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Investigating Time Series in Social Sciences Using ARIMA

This presentation introduces Time Series, ARIMA, and its application in social sciences. Learn about interrupted time series analysis, ARIMA assumptions, modeling, and issues in time series analysis. Explore practical and theoretical aspects with examples.

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Investigating Time Series in Social Sciences Using ARIMA

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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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