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.
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 (sum-of-squares), then that statistic is chi-square distributed over degree of freedom, directly dependent on the k number of lags.
I will demonstrate this with example:
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So far, we have managed to find the sum of squares of a acf-series with k = 10 = number of lags.
Now, we will check whether or not it is less than quantile 0.95 of a
k degree of freedom.
For that, include
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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