Bayesian Decision Analysis For Benchmarking Daily And Monthly Time Series

Abstract

In Business Time Series analysis, daily disaggregation of monthly time series is often needed when adjusting financial series (stock options, swaps, mortgages or other loans). The classical stochastic adjustment methods only allow quarterly or monthly benchmarks to be estimated and can only be applied when high frequency is a regular multiple of low frequency. Thus, they fail to offer solutions for such problems, thereby evidencing the need to develop tools and methods for high-frequency series (daily or weekly ones). This paper obtains the first known method for using daily indicators, taking into account the different number of days for each month. The proposed Bayesian (normal-gamma) method can employ several indicators for the likelihood model, also obtaining an explicit (non iterative) solution for the optimal estimate of high frequency series. It is also important to observe that the model includes a correction mechanism for volatile indicators, as is often found in benchmarking problems for small areas. The methodology, in the line of normal-gamma specifications, allows Bayesian Credibility intervals for the estimated daily series.