Doin

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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

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• Brief Introduction to
• Time Series
• ARIMA
• Interrupted Time Series
• Application of the Technique

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Introduction to Time Series

• Ordered time sequence of n observations (x0, x1,
  x2, . . . , xt-1, xt, xt1, . . . , xT ).
• Type of regression analysis that takes into
  account the fact that observations are not
  independent (autocorrelation)

(McCleary and Hay 1980)
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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)

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Example of Time Series
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ARIMA(auto-regressive integrated moving average)
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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

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ARIMA

• Identification (p,d,q)
• Estimation
• Diagnosis

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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)

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Interrupted Time Series Analysis

• Mimics a quasi-experiment
• Intervention
• Transfer function
• Onset (abrupt, gradual)
• Duration (temporary, permanent)

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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

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Issues with Time Series

• Theoretical
• Practical

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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).
  LondonChapman 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.