Implementing Minimum Message Length to the Modelling of Denpasar City Inflation Rate

Inflation is an economic indicator that is used to evaluate economic performance of an area. It is an important indicator in managing consumer’s purchasing power. Rising inflation rate can influence the interest rate. Studies have conducted in regard to inflation with the main focus of developing time series and forecasting models. However, for the modelling, pattern changes in time series and existence of outlier values have not been analyzed. For the purpose, a study was conducted in looking at the pattern existing in the inflation rate data using the monthly inflation rate in Denpasar City of Bali, Indonesia during January 2010, and April 2023. The study was performed by implementing the Minimum Message Length (MML) principle through the process of mixture modelling. Two distributions are considered in this study i.e., Gaussian and Student t distributions. Based on the conducted modelling, it was found that the best MML model for the dataset was a one Student t class mixture model. This shows that outliers exist in the inflation rates data in Denpasar City of Bali, Indonesia. The resulting MML model has also produced a slightly better probability bit costing compared to the Akaike Information Criterion (AIC) and Schwarz’s Bayesian Information Criterion (BIC) models. Further modelling for different time range of the data shows that inflation rates during the year 2010 to 2014 was fitted best using a one Student t class model, whereas the inflation rates during the year of 2015 to 2019 resulted in a one Gaussian class model. This shows that outliers exists during the former time range, whereas during the latter time range, the rates were managed better. For the data during the pandemic Covid-19, MML resulted in a one Gaussian class model, whereas AIC and BIC resulted in a two Gaussian classes model. This proves that MML accommodates a certain degree of uncertainty in data during the modelling.