One common trading rule used by chartists is the moving average rule (Taylor and Allen, 1992). In its simplest form, a buy signal is generated when the market price is above a (long-period) moving average of that market price:
where s is the market price and n is the number of days in the moving average. Otherwise, a sell signal is generated.12
In practice, eq. (3.1) is replaced by more advanced trading rules."' For example, the market price today may be replaced by a short-period moving average. Thus, when a short-period moving average is above a long-period moving average, a buy signal is generated. The most popular moving average rules used in technical analysis are the 1-50, 1-150, 1-200, 2-200 and the 5-200 rules (Gencay, 1996b).
The 5-200 rule, for example, means that the short-period moving average includes 5 days and that the long-period moving average includes 200 days. Moreover, to avoid socalled whiplash signals, which are generated when the short-period and the longperiod moving averages are similar, a band between these moving averages may be introduced.
domestic currency one has to pay for one unit of foreign currency, a buy signal is generated when the market price, i. e. the exchange rate, is below a moving average of that market price. This is because a rising exchange rate indicates that the currency is losing value. 1 3" Assuming that the time evolution is continuous, Paper [iv] shows that an exponential moving
average of the past history of market prices:
where
where
Thus. this exponential moving average of the past history of market prices can be written as the market price today plus an infinite series of time derivatives of the market price today.
This observation may shed light on why delay coordinates, discussed in Section 2 above, work as a tool of phase space reconstruction, i. e. that the past and the future of an observed scalar time series contain information about unobserved state variables that can be used to define a state
Prof. Mikael Bask
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