In this lecture, we'll be talking about Introduction to moving average processes.
We only have one objective.
Objective is a full living.
We would like to be able to identify moving average processes.
So, let me give you an intuition using some stock price example.
Let's say, Xt is a stock price of some company and
each daily announcement of the company to the press,
to the public is modeled as a noise.
So we have Xt which is the price of the company and then there's a noise,
a noise of announcements.
Noises are the announcements of the company and let's say, these announcements
are affecting the stock price and that's the natural thing to assume.
If there is an announcement today, well, it will have an effect on the stock
price and it is possible that effect of the announcement might last a few days.
Let's say, each announcements affects my class two days,
then we can think of stock price as a model.
We can think of the stock price as a linear combination of
the noises until two days back.
So basically, Zt is the noise today.
Zt-1 is the noise yesterday.
Zt-2 is the noise from other day and
all of them contributes to my stock price today.
Now Zt stand outs when it directly contributes to the stock price, but
it is possible that yesterday's noise,
yesterday's announcement might have less effect.
So, we have a weight on it.
So take the one or take the two would be weight of announcements from yesterday and
the other day, and this model is basically one example of a moving average processes.
This is called the moving average model of order two.
This is called order two, because we go two dates backs.
Now, you can think of MA(q) model.
Q is the order of moving average model.
Zt is a noise, it contributes to the stock price or Xt.
Zt-1 contributes to Xt and it can go two days back
as Zt-q also contributes to the stock price Xt, today.
So basically, Xt is a linear combination of these noises few days back and
I have theta 1, theta 2, theta q.
These are the weights of the noises from yesterday and so forth.
And Zis here are basically independent,
identically distributed random variables and they are modeled
as a normal random variable with some mean and standard deviation.
So, what have you learned in this lecture?
You have learned how to identify moving average processes MA(q) where
q is the order.