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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

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

slide2

Brief Introduction to:

    • Time Series
    • ARIMA
    • Interrupted Time Series
  • Application of the Technique
introduction to time series
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
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
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
ARIMA
  • Identification (p,d,q)
  • Estimation
  • Diagnosis
arima9
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
Interrupted Time Series Analysis
  • Mimics a quasi-experiment
  • Intervention
  • Transfer function
    • Onset (abrupt, gradual)
    • Duration (temporary, permanent)
interrupted time series analysis11
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
Issues with Time Series
  • Theoretical
  • Practical
works cited
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.
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