Abstract
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 smoothing and filtering algorithms used in the estimation/calibration procedures we proposed to infer on the switching model parameters.
Highlights
Many financial time series are characterized by abrupt changes in their behaviour, a phenomena that can be implied by a number of both endogeneous and exogeneous facts, often far from being forecasted
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 smoothing and filtering algorithms used in the estimation/calibration procedures we proposed to infer on the switching model parameters
In this work we have shown how a four-state Regime Switching Model can be successfully exploited to study the volatility parameter which strongly characterizes concrete financial time series
Summary
Many financial time series are characterized by abrupt changes in their behaviour, a phenomena that can be implied by a number of both endogeneous and exogeneous facts, often far from being forecasted Examples of such changing factors can be represented, for example, by large financial crises, government policy and political instabilities, natural disasters, and speculative initiatives. The simplest type of structure considers two regimes; that is, Ω = {1, 2} and at most one switch in the time series: in other words, the first m (unknown) observations relate regime 1, while the remaining n − m data concern regime 2 Such an approach can be generalized allowing the system to switch back and forth between the two regimes, with a certain probability.
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