## A Regression Approach to Time Series Analysis

Copyright © Richard B. Darlington. All rights reserved.
There are a number of approaches to time series analysis, but the two best known
are the regression method and the Box-Jenkins (1976) or ARIMA
(AutoRegressive Integrated Moving Average) method. This document introduces
the regression method. I consider the regression method far superior to ARIMA
for three major reasons:

- Regression is far more flexible and powerful, producing better models.
This point is developed in numerous spots throughout the work.
- Regression is far easier to master than ARIMA, at least for those already
familiar with the use of regression in other areas.
- Regression uses a "closed" computational algorithm that is essentially
guaranteed to yield
results if at all possible, while ARIMA and many other methods use iterative
algorithms that often fail to reach a solution. I have often seen the ARIMA
method "hang up" on data that gave the regression method no problem.

I assume a solid understanding of regression and the general linear model, including
the use of polynomial and interaction terms and the use of coded variables to
represent multicategorical variables. This document is intended to serve three
audiences:
- Readers new to time series analysis, who want to introduce themselves
to the topic as quickly as possible.
- Readers familiar with ARIMA who want to see why I prefer regression.
- Readers familiar with a basic autoregression approach to time series analysis,
who want to see extensions to that basic approach.

Aside from this brief introductory section, this work has four sections that can be
called up separately:
- Introduction to the regression approach to
time series analysis.
- The advantages of regression over
ARIMA. This section
also explains why I often suggest using substantially more terms in a
regression analysis than is usually done.
- More advanced variants of the regression
method.
- Three examples.

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