In our model, the conditional mean µt and the conditional variance ht of log exchange rate changes ∆_et are allowed to follow two different regimes, indicated by an unobservable state variable S_t. If S_t = 0, the exchange rate is driven by changes of observable fundamentals so that standard fundamentalist analysis provides sufficiently accurate forecasts. If, however, S_t = 1, dynamics of hidden fundamentals are predominant, suggesting the superior performance of technical analysis. The regime indicator S_t is parameterised as a first-order Markov process and the switching or transition probabilities P and Q have the typical Markov structure:

(21)

Thus, under conditional normality, an observed realization ∆_et is presumed to be drawn from a distribution if S_t= 0, whereas ∆_et is distributed if S_t = 1. The evolution of the log first differences of exchange rates can therefore be written as

(22)

where ε_t is an i.i.d. standard normal variable. The parameter estimations of the mean ( µ _t ) and variance (h_t) equations in the regime-switching model are derived from maximization of the log-likelihood function

(23)

is the probability that the analyzed process is in regime 1 at time t and is updated by means of Bayesian inference using information available at time t – 1. In the following, we specify the two types of forecasting strategies. Fundamentalist forecasts use external information to calculate a long-run equilibrium , to which the exchange rate reverts with a given speed θ over time, i.e.

(24)

We assume that the fundamental value can be described by purchasing power parity (ppp). Taylor and Allen (1992) provide evidence from survey data that foreign exchange market participants only accept ppp as a valid relationship in the long run, implying low values for θ. This view has recently been supported by Taylor and Peel (2000) and Taylor et al. (2001), showing that due to its nonlinear dynamics the exchange rate reverts to the ppp level, but only in the long run. Clearly, at the centre of the empirical examination is the oscillator model derived in the theoretical part of the paper. Following eq. (20), technical analysis predicts a future exchange rate increase by a positive difference between the short-run moving average (mashort) and longrun moving average (malong), and vice versa:

(25)

where parameter ψ is expected to be positive. As the theoretical results of section 3 suggest, the span of the short-run and long-run moving average should have little impact on the trading rule forecasting performance. Due to the interest parity condition, a significant fraction of daily exchange rate changes might be explained by changes of the interest differential. Since this is clearly not a matter of technical or fundamental analysis, either regime is augmented by the interest differential. To check for remaining autocorrelations we add an autoregressive term so that the mean equation of the regimes are estimated as follows⁶:

(26)(27)

The variance of ∆_et, i.e. the volatility of e_t, is assumed to be constant within regimes h_0t = σ²_F and h_1t = σ²_Cso that the only source of conditional heteroskedasticity is the regime-switching behavior. Since the quality of the trading signal (20) is sensitive to the impact of noise, chartist analysis is expected to be assigned to the low volatility regime.

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6 We have also experimented with a regime-dependent drift term. The resulting parameter estimates were statistically insignificant at all conventional levels so we omit them from the subsequent analysis.

Prof. Stefan Reitz

Next: Estimation results and specification tests

Summary: Index