CHAPTER ONE

INTRODUCTION

1.1 Background to the Study

Insurance business is inherently forward-looking: premiums are priced, reserves are set aside, and capital is allocated today against claims that will only be settled in the future. Accurate forecasting of insurance claims is therefore central to the solvency and profitability of insurance companies. Time series methods, particularly the Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) family of models, have long been applied in the insurance and actuarial literature for forecasting quantities such as claim counts, claim amounts and penetration rates (Box et al., 2015).

In the Nigerian context, ARIMA modelling has been used to project the country's insurance penetration rate using annual data spanning 1981 to 2018, with results indicating that the penetration rate would continue on a slow downward trajectory in the absence of policy intervention (Hafiz et al., 2021). Similar techniques have also been applied to forecast motor insurance claim amounts, where an ARIMA(1,0,1) model fitted to thirty-six years of own-damage claims data was found to provide a stable and reliable basis for prediction (Kumar et al., 2020). These studies illustrate that, although many insurance companies still rely on simple linear regression to construct forecast models, time series techniques such as ARIMA have repeatedly been shown to give more reliable projections of claims behaviour than conventional regression-based approaches.

Given the exposure of the Nigerian insurance industry to macroeconomic shocks, including currency depreciation, inflation and fluctuating economic activity, which can introduce volatility and structural change into claims data, there is a strong case for the systematic application of time series forecasting models to insurance claims data in Nigeria. This study is therefore designed to apply appropriate time series techniques to forecast insurance claims and thereby generate evidence that can support reserving, pricing and risk-management decisions within the industry.

1.2 Statement of the Problem

Notwithstanding the demonstrated value of time series techniques in claims forecasting, Nigerian insurers have continued to depend largely on simple linear trend or regression-based methods to project future claims, an approach that has been found to be less reliable than a properly specified ARIMA model (Hafiz et al., 2021). This mismatch between the stochastic, often non-stationary nature of claims data and the relatively simple forecasting tools in use exposes insurers to the risk of reserve inadequacy, mispriced premiums and, ultimately, solvency problems. There is therefore a need to investigate the time series properties of insurance claims data in Nigeria, to identify an appropriately specified stochastic model, and to demonstrate its forecasting performance relative to simpler alternatives, so as to provide a more robust basis for claims projection within the industry.

1.3 Objectives of the Study

The main objective of this study is to forecast insurance claims in Nigeria using time series models. The specific objectives are to:

i. examine the trend and stationarity properties of the insurance claims time series data;

ii. identify and fit an appropriate Box-Jenkins (ARIMA) model to the claims data;

iii. use the fitted model to forecast future values of insurance claims;

iv. evaluate the diagnostic adequacy and forecast accuracy of the fitted model; and

v. compare the forecasting performance of the time series model with that of a conventional linear regression model.

1.4 Research Questions

The study is guided by the following research questions:

1. Is the insurance claims time series data in Nigeria stationary?

2. What ARIMA model best fits the insurance claims data?

3. What are the projected future values of insurance claims based on the fitted model?

4. How adequate and accurate is the fitted forecasting model?

5. How does the forecasting performance of the time series model compare with that of a linear regression model?

1.5 Research Hypotheses

The following null hypotheses are formulated to guide the study:

H01: The insurance claims time series data is not stationary.

H02: The fitted ARIMA model does not adequately represent the underlying pattern of the insurance claims data.

H03: There is no significant difference between the forecasting accuracy of the ARIMA model and that of a linear regression model.

1.6 Significance of the Study

This study will benefit insurance companies by providing a more reliable, statistically grounded tool for projecting future claims, which is essential for reserving and solvency management. It will assist the National Insurance Commission and other regulators in monitoring systemic risk arising from claims volatility across the industry. Reinsurers and capital providers will find the forecasting evidence useful for capital allocation and treaty pricing decisions. The study will also contribute to closing the gap in the literature on insurance forecasting methodology in Sub-Saharan Africa, a region that has received comparatively little research attention on this subject (Hafiz et al., 2021), and will serve as a resource for students and researchers in actuarial science and statistics.

1.7 Scope and Limitation of the Study

The study covers time series analysis and forecasting of a specific class or aggregate of insurance claims in Nigeria, using secondary annual or quarterly data obtained from the National Insurance Commission and/or selected insurers over a defined period. The analysis is restricted to univariate Box-Jenkins methodology and does not extend to multivariate or machine-learning-based forecasting techniques. The study is limited by the length and quality of available historical data, the possibility of structural breaks arising from regulatory or macroeconomic changes, and the fact that no forecasting model can perfectly anticipate future shocks.

1.8 Definition of Terms

Time Series: A sequence of observations on a variable recorded at successive, usually equally spaced, points in time.

Forecasting: The process of using historical and current data to predict future values of a variable.

Stationarity: A property of a time series whose statistical characteristics, such as mean and variance, do not change over time.

ARIMA Model: An Autoregressive Integrated Moving Average model used to describe and forecast time series data by combining autoregressive and moving-average terms with differencing.

Box-Jenkins Methodology: An iterative model-building approach involving identification, estimation, diagnostic checking and forecasting, commonly used to fit ARIMA models.

Autocorrelation: The correlation of a time series with a lagged version of itself.

Trend: The long-term movement or general direction observed in a time series.

Residual (White Noise): The unexplained, random component that remains after a model has been fitted to a time series.

Insurance Claim: A demand made by a policyholder for payment under the terms of an insurance policy.

Model Diagnostics: Statistical checks, such as residual analysis and information criteria, used to assess how well a fitted model represents the data.

REFERENCES

Box, G. E. P., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis: Forecasting and control (5th ed.). Wiley.

Hafiz, U. A., Salleh, F., Garba, M., & Rashid, N. (2021). Projecting insurance penetration rate in Nigeria: An ARIMA approach. Revista Geintec-Gestão Inovação e Tecnologias, 11(3), 63–75.

Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and practice (3rd ed.). OTexts.

Kumar, V. S., Satpathi, D. K., Kumar, P. P., & Haragopal, V. V. (2020). Forecasting motor insurance claim amount using ARIMA model. AIP Conference Proceedings, 2246(1), Article 020005.

National Insurance Commission. (2023). Annual statistical market report 2022. NAICOM.