Modeling Customers’ Complaint Using Overdispersed Timeseries Count Data Models: Evidence from Nigerian Public Complaint Commission

Abstract

This study compares overdispersed count time series models for analysing and forecasting monthly customer complaints received by the Nigerian Public Complaints Commission (NPCC). Complaint data are inherently discrete, non-negative, and typically exhibit overdispersion and strong temporal dependence, making classical Gaussian-based time series models inappropriate. To address these challenges, three competing models were considered: the first-order Integer-Valued Autoregressive model with Poisson innovations [INAR(1)-P], the INAR(1) model with Negative Binomial innovations [INAR(1)-NB], and the Autoregressive Conditional Poisson (ACP) model. The models were fitted to NPCC monthly complaint data, and their performance was evaluated using log-likelihood, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). Preliminary diagnostic tests confirmed the presence of significant autocorrelation and overdispersion in the data, justifying the use of specialized count time series models. Empirical results revealed that all models captured strong persistence in complaint dynamics, with autoregressive coefficients close to unity, indicating high temporal dependence. Comparative model assessment showed that the ACP(1,1) model outperformed both INAR(1) specifications, yielding the highest log-likelihood and the lowest AIC and BIC values. This suggests that incorporating both past observed counts and past conditional means provides a superior representation of the underlying complaint-generating process. Based on the preferred ACP(1,1) model, forecasts for 2026 indicate a steady upward trend in complaint volumes, with projected monthly complaints increasing from approximately 53,799 in January to 64,640 in December. The findings demonstrate that ACP models provide a more robust framework for modelling overdispersed and highly persistent complaint count data compared to traditional INAR formulations. The study contributes to the growing literature on integer-valued time series modelling and offers practical insights for forecasting and resource planning within public-sector complaint management systems.