Applications of state space models in finance

Chapter 4
Markov regime switching
Markov switching models of changing regimes are latent variable time series models.
The observation-generating distribution depends on an unobserved, or hidden, state
variable modeled as a Markov chain. Markov switching models, also commonly known
as hidden Markov models (HMMs), offer a high degree of flexibility and can be employed
for both univariate and multivariate series. A hidden Markov model represents a special
class of dependent mixtures and consists of two processes: an unobservable m-state
Markov chain that determines the state, or regime, and a state-dependent process of
observations. The hidden Markov model is closely related to the general linear Gaussian
state space model introduced in Chapter 3. Both models are state space models. The
major difference is that HMMs have discrete states, while the Kalman filter based state
space approach deals with unobserved continuous states. 9
While HMMs have been employed by engineers in the context of signal-processing,
over the last two decades extensive literature developed in automatic speech recognition,
biosciences, image processing and climatology, among others. Important references include
Baum and Petrie (1966), the tutorial by Rabiner (1989) and Ephraim and Merhav
(2002). Economic and financial researchers are also frequently confronted with time
series that experience changes in regime that are evoked by third factors. The shifts are
not observed directly, and usually it is unknwown which regime currently prevails. However,
it was not until the seminal works of Hamilton (1988, 1989, 1990) that economists
and financial econometricians started to apply HMMs. Hamilton introduced a homogeneous
Markov switching vector autoregressive model, in which the latent state process is
independent from exogenous variables. Lahiri and Wang (1996) studied the comparative
performance of various interest rate spreads as leading indicators for turning points of
the U.S. business cycle. They assumed the U.S. economy to shift between two states
with the shift between regimes being governed by a two-state Markov process. Fridman
(1994) proposed a two-state CAPM where the states represent two market regimes
of high and low volatility. The parameters are determined by an unobserved Markov
chain. Another well-known application to finance is conducted by Rydén et al. (1998)
9 For a review of the common properties of both concepts, see Roweis and Ghahramani
(1999).