Abstract Both professional auditing standards and academic research suggest that the usefulness of analytical procedures (APs) may be enhanced by utilizing multiple sources of less aggregate financial and nonfinancial information. To date, however, no research has directly tested this possibility. This study extends the auditing literature by comparing eight multivariate and univariate AP expectation models using relatively stable quarterly and monthly financial and nonfinancial data from a university. A new modeling technique and forecasting tool called VAR (vector autoregression) is introduced to the auditing literature. The eight models are: VAR, three ARIMA (autoregressive integrated moving average) models, two regression models, and two random walk models. Three sets of criteria are used: model goodness-of-fit and prediction accuracy, incidence (not the rate) of Type-I and Type-ll errors, and test-of-details sample size and achieved detection risk. Data series used in this study are the Tuitions and Fees revenue. Instructional Expenses, and Enrollment account balances of a mid-size university, and an industry index. Time-series plots and formal tests are performed to analyze the data series' properties in order to find the best models. A simulation then generates 100 additional data sets from the variance/covariance matrix of the university data set. The eight models are first fitted with the quarterly data series and compared using the three sets of criteria with randomly seeded errors and the STAR investigation rule, with statistical significance determined by Wilcoxon signed rank test and Friedman ANOVA (analysis of variance) test. Some of these tests are then repeated using monthly data. The results suggest that: (1) VAR significantly outperformed all the univariate models and the multivariate regressions using all three criteria; (2) a formal ADF (augmented Dickey-Fuller) stationarity test can help auditors determine the model form of time series data, i.e., how many levels of differencing are needed to achieve stationarity; (3) account- and firm-specific ARIMA models may in some cases outperform the general ARIMAs suggested by Lorek et al. (1992); (4) well-specified multivariate AP expectation models, which can potentially make use of more information sources, seem to outperform well-specified univariate models; (5) consistent with what SAS No. 56 suggests, less aggregate data (in fhis case monthly vs. quarterly) can increase a time-series AP expectation model's precision and thereby enhance the related AP's efficiency and effectiveness to the extent of being acceptable to practitioners. Given these findings, it is suggested that practitioners experiment with VARs in real audit settings using disaggregate data in order to determine VAR's cost/benefit characteristics relative to those of multiple regressions.
Simon C. Dzeng (Thu,) studied this question.