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.