# Doin’ Time: Applying ARIMA Time Series to the Social Sciences - PowerPoint PPT Presentation

1 / 16

Doin’ Time: Applying ARIMA Time Series to the Social Sciences. Doin’ Time: Applying ARIMA Time Series to the Social Sciences. KATIE SEARLES Washington State University . Katie Searles. Brief Introduction to: Time Series ARIMA Interrupted Time Series Application of the Technique.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Doin’ Time: Applying ARIMA Time Series to the Social Sciences

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

Doin’ Time: Applying ARIMA Time Series to the Social Sciences

## Doin’ Time: Applying ARIMA Time Series to the Social Sciences

KATIE SEARLES

Washington State University

Katie Searles

• Brief Introduction to:

• Time Series

• ARIMA

• Interrupted Time Series

• Application of the Technique

### Introduction to Time Series

• Ordered time sequence of n observations* (x0, x1, x2, . . . , xt−1, xt, xt+1, . . . , xT ).

• Type of regression analysis that takes into account the fact that observations are not independent (autocorrelation)

* (McCleary and Hay 1980)

### Time Series Basics

• Two goals of Time Series analysis:

• Identifying patterns represented by a sequence of observations

• Forecasting future values

• Time series data consists of 2 basic components: an identifiable pattern, and random noise (error)

### ARIMA Assumptions

• Absence of outliers

• Shocks are randomly distributed with a mean of zero and constant variance over time

• Residuals exhibit homogeneity of variance over time, and have a mean of zero

• Residuals are normally distributed

• Residuals are independent

### ARIMA

• Identification (p,d,q)

• Estimation

• Diagnosis

### ARIMA

• (p, d, q)

• random shocks affecting the trend

• p: the auto-regressive component (autocorrelation)

• d: integrated component

• q: the moving average component (randomizes shocks)

• Specification of the model relies on an examination of the autocorrelation function (ACF) and the partial autocorrelation function (PACF)

### Interrupted Time Series Analysis

• Mimics a quasi-experiment

• Intervention

• Transfer function

• Duration (temporary, permanent)

### Interrupted Time Series Analysis

• The dependent series is “prewhitened”

• A transfer function is selected to estimate the influence of the intervention on the prewhitened time-series

• Diagnostic checks are run to ensure the model is robust

• Theoretical

• Practical

### Works Cited

• Box, G.E.P. and G.M. Jenkins (1976). Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day.

• Brockwell, P. J. and Davis, R. A. (1996). Introduction to Time Series and Forecasting. New York: Springer-Verlag.

• Chatfield, C. (1996). The Analysis of Time Series: An Introduction (5th edition). London:Chapman and Hall.

• Cochran, Chamlin, and Seth (1994). Deterrence or Brutalization? Criminology, 32, 107-134.

• Granger, C.W.J. and Paul Newbold 1986 Forecasting Economic Time Series. Orlando: Academic Press.

• McCleary, R. and R.A. Hay, Jr. (1980). Applied Time Series Analysis for the Social Sciences. Beverly Hills, Ca: Sage.