## A Regression Approach to Time Series Analysis

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:
1. Introduction to the regression approach to time series analysis.
2. 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.
3. More advanced variants of the regression method.
4. Three examples.