White noise

I'd like to talk about a very special time series in this section: the white noise series. White noise is an important topic of physics, psychoacoustics, computer science, electronics, and even medicine. As you might expect, the concept of the white noise series is an important fundamental in time series analysis and forecasting, as well.

If you've ever turned your radio on between stations, you've heard white noise in action but what is it really?

White noise (in the strict sense of the term) is a random series whose samples are identically distributed and statistically independent. For example, the time series we made from sampling from the normal distribution 100 times was a white noise series. At every point in time, the mean of the distribution which gave rise to the samples was constant, and every sample was completely independent of the sample before it.

More specifically, the series we created from random sampling is called a Gaussian white noise series, since the observations...