We model the empirical observation that is described in the Introduction in the following way:
where Ec (.) and Ef (.) denote expectations of chartists and fundamentalists, respectively. E (.) is a weighted average of these expectations, where τ, the planning horizon, determines the weights. The most common model used by chartists is the moving average model (Taylor and Allen, 1992, and Lui and Mole, 1998). In this model, buying and selling signals are generated by two moving averages; a short-period and a long-period moving average, where a buy (sell) signal is generated when the short-period moving average rises above (falls below) the long-period moving average.
In its simplest form, the short-period moving average is the current exchange rate and the long-period moving average is an exponential moving average of past exchange rates (Bishop and Dixon, 1992). Thus, chartists expect an increase (a decrease) in the exchange rate when the current exchange rate is above (below) an exponential moving average of past exchange rates:
where η and MA denote the expected adjustment speed of the exchange rate and an exponential moving average of past exchange rates, respectively. Moreover, we model the long-period moving average as
Finally, following Dornbusch (1976), the expectations of fundamentalists are
where θ is the expected adjustment speed of the exchange rate to long-run equilibrium.
By Mikael Bask