Hi everyone,
After completing and verifying the integrity of all tests and Ruby versions, I and Claudio started with implementation of Wald Test. He explained it pretty well and was very patient. :)
Wald test is used to test if a series of n acf or pacf indeces are equal to 0.
For acf
, the distribution for a white noise sationary process are approximately independent and identically distributed normal random variables with mean 0 and variance n^{1.}
What that means is, if terms in an acf
of a timeseries with k lags are squared and added (sumofsquares), then that statistic is chisquare distributed over degree of freedom, directly dependent on the k number of lags.
I will demonstrate this with example:
1 2 3 4 5 6 7 8 9 10 11 12 

So far, we have managed to find the sum of squares of a acfseries with k = 10 = number of lags.
Now, we will check whether or not it is less than quantile 0.95 of a chisquare
with k
degree of freedom.
For that, include Distribution
as:
1 2 3 4 5 6 7 

This verifies the Wald test.
The tests can be found on Github repository at: https://github.com/AnkurGel/statsample/blob/master/test/test_wald2.rb
Cheers,
Ankur Goel