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

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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.

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### 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
Issues with Time Series
• 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.