doin’ time: applying arima time series to the social sciences katie searles doin’ time: applying...
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Doin’ Time: Applying ARIMA Time Series to
the Social Sciences
Katie Searles
Doin’ Time: Applying ARIMA Time Series to the Social Sciences
KATIE SEARLESWashington State University
•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)
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)
Time Series Basics
Example of Time Series
ARIMA(auto-regressive integrated moving average)
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
1. Onset (abrupt, gradual)
2. Duration (temporary, permanent)
Interrupted Time Series Analysis
1. The dependent series is “prewhitened”2. A transfer function is selected to estimate
the influence of the intervention on the prewhitened time-series
3. Diagnostic checks are run to ensure the model is robust
Issues with Time Series
Theoretical Practical
date2/1/20058/1/20042/1/20048/1/20032/1/20038/1/20022/1/20028/1/2001
BU
SH
_O
PIN
ION
90.00
80.00
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40.00
*Data collected by the Gallup Poll
Approval Ratings for President Bush's First Term
en
em
_w
ee
k
300.00
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150.00
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0.00
date09/01/200404/01/200411/01/200306/01/200301/01/200308/01/200203/01/200210/01/200105/01/2001
Average Enemy Imagery Per Week for President Bush's First Term
date09/01/200404/01/200411/01/200306/01/200301/01/200308/01/200203/01/200210/01/200105/01/2001
en
em
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eek
300.00
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100.00
50.00
0.00
Average Enemy Images Used Per Week for Bush's First Term with Intervention
*Each red line represents a 3 point decrease in President's Bush's approval ratings during his first term.
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.