Forex Analysis Models - Simple Sinusoidal Model

In Forex trading, if security prices were not cyclical, they would tend to go off the top or bottom of the charts. This alone justifies the examination of a simple sinusoidal model. The current method identifies the most dominant sinusoidal in the time series using the conventional model:
where,

Y (x ) = A * cos(x * θ)+ B * sin(x * θ)+ µ

x the independent variable, time

Y(x) the dependent variable, the price at time index x

A cosine amplitude

B sine amplitude

frequency, expressed as cycles per time unit

the arithmetic mean of the time series.

The crux of this regression is based on a fundamental trigono- metric identity, specifically the following multiple-angle relationship:

cos nθ = 2 cosθ cos(n − 1)θ − cos(n − 2)θ

Once the frequency has been isolated and extracted, the two amplitudes can be calculated relatively simply.

In forex trading, unfortunately, very few security time series exhibit a distinct single-cycle property for prolonged periods of time. However, the sinusoidal regression may be applied iteratively. That is, calculate the primary cycle coefficients, and remove that cycle from the original time series. Then perform the regression a second or third time.