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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

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Doin time applying arima time series to the social sciences l.jpg

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, xt+1, . . . , 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

  • 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


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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). 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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