Forex Analysis Method- Autoregression

The premise behind autoregressive methods is that previous values in the time series directly influence the current value in the time series. Mathematically, this can be expressed as

Yx +1 = AYx + BYx −1 + CYx −2 + ε

where,

x the time increment

Y(x) the price at time index x

A the first regression coefficient

B the second regression coefficient

C the third regression coefficient

ε the error factor, whose sum approximates zero

This equation infers that the time-series closing price on any given day is the sum of the closing prices on the three previous days, all adjusted by regression coefficients. The number of inde- pendent variables on the right side of the equation determines the autoregressive order of the model.

Autoregression has numerous supporters in the realm of techni- cal analysis. It also has several variations and enhancements, such as the autoregressive integrated moving-average (ARIMA) time-series model introduced by George Box and Gwilym Jenkins in the early 1970s. This model frequently is designated as the ARIMA( p, d, q ) model, where p is the autoregressive order, d is differencing order, and q is the moving-average order.

Forex Analysis Models - Fourier Transform Model

In Forex trading, the fast Fourier transform is another popular method among technical analysts for extracting cycles from a time series. The basic assumption is that any (well-behaved) curve can be approximated as the sum of a finite number of sinusoidals and is based on the following Fourier series:

Yx = A0 /2 + ΣAn cos(nπx /L)+ ΣBn sin(nπx /L)

The transform operations calculate the values for the cosine amplitudes A and the sine amplitudes B in a similar fashion to the simple trigonometric regression above. Most analysts prefer to download an Internet utility to handle the complexities rather than code it themselves.

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.

Forex Analysis-Formula

In Forex trading, within the technical analysis family, econometric models are unique because they belong to the only category that generates a continuous stream of discrete numeric values as the forecast. For example, if the analyst has determined that a particular time series exhibits distinctly linear properties, then the following linear regression model should be used:

Y (x ) = Ax + B + ε

where,

x the independent variable, time


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

A the slope

B the intercept

ε the error factor whose sum approximates zero.

By solving for the regression coefficients A and B, the trader can estimate the next value in the time series Y(·) by incrementing the value of x in the linear model.

Technical FOREX Analysis

Technical analysis consists primarily of a variety of technical studies, each of which can be interpreted to predict market direction or to generate buy and sell signals. Many technical stud- ies share one common important tool: a price-time chart that emphasizes selected characteristics in the price motion of the underlying security. One great advantage of technical analysis is its “visualness.”

FOREX-IDENTIFYING PRICE FORMATIONS
In forex trading, proper identification of an ongoing trend can be a tremendous asset to a trader. However, the trader also must learn to recognize recurring chart patterns that disrupt the continuity of trend lines. Broadly speaking, these chart patterns can be categorized as reversal patterns and continuation patterns.

FOREX-REVERSAL PATTERNS
In forex trading, reversal patterns are important because they inform the trader that a market entry point is unfolding or that it may be time to liq- uidate an open position.

FOREX-CONTINUATION PATTERNS
In forex trading, continuation pattern implies that while a visible trend was in progress, it was interrupted temporarily and then continued in the direction of the original trend.

The proper identification of a continuation pattern may prevent a trader from entering a new trade in the wrong direction or from exiting a winning position too early.