Nonstationary Markov switching models of exchange rates: The pound-dollar exchange rate

The Markov switching model (MSM) is considered interesting because it captures nonlinearity and structural instability of economic time series subject to occasional regime shifts. Engel and Hamilton (1990) apply a MSM in an exchange rate analysis using a constant transition probability function. That is, they assume that the probability of switching from one state to the other is constant regardless of the status of the economy. However, the likelihood of government intervention or regulation--the main causes of regime changes-- usually is not independent of a country\u27s economic status. This dissertation proposes a nonstationary MSM, in the sense that the transition probability function is time varying and a function of market fundamentals. This specification emphasizes the role of real interest rate differentials in determining the direction of exchange rate movements. This dissertation develops maximum likelihood estimation procedures for four different specifications of the transition probability function--constant, linear, step, and logit--using the EM algorithm. Nonstationary MSM\u27s are estimated using quarterly data of the pound-dollar exchange rate from 1974 to 1989. Forecasting results show that nonstationary MSM\u27s outperform the constant transition probability model as well as the random walk model. For out-of-sample forecasting, nonstationary MSM\u27s outperform the random walk model, while the Engel-Hamilton mode does not. The results provide strong support for the nonstationary MSM; i.e., the exchange rate follows a switching-regime stochastic process which is driven by the real interest rate differential. The asymptotic properties of parameter estimates for MSM are investigated. This dissertation shows the consistency and asymptotic normality of maximum likelihood estimates for MSM and suggests the asymptotic covariance matrix which should consider the average outer product of score vectors as well as the second derivatives of the likelihood function