A Complete Introduction To Time Series Analysis

A Complete Introduction To Time Series Analysis (with R):: Linear processes II. Last time, we left off at the representing Linear Processes in terms of the backward-shift operator.

Last time, we left off at the representing Linear Processes in terms of the backward-shift operator:

where Psi is the polynomial such that

, and we said that this representation will be useful later, especially when dealing with ARMA, ARIMA, and SARIMA models. This time, we will continue exploring some important properties and concepts related to Linear processes. Let’s start by giving a simple but illustrative example!

MA(p)

As you may have guessed from the MA(1) process, the MA(p) is just a generalization to going p-steps back into time, collecting past noise as a weighted average. Indeed, we can write

that is, we have that

. Not so hard eh! We will see more examples of linear processes later.

More Cauchy-Schwarts

Well, here we go again. Guess why the following proposition is true?

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