Intervention effect analysis in time-series processes

Much of statistical methodology is concerned with models in which the observations are assumed to vary independently. Randomization of the experimental design is introduced to validate analysis conducted as if the observations were independent. However, a great deal of data occur in the form of time series where observations are dependent and where the nature of this dependence is of interest. The technique available for the analysis of such series of dependent observations is called time series analysis. Time series models are techniques that allow the researcher to identify the structure of a time series and to determine if a discrete intervention accounts for a statistically significant change in the level of the series without artificial experimental conditions.;The results indicate that correctly identified ARIMA models gave fairly accurate estimates of the intervention effect. However, the length of the time series realization plays a crucial role in determining the accuracy of estimates examined in this investigation. The magnitude of the standard errors, the inaccuracy of the estimated standard error, inflation of Type I error rates, and lack of power, are quite severe in short time series realization. Also, extreme serial dependence magnifies the problems observed in estimation procedures of the autocorrelation function as well as the intervention component. Intervention effect estimates were inaccurate when the ARIMA model was inadequately differenced, having a detrimental effect on power.;Time series analysis techniques provide the tools for analyzing unique behavioral fluctuations through time and a framework for predicting future changes in the individual. The inherent limitations in the statistical procedures will be helpful in applying time series analysis techniques to research problems. The application of time series analysis to clinical research may provide a scientist-practitioner model for developing knowledge.;Monte Carlo studies were used to analyze issues in time series procedures with small data sets. Five Autoregressive-Integrated Moving Average (ARIMA) models with 20 and 40 data points were generated; a constant intervention effect was added to each time series; values of the correlation and intervention parameters were varied. The size of the intervention effect and the bias in intervention effect estimates were calculated for the true and misidentified ARIMA models. A second set of Monte Carlo simulations was used to investigate the procedures used in the model identification stage of time series analysis. ARIMA model identification is a crucial step in the assessment of intervention effects in interrupted time series experiments.