Time Series Analysis for Financial Data II — Auto-Regressive Models

Download the iPython notebook here

In the first post on Time Series Analysis, we talked about the basics of time series analysis - Staionarity and AutoCorrelation. We also talked about simple time series models, White Noise and Random Walks.

In this post, we take the concept forward and introduce a more sophisticated time series model, namely Auto Regressive(AR) model.

AutoRegressive Models

The autoregressive model is simply an extension of the random walk. It is a regression model which depends linearly on the previous terms. An order 1 regression model, AR(1) is:

x(t) = a*x(t-1) + w

where a is the auto-regressive coefficient and w is the white noise term. In simple words, the current value only depends on the previous value of the system. Note that an AR(1) model with a set equal to 1 is a random walk!

In the next post, we will talk about another class of models, Moving Average models (not to be confused with simple moving average — a rolling measure of average).