EdgeWare FastGraph Version 3 - Manual (Page 56)

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Where:
X = A simple moving average =
Σ
X
i
/ N
X
i
= The daily NAV for days = 1, N
N = Total number of days for the calculation. The recommended value is 20 days.
σ = Standard Deviation =
[ Σ(
X
i
- X) / N
] 0.5
Adaptive Moving Average (AMA)
There are a number of different methods to calculate adaptive moving averages. Fast-
Graph uses the following equation:
AMA(day) = EMA ( N x EMA(day) - (N-1) x EMA(day
-1
))
Where:
day = current point in time series
day
-1
=current point in time series minus one
EMA = Exponential Moving Average
N = number of periods in the time series to use for smoothing
Hurst Exponent
A good book on the subject of the Hurst Exponent (HE) is Fractal Market Analysis by
Edgar E. Peters.
Interestingly, the HE development grew out of work by Einstein who found that the dis-
tance a random particle covers increases with the square root of time:
R = T
0.5
Where R = the distance covered
T = a time index
A process that changes with an exponent greater than 0.5 is said to be persistent or in
market terms, trending. A process that changes with an exponent less than 0.5 is antiper-
sistent or in market terms, trading range.
H.E. Hurst (1900-1978) studied river flows in his work as a dam builder. He noticed that
flood years tended to be followed by other flood years, i.e., not a random occurrence. He
developed a method to measure how persistent a process may be. The method is very