00:01
Okay, so for a, we want to determine if the random walk model is stationary.
00:08
So, as a definition, a process yt is said to be stationary if its statistical properties do not change over time.
00:17
Specifically, for a process to be strictly stationary, the joint distribution of yt1 through ytk must be the same as the joint distribution of yt1 plus h to ytk plus h.
00:41
For all t1 through tk, h where k is any positive integer and h is any time shift.
00:55
So the standard model, random walk model is given as yt equals yt minus 1 plus ut, where ut is a random shock with mean 0 and some finite variance sigma squared, some random variable with mean 0 and variance sigma squared.
01:20
So as for the mean, the mean of yt depends on the sum of all previous shocks ui, which increases in magnitude as t increases, though its expected value remains 0.
01:37
Therefore, the mean of yt is not constant over time.
01:41
So mean of yt not constant.
01:48
As for the variance, the variance yt increases over time because it is the sum of the variances of the individual ut terms.
01:57
Specifically, the variance of yt after t periods is t times sigma squared, which clearly depends on t.
02:08
Now, since both the mean and variance yt change over time, the random walk model is not stationary.
02:23
B, so we want to answer is the random walk model difference walk model different stationary.
02:31
So a process is different stationary if difference in the series once results in stationary stationary process once or more times.
02:41
So consider we want to consider the first difference of yt which is yt minus yt minus 1 equals ut.
02:54
Now for mean we have that it is 0 and does not depend on t and for variance of delta yt the difference the variance of delta yt is the variance of ut which is sigma squared and also does not depend on t...