A Complete Introduction To Time Series Analysis (with R):: Classical Decomposition Model part I
In the last chapter, we studied the definition of stationary processes along with a couple of important examples: the IID Noise, White Noise, Random Walks, and the AR(1) and MA(1) processes, along with their respective expectations and autocovariance functions. We will now switch gears to what we saw some time ago about the trend and the seasonality, two important factors that together form the so-called classical decomposition model. In this article, we will study the classical decomposition model definition and how to estimate the trend. Let’s jump right into it!
Classical Decomposition Model
In order to perform analysis, we would like our series to be stationary, as this often helps to often fit simpler and more efficient models for prediction. The idea is very simple; consider the image above. This is saying that our model is essentially a composition of three components:
The question is, given some data, how can we know what mt or sd are? The simple answer is we don’t! However, there are techniques to perform the estimation. Let’s start with the trend.
