Imputation of Gaps in Transaction Sequences

For historical data, sequences of transactions that are supposed to be consecutive may contain gaps. A hot-deck based method of imputation, combined with a degree of randomization, is proposed. It is common in sequences of financial transactions to periodically “pay off the balance” with a single payment, returning the balance to zero. This feature is incorporated into the imputation procedure. The imputation procedure has been developed for imputing gaps in sequences of transactions in financial accounts. The procedures will be illustrated on data that are fictitious but retain interesting features found in the real world data that the method was devised to address. 1. Description of Problem and Data The purpose of this paper is to illustrate how an accounting problem with an incomplete dataset can be set up for sampling with the application of different imputation techniques. The task at hand is to estimate the error rate of financial transaction data that are in a chronological sequence. Suppose a bank or a credit card company is interested in testing the reliability of its processing system. A two stage sample design is used to first sample accounts from the account population of interest and then transactions from the sampled accounts. Let’s suppose furthermore that some of these accounts go back in time far enough that the transaction sequence exists on paper records only. Constructing the second stage sampling frame that is complete requires finding all the paper ledgers for the sampled accounts which can get very expensive and time consuming. Proceeding with an incomplete frame can lead to a potential bias in the estimate. One option is to statistically impute the ledger gaps to complete the transaction sequence before the second stage transaction sample is selected. This approach is reasonable especially when there is a regular pattern in the transaction data over time in dollar amount, income type, and time interval at which they are posted. Sampling from the frame with imputed data gaps, however, means any of these imputed transactions can be sampled. Since they are not real transactions, if sampled, they cannot be reconciled against the supporting documents to determine the accuracy. Hence, another level of imputation is needed to identify actual transactions that can be reconciled as close substitutes for the imputed transactions drawn into the final sample.