1
00:00:00,880 --> 00:00:07,164
In this lecture, we'll be talking about
Introduction to moving average processes.

2
00:00:07,164 --> 00:00:08,501
We only have one objective.

3
00:00:08,501 --> 00:00:09,546
Objective is a full living.

4
00:00:09,546 --> 00:00:15,596
We would like to be able to
identify moving average processes.

5
00:00:15,596 --> 00:00:20,397
So, let me give you an intuition
using some stock price example.

6
00:00:20,397 --> 00:00:24,650
Let's say,
Xt is a stock price of some company and

7
00:00:24,650 --> 00:00:29,208
each daily announcement of
the company to the press,

8
00:00:29,208 --> 00:00:32,262
to the public is modeled as a noise.

9
00:00:32,262 --> 00:00:36,043
So we have Xt which is the price of
the company and then there's a noise,

10
00:00:36,043 --> 00:00:37,502
a noise of announcements.

11
00:00:37,502 --> 00:00:42,891
Noises are the announcements of the
company and let's say, these announcements

12
00:00:42,891 --> 00:00:47,587
are affecting the stock price and
that's the natural thing to assume.

13
00:00:47,587 --> 00:00:52,881
If there is an announcement today, well,
it will have an effect on the stock

14
00:00:52,881 --> 00:00:58,360
price and it is possible that effect of
the announcement might last a few days.

15
00:00:58,360 --> 00:01:04,213
Let's say, each announcements
affects my class two days,

16
00:01:04,213 --> 00:01:08,353
then we can think of
stock price as a model.

17
00:01:08,353 --> 00:01:12,692
We can think of the stock price
as a linear combination of

18
00:01:12,692 --> 00:01:15,195
the noises until two days back.

19
00:01:15,195 --> 00:01:18,584
So basically, Zt is the noise today.

20
00:01:18,584 --> 00:01:21,137
Zt-1 is the noise yesterday.

21
00:01:21,137 --> 00:01:25,361
Zt-2 is the noise from other day and

22
00:01:25,361 --> 00:01:30,955
all of them contributes
to my stock price today.

23
00:01:30,955 --> 00:01:35,865
Now Zt stand outs when it directly
contributes to the stock price, but

24
00:01:35,865 --> 00:01:38,778
it is possible that yesterday's noise,

25
00:01:38,778 --> 00:01:42,540
yesterday's announcement
might have less effect.

26
00:01:42,540 --> 00:01:43,632
So, we have a weight on it.

27
00:01:43,632 --> 00:01:49,083
So take the one or take the two would be
weight of announcements from yesterday and

28
00:01:49,083 --> 00:01:54,957
the other day, and this model is basically
one example of a moving average processes.

29
00:01:54,957 --> 00:01:58,162
This is called the moving
average model of order two.

30
00:01:58,162 --> 00:02:03,954
This is called order two,
because we go two dates backs.

31
00:02:03,954 --> 00:02:05,989
Now, you can think of MA(q) model.

32
00:02:05,989 --> 00:02:09,021
Q is the order of moving average model.

33
00:02:09,021 --> 00:02:13,840
Zt is a noise,
it contributes to the stock price or Xt.

34
00:02:13,840 --> 00:02:19,353
Zt-1 contributes to Xt and
it can go two days back

35
00:02:19,353 --> 00:02:25,668
as Zt-q also contributes to
the stock price Xt, today.

36
00:02:25,668 --> 00:02:31,040
So basically, Xt is a linear combination
of these noises few days back and

37
00:02:31,040 --> 00:02:33,738
I have theta 1, theta 2, theta q.

38
00:02:33,738 --> 00:02:37,935
These are the weights of the noises
from yesterday and so forth.

39
00:02:37,935 --> 00:02:41,492
And Zis here are basically independent,

40
00:02:41,492 --> 00:02:46,980
identically distributed random
variables and they are modeled

41
00:02:46,980 --> 00:02:52,784
as a normal random variable with
some mean and standard deviation.

42
00:02:52,784 --> 00:02:54,223
So, what have you learned in this lecture?

43
00:02:54,223 --> 00:02:58,798
You have learned how to identify
moving average processes MA(q) where

44
00:02:58,798 --> 00:02:59,780
q is the order.