A high-order Markov-switching model for risk measurement

In this paper, we introduce a discrete-time higher-order Markov-switching (HMS) model for measuring the risk of a portfolio. We suppose that the logarithmic returns from a risky portfolio is governed by a HMS model with the drift and the volatility switch over time according to the states of a discrete-time higher-order hidden Markov model (HHMM). We interpret the states of the HHMM as unobservable states of an economy. The HHMM can incorporate the persistence or the long-range dependence of the economic states, which may due to business cycles. We adopt Value-at-Risk (VaR) as proxies of risk and investigate the impact of long-range dependence on risk measurement by comparing the VaR obtained from the HMS model and those evaluated from the first-order Markov-switching model through back-testing.