یک حسابرس سیستم پشتیبانی تصمیم گیری مبتنی بر شبکه های عصبی مصنوعی با استفاده از قانون بنفورد

While there is a growing professional interest on the application of Benford's law and “digit analysis” in financial fraud detection, there has been relatively little academic research to demonstrate its efficacy as a decision support tool in the context of an analytical review procedure pertaining to a financial audit. We conduct a numerical study using a genetically optimized artificial neural network. Building on an earlier work by others of a similar nature, we assess the benefits of Benford's law as a useful classifier in segregating naturally occurring (i.e. non-concocted) numbers from those that are made up. Alongside the frequency of the first and second significant digits and their mean and standard deviation, a posited set of ‘non-digit’ input variables categorized as “information theoretic”, “distance-based” and “goodness-of-fit” measures, help to minimize the critical classification errors that can lead to an audit failure. We come up with the optimal network structure for every instance corresponding to a 3 × 3 Manipulation–Involvement matrix that is drawn to depict the different combinations of the level of sophistication in data manipulation by the perpetrators of a financial fraud and also the extent of collusive involvement.

Analytical review procedure (ARP) is one of a number of tools in an external auditor's toolbox to ascertain the credibility of an organization's financial reports. As per SAS 99 auditors are now expected to collect and consider a much more information than they did in the past in order to better assess fraud risks [36]. However fraud detection is still not universally perceived as being the primary responsibility of an external auditor. There exists a serious “expectation gap” between what various stakeholders perceive as auditor's primary responsibilities and what auditors are capable of doing or are equipped to do given time and budget constraints [45]. Of course; if a fraud has been committed chances are that some numbers would appear ‘out of place’ to an auditor, thus causing “red flags” to be raised and warranting a deeper investigation. ARPs are specialized auditor decision support systems intended to make the audit process more efficient by quickly identifying the ‘out of place’ numbers. ARPs have been attributed with the ability to detect more anomalies than they are typically given credit for if other detection procedures had failed [44]. However some degree of subjectivity is involved in traditional ARPs which rely heavily on the auditors' judgment. Our main research objective here is to try and build on earlier research on an ANN-based ARP that applies a particularly useful statistical law known as Benford's law and is less prone to subjective factors. Towards this objective, we firstly review relevant literature in Section 2. Secondly, in Section 3, we propose an ANN-based auditor decision support system to re-examine the efficacy of Benford's law in helping to correctly discriminate between data sets that are naturally occurring and others which aren't. Thirdly, in Section 4, we specify a proposed ANN-based auditor decision support system with an aim to improve on the classification results obtained by earlier researchers by identifying and testing input variables to minimize the number of critical errors. Finally, in 5 and 6, we analyse our system output, compare it with the results of earlier researchers, draw conclusions and identify limitations.

In this paper, we used the Manipulation–Involvement hypothesis to build and test a ANN-based system for binary data set classification based on whether or not a data set conforms to Benford's law. This we contend could be a very useful tool in the form of an ARP as was previously proposed [7]. Our study, being based on the M–I hypothesis, likely possesses a more solid theoretical foundation than the prior examples; thereby making what we believe is a significant contribution to existing body of knowledge on quantitative methods for financial fraud detection. In addition to the first and second significant digit frequencies and related descriptive statistics, our posited system additionally uses a number of non-digit input variables and results indicate that this decision support system has fewer “Failed Alarm” errors. Of particular interest is the relatively higher level of ‘fitness’ with respect to reducing “Failed Alarm” training error displayed by the cumulative entropy differential and the discrete Kolmogorov–Smirnov goodness-of-fit statistic. This warrants further research in the future to identify and construct better-refined information theoretic and goodness-of-fit measures to be used as input variables in ANN-based systems. As we have already stated, a binary logistic regression model may provide an alternative methodological approach distinct from neural networks if the problem of multicollinearity can be adequately addressed. Due to large-scale redundancies in their architecture, ANNs are better able to choose among explanatory variables in situations where multicollinearity is present as compared to alternative data classification systems like logistic regression and discriminant analysis [13]. Of course, ANNs are not an unmixed blessing as a data mining methodology. B&W [7] list some of the common drawbacks of using an ANN-based decision support tool most of which would be applicable to our ANN-based system as well. A potential drawback of this work lies in the use of simulated rather than actual financial data. Unfortunately it is extremely difficult to obtain enough quantity of real-life data that contains some degree of ‘contamination’. There are privacy issues as corporations don't like to disseminate information on in-house frauds in fear of hurting their public image and possibly their market value. Therefore much of the research on development of effective data mining tools for ARP must necessarily rely on simulated data which, to some extent, brings their generalizability into question. However, we contend that there are other sciences (notably the atmospheric and geophysical sciences) where much of the research data must also be generated by simulation as real-life data may not simply be obtainable. We have followed the methodological footsteps of B&W in using simulated data and we cite a few well-regarded published works to back our chosen methodology [5], [18] and [19]. With respect to the GA optimization, we acknowledge that the population size and number of generations is rather low. However we have used GA to primarily demonstrate its efficacy in setting up the optimal ANN structures without a compelling need to perform comparative analyses with alternative structures. GAs take a long time to converge to optimal solutions and this is further compounded by the highly complex and unstructured nature of the network optimization problem. Running the GAs with a larger population of networks or over a large number of generations will potentially offset the efficiency gains of using a GA in the first place to set up the optimal ANNs. However having said that we do believe there are ample areas of further improvement in the way that we have applied GA optimization to setup our ANNs and this provides fertile ground for future work. The relationship between insider trading and financial statements fraud has already been computationally investigated [40]. An interesting related future research from an applied perspective will be to test whether Benford's law in conjunction with a data mining system can be used to identify financial securities price anomalies due to dubious stock market activities like insider trading, pumping and dumping and market cornering.