A Complete Introduction To Time Series Analysis (with R):: Semi-parametric Models

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In the last article, we saw the general strategy to think about any time series model, and how we don’t want either too much or too little dependence in our models. We would now like to explore this more in-depth.

Notation

Just a quick note; remember that

is just a shorthand for

i.e. some time series. Keeping this in mind, let’s dive into the examples.

Semi-Parametric Models

Let’s first take a look at the definition of semi-parametric models

So essentially a model is semi-parametric if we don’t specify its distribution, but we know what it’s expectation and covariance (note the funky h, this is called a lag).

Let’s see some examples!

IID Noise

IID stands for “Independent and Identically Distributed”, i.e., each…