Time Series Analysis for Financial Data II

Summary

This context introduces Auto-Regressive (AR) models in time series analysis, particularly for financial data, as an extension of random walk models, and provides a link to an iPython notebook for practical application.

Abstract

The web content delves into the concept of Auto-Regressive (AR) models as part of a series on time series analysis for financial data. It builds upon the foundational topics of stationarity, autocorrelation, and simple models like White Noise and Random Walks, which were covered in the first post. The current post specifically focuses on the AR model, detailing its nature as a linear regression model that predicts future values based on past observations. An example of an AR(1) model is provided, illustrating how the current value is a function of the previous value and a white noise term. The post also offers a hands-on iPython notebook for readers to engage with the concepts discussed, and it teases the next installment in the series, which will cover Moving Average models.

Opinions

The author considers the Auto-Regressive model to be a more sophisticated approach compared to the simple models previously discussed.
There is an emphasis on the practical application of the concepts, as evidenced by the provision of an iPython notebook for readers to download and use.
The author differentiates Moving Average models from simple moving average calculations, hinting at the content of the upcoming post in the series.
The author equates an AR(1) model with the auto-regressive coefficient 'a' set to 1 with a random walk, suggesting a close relationship between the two concepts.

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).