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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. 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

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  1. 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

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

  3. 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)

  4. 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)

  5. Example of Time Series

  6. ARIMA(auto-regressive integrated moving average)

  7. 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

  8. ARIMA • Identification (p,d,q) • Estimation • Diagnosis

  9. 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)

  10. Interrupted Time Series Analysis • Mimics a quasi-experiment • Intervention • Transfer function • Onset (abrupt, gradual) • Duration (temporary, permanent)

  11. 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

  12. Issues with Time Series • Theoretical • Practical

  13. 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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