1984: Ctss/cusum Applications to Intervention Analysis

Most surveys used in monitoring undergo periodic changes by adding or deleting respondents, questions or calculations used in deriving estimates. The results of such "interventions" need to be considered when one analyzes time-series data generated from such surveys. This paper addresses the applicability of Cumulative Transitional State Score (CTSS), Transitional Scores (TS) and Cumulative Sums (CUSUMs) to detect the significance of interventions. It demonstrates the application of an adjustment to the mean value with CUSUMs when a significant change is detected. The data used in the analyses is the Energy Information Administration monthly estimates of stocks of motor gasoline, distillate fuel oil, residual fuel oil and crude oil 19761982. The above index computations are applied to series seasonally adjusted using X-II. A BoxJenkins time-series analysis of CTSS and TS scores explores the charactistics of these indices and graphically displays the pattern in the partitioned successive evaluations. I. FRAMEWORK FOR CTSS AND CUSUM INDICES The Cumulative Transitional State Score (CTSS) and Cumulative Sums (CUSUMs) represent two types of scoring techniques which may be applied to monitoring changes in time-series data. CTSS was developed by Gardenier (1974, 1979); the principles underlying CUSUMs have been described in Barnard (1959), Johnson (1961), Johnson and Leone (1962) and DeBruyn (1961). CUSUMs are based on Wald's sequential probability ratio test (SPRT) in the early 1940's which Page (1961) applied to test sequential hypotheses. In depicting the short-term pattern of fluctuations in time-series data, CTSS has advantages over CUSUMs. Both tests are oriented toward identifying whether statistically significant changes are apparent in the data prior to and post-intervention. CUSUMs also incorporate an adjustment to the long-term process mean value when a significant shift is observed. A. Methodol0~ical Background CUSUMs aggregate deviations from a long-term process average; thus one cumulates the sum of (Xi-m), where m corresponds to a reference value or a long-term process average. In applying CUSUMs, one uses two parameters, h and k in deciding whether or not the overall process has changed, k is usually expressed in standard deviation units and is added to or subtracted from the mean prior to cumulating deviations. That is, an interval X ± k~ is established as an acceptable region beyond which deviations are cumulated. If the cumulative deviations reach h, the decision is made that the process has shifted to a new mean. The choice of k is usually done by