11 March, 2016

Number of Nicholas Cage Movies
versus
Drownings by Falling into a Swimming Pool

From: tylervigen.com.

Standard statistical methods applied to general time series might not work.


Cointegration extends regression methods to cover more cases.


I'll talk about implementation of solution methods.

Background

Generating model

I(0) time series are formally expressed

Vector of n most recent values



Integration order

A series xt is called I(1) if



Cointegration

The I(1) vector xt is cointegrated if there exists a vector β such that



An autoregressive model





Simplified. The VECM extends this.

Cointegration from this view

The I(1) series xt has cointegration rank 1 if


Rank r cointegration of k series

Require each series to be I(1).



α, β full column rank

Intuition

Drunk man. Walking his dog. Cointegration.