obtained to ensure that the zero solution of reaction–diffusion systems with Markov switching is almost surely exponential stable or exponentially stable in the mean square. By using Theorem 7.3 in [R. Durrett, Probability: Theory and Examples, Duxbury Press, Belmont, CA, 2005], we also investigate the stability of reaction–diffusion systems with independent and identically distributed switching. Meanwhile, an example with simulations is provided to certify that the stochastic switching plays an essential role in the stability of systems.

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19

Anh, Nguyen Bao, and Yiqiang Q. Zhao. "Half Century of Gold Price: Regime-Switching and Forecasting Framework." International Journal of Financial Research 12, no. 3 (January 11, 2021): 1. http://dx.doi.org/10.5430/ijfr.v12n3p1.

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This paper studies the history of gold price in the international context using Markov-switching models. The literature surrounding the Markov-switching model is reviewed from the earliest iterations of Hamilton to recent developments. We show applicability of Markov stochastic process in forecasting commodity prices; in particular, the gold spot price. The research imposes the features of Markov regime-switching models, considering gold as a financial asset to offer a comprehensive methodology for forecasting commodity price. The paper discovers that applying Markov regime-switching could significantly improve the forecast abilities in commodity prices. Analysis of the model outcome indicates that the abnormal increases of gold price in history always resulted from special economic conditions. This study makes a novel contribution to the field by demonstrating that the impact of CPI change to gold price is subject to the regimes, which is more sophisticated than what has been commonly accepted in economics literature to date.

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20

Anh, Nguyen Bao, and Yiqiang Q. Zhao. "Half Century of Gold Price: Regime-Switching and Forecasting Framework." International Journal of Financial Research 12, no. 3 (January 11, 2021): 1. http://dx.doi.org/10.5430/ijfr.v12n3p1.

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This paper studies the history of gold price in the international context using Markov-switching models. The literature surrounding the Markov-switching model is reviewed from the earliest iterations of Hamilton to recent developments. We show applicability of Markov stochastic process in forecasting commodity prices; in particular, the gold spot price. The research imposes the features of Markov regime-switching models, considering gold as a financial asset to offer a comprehensive methodology for forecasting commodity price. The paper discovers that applying Markov regime-switching could significantly improve the forecast abilities in commodity prices. Analysis of the model outcome indicates that the abnormal increases of gold price in history always resulted from special economic conditions. This study makes a novel contribution to the field by demonstrating that the impact of CPI change to gold price is subject to the regimes, which is more sophisticated than what has been commonly accepted in economics literature to date.

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21

Djafri, Houria, and Soumia Kharfouchi. "Unilateral 2D Markov-switching autoregressive model." International Journal of Mathematics in Operational Research 18, no. 4 (2021): 433. http://dx.doi.org/10.1504/ijmor.2021.114208.

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22

Bohl,, Martin T., Arne C. Klein,, and Pierre L. Siklos. "A Markov Switching Approach to Herding." Credit and Capital Markets – Kredit und Kapital 49, no. 2 (June 2016): 193–220. http://dx.doi.org/10.3790/ccm.49.2.193.

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23

Boot, Tom, and Andreas Pick. "Optimal Forecasts from Markov Switching Models." Journal of Business & Economic Statistics 36, no. 4 (June 1, 2017): 628–42. http://dx.doi.org/10.1080/07350015.2016.1219264.

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24

Guérin, Pierre, Danilo Leiva-Leon, and Massimiliano Marcellino. "Markov-Switching Three-Pass Regression Filter." Journal of Business & Economic Statistics 38, no. 2 (October 16, 2018): 285–302. http://dx.doi.org/10.1080/07350015.2018.1497508.

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25

Cheung, Yin-Wong, and Ulf G. Erlandsson. "Exchange Rates and Markov Switching Dynamics." Journal of Business & Economic Statistics 23, no. 3 (July 2005): 314–20. http://dx.doi.org/10.1198/073500104000000488.

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26

Cheng, J. "A transitional Markov switching autoregressive model." Communications in Statistics - Theory and Methods 45, no. 10 (April 18, 2016): 2785–800. http://dx.doi.org/10.1080/03610926.2014.894065.

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27

Breunig, Robert, Serinah Najarian, and Adrian Pagan. "Specification Testing of Markov Switching Models*." Oxford Bulletin of Economics and Statistics 65, s1 (December 2003): 703–25. http://dx.doi.org/10.1046/j.0305-9049.2003.00093.x.

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28

Murray, Christian J., Alex Nikolsko-Rzhevskyy, and David H. Papell. "MARKOV SWITCHING AND THE TAYLOR PRINCIPLE." Macroeconomic Dynamics 19, no. 4 (May 12, 2014): 913–30. http://dx.doi.org/10.1017/s1365100513000667.

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Early research on the Taylor rule typically divided the data exogenously into pre-Volcker and Volcker–Greenspan subsamples. We contribute to the recent trend of endogenizing changes in monetary policy by estimating a real-time forward-looking Taylor rule with endogenous Markov switching coefficients and variance. The response of the interest rate to inflation is regime-dependent, with the pre- and post-Volcker samples containing monetary regimes where the Fed did and did not follow the Taylor principle. Although the Fed consistently adhered to the Taylor principle before 1973 and after 1984, it followed the Taylor principle from 1975 to 1979 and did not follow the Taylor principle from 1980 to 1984. We also find that the Fed only responded to real economic activity during the states in which the Taylor principle held. Our results are consistent with the idea that exogenously dividing postwar monetary policy into pre- and post-Volcker samples is misleading. The greatest qualitative difference between our results and recent research employing time-varying parameters is that we find that the Fed did not adhere to the Taylor principle during most of Paul Volcker's tenure, a finding that accords with the historical record of monetary policy.

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29

Chauvet, Marcelle, Chinhui Juhn, and Simon Potter. "Markov switching in disaggregate unemployment rates." Empirical Economics 27, no. 2 (March 1, 2002): 205–32. http://dx.doi.org/10.1007/s001810100101.

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30

Kim, Chang-Jin. "Dynamic linear models with Markov-switching." Journal of Econometrics 60, no. 1-2 (January 1994): 1–22. http://dx.doi.org/10.1016/0304-4076(94)90036-1.

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31

Krämer, Walter. "Long memory with Markov-Switching GARCH." Economics Letters 99, no. 2 (May 2008): 390–92. http://dx.doi.org/10.1016/j.econlet.2007.09.027.

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32

Taddy, Matthew A., and Athanasios Kottas. "Markov switching Dirichlet process mixture regression." Bayesian Analysis 4, no. 4 (December 2009): 793–816. http://dx.doi.org/10.1214/09-ba430.

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33

Otranto, Edoardo. "Adding flexibility to Markov Switching models." Statistical Modelling 16, no. 6 (November 28, 2016): 477–98. http://dx.doi.org/10.1177/1471082x16672025.

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Abstract: Very often time series are subject to abrupt changes in the level, which are generally represented by Markov Switching (MS) models, assuming that the level is constant within a certain state (regime). This is not a realistic framework because in the same regime the level could change with minor jumps with respect to a change of state; this is a typical situation in many economic time series such as the Gross Domestic Product (GDP) or the volatility of financial markets. We propose to make the state flexible, introducing a very general model which provides oscillations of the level of the time series within each state of the MS model; these movements are driven by a forcing variable. The new model allows for consideration of extreme jumps in a parsimonious way, without the adoption of a large number of regimes (in our examples the two-state MS models are used). Moreover, this model increases the interpretability and in particular the out-of-sample performance with respect to the most used alternative models. This approach can be applied in several fields, also using unobservable data. We show its advantages in three distinct applications, extending particular MS models, which involve macroeconomic variables, volatilities of financial markets and conditional correlations.

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34

Aliat, Billel, and Fayçal Hamdi. "On Markov-switching periodic ARMA models." Communications in Statistics - Theory and Methods 47, no. 2 (September 8, 2017): 344–64. http://dx.doi.org/10.1080/03610926.2017.1303734.

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35

Billio, Monica, and Silvio Di Sanzo. "Granger-causality in Markov switching models." Journal of Applied Statistics 42, no. 5 (January 22, 2015): 956–66. http://dx.doi.org/10.1080/02664763.2014.993367.

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36

Otranto, Edoardo. "The multi-chain Markov switching model." Journal of Forecasting 24, no. 7 (2005): 523–37. http://dx.doi.org/10.1002/for.965.

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37

Lanne, Markku, Helmut Lütkepohl, and Katarzyna Maciejowska. "Structural vector autoregressions with Markov switching." Journal of Economic Dynamics and Control 34, no. 2 (February 2010): 121–31. http://dx.doi.org/10.1016/j.jedc.2009.08.002.

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38

Karamé, Frédéric. "Asymmetries and Markov-switching structural VAR." Journal of Economic Dynamics and Control 53 (April 2015): 85–102. http://dx.doi.org/10.1016/j.jedc.2015.01.007.

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39

Farmer, Roger E. A., Daniel F. Waggoner, and Tao Zha. "Understanding Markov-switching rational expectations models." Journal of Economic Theory 144, no. 5 (September 2009): 1849–67. http://dx.doi.org/10.1016/j.jet.2009.05.004.

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40

Nikolsko-Rzhevskyy, Alex, and Ruxandra Prodan. "Markov switching and exchange rate predictability." International Journal of Forecasting 28, no. 2 (April 2012): 353–65. http://dx.doi.org/10.1016/j.ijforecast.2011.04.007.

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41

Foroni, Claudia, Pierre Guérin, and Massimiliano Marcellino. "Markov-switching mixed-frequency VAR models." International Journal of Forecasting 31, no. 3 (July 2015): 692–711. http://dx.doi.org/10.1016/j.ijforecast.2014.05.003.

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42

Johannesson, Pär. "Rainflow Cycles for Switching Processes with Markov Structure." Probability in the Engineering and Informational Sciences 12, no. 2 (April 1998): 143–75. http://dx.doi.org/10.1017/s026996480000512x.

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The concept of rainflow cycles is often used in fatigue of materials for analyzing load processes. Methods are developed for computation of the rainflow matrix for a random load that is changing properties over time due to changes of the system dynamics; for example, for a random vehicle load it could reflect different driving conditions. The random load is modeled by a switching process with Markov regime; that is, the random load changes properties according to a hidden (not observed) Markov chain.An algorithm is developed for a switching process where each part of the load is modeled by a Markov chain. As only the local extremes are of importance for rainflow analysis, another approach is to model the sequence of turning points by a Markov chain. The main result of this paper is an algorithm for computation of the rainflow matrix for a switching process where each part is described by a Markov chain of turning points. The algorithms are illustrated by numerical examples.

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43

Kim, Chang-Jin, Jeremy Piger, and Richard Startz. "Estimation of Markov regime-switching regression models with endogenous switching." Journal of Econometrics 143, no. 2 (April 2008): 263–73. http://dx.doi.org/10.1016/j.jeconom.2007.10.002.

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44

Vigfusson, Robert. "Switching between chartists and fundamentalists: a Markov regime-switching approach." International Journal of Finance & Economics 2, no. 4 (October 1997): 291–305. http://dx.doi.org/10.1002/(sici)1099-1158(199710)2:4<291::aid-jfe55>3.0.co;2-m.

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45

Ji, Hankang, Yuanyuan Li, Xueying Ding, and Jianquan Lu. "Stability analysis of Boolean networks with Markov jump disturbances and their application in apoptosis networks." Electronic Research Archive 30, no. 9 (2022): 3422–34. http://dx.doi.org/10.3934/era.2022174.

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<abstract><p>In this paper, the finite-time stability (FTS) of switched Boolean networks (SBNs) with Markov jump disturbances under the conditions of arbitrary switching signals is studied. By using the tool of the semi-tensor product, the equivalent linear-like form of SBNs with Markov jump disturbances is first established. Next, to facilitate investigation, we convert the addressed system into an augmented Markov jump Boolean network (MJBN), and propose the definition of the switching set reachability of MJBNs. A necessary and sufficient criterion is developed for the FTS of SBNs with Markov jump disturbances under the conditions of arbitrary switching signals. Finally, we give two examples to illustrate the effectiveness of our work.</p></abstract>

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46

Zhang, Mengzhe, and Leunglung Chan. "Saddlepoint Method for Pricing European Options under Markov-Switching Heston’s Stochastic Volatility Model." Journal of Risk and Financial Management 15, no. 9 (September 6, 2022): 396. http://dx.doi.org/10.3390/jrfm15090396.

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This paper evaluates the prices of European-style options when dynamics of the underlying asset is assumed to follow a Markov-switching Heston’s stochastic volatility model. Under this framework, the expected return and the long-term mean of the variance of the underlying asset rely on states of the economy modeled by a continuous-time Markov chain. There is evidence that the Markov-switching Heston’s stochastic volatility model performs well in capturing major events affecting price dynamics. However, due to the nature of the model, analytic solutions for the prices of options or other financial derivatives do not exist. By means of the saddlepoint method, an analytic approximation for European-style option price is presented. The saddlepoint method gives an effective approximation to option prices under the Markov-switching Heston’s stochastic volatility model.

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47

Liu, Kai, Xiaowu Mu, and Jumei Wei. "Stochastic Stability of Discrete-Time Switched Systems with a Random Switching Signal." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/191458.

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Necessary and sufficient condition for stochastic stability of discrete-time linear switched system with a random switching signal is considered in this paper, assuming that the switching signal allows fixed dwell time before a Markov switch occurs. It is shown that the stochastic stability of the system is equivalent to that of an auxiliary system with state transformations at switching time, whose switching signal is a Markov chain. The stochastic stability is studied using a stochastic Lyapunov approach. The effectiveness of the proposed approach is demonstrated by a numerical example.

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48

Valencia-Herrera, Humberto, and Francisco López-Herrera. "Markov Switching International Capital Asset Pricing Model, an Emerging Market Case: Mexico." Journal of Emerging Market Finance 17, no. 1 (February 26, 2018): 96–129. http://dx.doi.org/10.1177/0972652717748089.

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The article shows how the international capital asset pricing model (ICAPM) with Markov regime switching can model the asset returns in the emerging market of Mexico. For most assets, although significant, the international risk premium factor is not subject to regime switching, but the domestic factor is. The probabilities of regimes are correlated with the volatility of assets. A GARCH(1,1) Markov regime switching model offers better adjustment than a non-GARCH. JEL Classification: C58, F36, F65, G12, G15

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49

Higgins, Matthew L., and Frank Ofori-Acheampong. "A Markov Regime-Switching Model with Time-Varying Transition Probabilities for Identifying Asset Price Bubbles." International Journal of Economics and Finance 10, no. 4 (March 3, 2018): 1. http://dx.doi.org/10.5539/ijef.v10n4p1.

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In this paper, a Markov regime-switching model with time-varying transition probabilities is developed to identify asset price bubbles in the S&P 500 index. The model nests two different methodologies; a state-dependent regime-switching model and a Markov regime-switching model. Three bubble regimes are identified; dormant, explosive, and collapsing. Time-varying transition probabilities are specified for each of the nine possible transitions in the Markov regime-switching model. Estimation of the model is done using conditional maximum likelihood with the Hamilton filter. Results show that transition probabilities depend significantly on trading volume and relative size of the bubble. Overall, the model works well in detecting multiple bubbles in the S&P 500 between January 1888 and May 2010. Explosive bubbles tend to immediately precede recession periods, while collapsing bubbles tend to coincide with recession periods.

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Palmowski, Zbigniew, Łukasz Stettner, and Anna Sulima. "Optimal Portfolio Selection in an Itô–Markov Additive Market." Risks 7, no. 1 (March 25, 2019): 34. http://dx.doi.org/10.3390/risks7010034.

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Abstract:

We study a portfolio selection problem in a continuous-time Itô–Markov additive market with prices of financial assets described by Markov additive processes that combine Lévy processes and regime switching models. Thus, the model takes into account two sources of risk: the jump diffusion risk and the regime switching risk. For this reason, the market is incomplete. We complete the market by enlarging it with the use of a set of Markovian jump securities, Markovian power-jump securities and impulse regime switching securities. Moreover, we give conditions under which the market is asymptotic-arbitrage-free. We solve the portfolio selection problem in the Itô–Markov additive market for the power utility and the logarithmic utility.

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