This is the well known ARMA model
AR stand for "Auto-Regressive" and MA stands for "Moving Average"
A moving average uses past input data, so price data in case of trading, and assigns weights to each price in the past.
this is also called a FIR filter (Finite Impulse Response)
FIR are best in a non realtime situation because they filter with linear phase conservation but wil a high group delay (n/2)
a very simple FIR filter is the SMA (Simple Moving Average)
but in, trading we don't really care about phase, we mostly care about low lag
this is where the IIR filter comes into play :
A regressive approach uses the output of the filter in the computation of the filter. so this is a recursive way of filtering
this is also called an IIR filter (Infinite Impulse Response)
a very simple IIR is the EMA (Exponential Moving Average)
of course you can combine both worlds, and EMAs NEED to have a Moving Average part, otherwise it would be always equals to zero;
example Y = 1.2 * Y(t-1) is always equals to 0 because the previous EMA value is unknown
let's look at formulas :
Code: Select all
SMA= (A0 + A1 + A2 + ... + An-1)/n
where:
An =Price of an asset at period n
n=Number of total periods
Code: Select all
EMA=Price(t)×k+EMA(y)×(1−k)
where:
t=today
y=yesterday
N=number of days in EMA
k=2÷(N+1)
another difference between the two, is that the EMA, because it uses EMA values from the previous day, will not be coherent from beginning to finish. the filter will slowly go towards its final value. It means that to be accurate, you need to process a high number of bars before having the EMA close to its right value
Two types of filters are not the only ones. Some imply much different types of filterings (like Jurik, SSA, ROF, Beltrami, Linear Regression, Wavelets, etc) to cite a few.
But this is not the purpose of this post.
Jeff
