A simple series with a collection of uncorrelated random variables with a mean of zero and a standard deviation of σ² is called white noise. In this, variables are independent and identically distributed. All values have the same variance of σ². In this case, the series is drawn from Gaussian distribution, and is called Gaussian white noise.

When the series turns out to be white noise, it implies that the nature of the series is totally random and there is no association within the series. As a result, the model can't be developed, and prediction is not possible in this scenario.

However, when we typically build a time series model with a nonwhite noise series, we try to attain a white noise phenomenon within the residuals or errors. In simple terms, whenever we try to build a model, the motive is to extract the maximum amount of information from the series so that no more information exists in the variable. Once we build a model, noise will always be part of it. The equation is...