Gibbs Sampling Approach to Markov Switching Models in Finance (original) (raw)
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Journal of Mathematics, 2014
We adopt aregime switchingapproach to study concrete financial time series with particular emphasis on their volatility characteristics considered in a space-time setting. In particular the volatility parameter is treated as an unobserved state variable whose value in time is given as the outcome of an unobserved, discrete-time and discrete-state, stochastic process represented by a suitable Markov chain. We will take into account two different approaches for inference on Markov switching models, namely, the classical approach based on the maximum likelihood techniques and the Bayesian inference method realized through a Gibbs sampling procedure. Then the classical approach shall be tested on data taken from theStandard & Poor’s 500and theDeutsche Aktien Indexseries of returns in different time periods. Computations are given for a four-state switching model and obtained numerical results are put beside by explanatory graphs which report the outcomes obtained exploiting both smoothi...
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Regime switching models, especially Markov switching models, are regarded as a promising way to capture nonlinearities in time series. Combining the elements of Markov switching models with full ARMA-GARCH models poses severe difficulties for the computation of parameter estimators. Existing methods can become completely unfeasible due to the full path dependence of such models. In this article we demonstrate how to overcome this problem. We formulate a full Markov switching ARMA-GARCH model and its Bayes estimator. This facilitates the use of Markov Chain Monte Carlo methods and allows us to develop an algorithm to compute the Bayes estimator of the regimes and parameters of our model. The approach is illustrated on simulated data and with returns from the New York Stock Exchange. Our model is then compared to other variants and proves clearly to be advantageous.
Parameter Estimation of Regime Switching Time Series Models using Gibbs Sampling
We study a method to estimate the unknown parameters of regime switching auto-regressive time series models of known order, where the switching process is Markov with unknown transition probabilities. We utilize Bayesian statistics to estimate the parameters through simulation with Gibbs sampling. Each of the parameters included in this model will have corresponding marginal posterior distributions. Once derived, the marginal posterior distributions provide a straightforward approach to the simulation. This method produces a sample from the joint posterior distribution of the parameters. We illustrate our implementation of the Gibbs sampler with plots of convergence. Full R source code is provided in the appendix.
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In this paper, the volatility of the return generating process of the market portfolio and the slope coefficient of the market model is assumed to follow a Markov switching process of order one. The results indicate very strong evidence of volatility switching behaviour in a sample of returns in the S&P500 index. In three of the thirty securities in the Dow Jones index, the estimated slope in the market model show strong switching behaviour. In these three securities the low risk state is more persistent than the high-risk state. For each security we estimate the conditional probabilities that the security is in the high (low) risk state given the market is in the high (low) volatility regime and show that this information can be used to classify securities into three distinct groups. There is no association between these groups and the securities' constant beta estimated in the market model and the Sharpe index. Some directions for further research are discussed.
Markov switching models for time series data with dramatic jumps
Sains Malaysiana, 2012
In this research, the Markov switching autoregressive (MS-AR) model and six different time series modeling approaches are considered. These models are compared according to their performance for capturing the Iranian exchange rate series. The series has dramatic jump in early 2002 which coincides with the change in policy of the exchange rate regime. Our criteria are based on the AIC and BIC values. The results indicate that the MS-AR model can be considered as useful model, with the best fit, to evaluate the behaviors of Iran's exchange rate.
This article makes an econometric analysis using the Markov Switching Autoregressive (MS-AR) model, with the objective of showing the dynamics presented by the main US stock market index, the S&P 500, because this index measures the performance of most capitalized companies in the United States market. The analysis covers the period from January 2005 to November 2020, when the subprime crisis occurred and the COVID-19 crisis began. In particular, two regimes (regime 1-low volatility and regime 2-high volatility) were used in the model so that the parameters of the S&P 500 index behave differently during economic crises with the representative regimes. The S&P 500 remained in regime 1 (low volatility) for five periods, totaling 110 months. In regime 2 (high volatility-2008 and 2020 crises), it remained for about 50 months, that is, 39 months in the 2008 crisis (including the global financial crisis-2009) and 11 months in the COVID-19 crisis. In addition, regime 1 is more persistent, that is, the probability of staying in that regime in a later period is 93,61% and a change to regime 2 of 6,39%. In regime 2, the probability of maintaining this regime in the period t + 1 is 92,52%, while the probability of changing to regime 1 is 7,42%.
Adding flexibility to Markov Switching models
Statistical Modelling, 2016
Very often time series are subject to abrupt changes in the level, which are generally represented by Markov Switching (MS) models, hypothesizing 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 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 flexibility of the model allows for consideration of extreme jumps in a parsimonious way (also in the simplest 2-state case), without the adoption of a larger number of regimes; moreover this model increases the interpretability and fitting of the data with respect to the analogous MS model. This approach can be applied in several fields, also using unobservable data. We show its advantages in three distinct applications, involving macroeconomic variables, volatilities of financial markets and conditional correlations.