FORECASTING INSURANCE PREMIUM REVENUE USING TIME SERIES ANALYSIS

CHAPTER ONE

INTRODUCTION

1.1 Background to the Study

Premium revenue is the principal income stream of an insurance company and the base on which the industry's contribution to financial intermediation rests. Because premium income determines the resources available for claims settlement, reinvestment, capital accumulation and expansion, its future path is an input to almost every strategic and regulatory decision an insurer or supervisor makes. Forecasting that path is therefore a recurring practical problem, and time series analysis is the standard statistical response to it.

The Box–Jenkins Autoregressive Integrated Moving Average (ARIMA) methodology remains the workhorse of univariate forecasting. Its appeal lies in its parsimony and in its systematic identification–estimation–diagnostic cycle, which permits a model to be selected from the autocorrelation structure of the data itself rather than from prior theory. Exponential smoothing methods, particularly the Holt–Winters formulation, offer an alternative for series with trend and seasonality, while more recent applications have compared both against machine-learning estimators. Adeleke, Dosumu and colleagues, for example, compared ARIMA and Holt–Winters against a group method of data handling neural network in forecasting Nigerian under-five mortality, finding that all three achieved high efficiency but with differing error profiles. In the insurance domain specifically, Hafiz, Salleh, Garba and Rashid (2021) applied ARIMA to project Nigerian insurance penetration from 2019 to 2030, obtaining a mean absolute percentage error of approximately 10.35 per cent and forecasting a continuing decline in penetration, while parallel work has applied ARIMA to insurance penetration in Ghana and to claim volumes elsewhere.

The Nigerian premium series now presents a forecasting problem of unusual interest, because its recent behaviour departs sharply from its historical pattern. Gross premiums written rose from ₦1.003 trillion in 2023 to ₦1.56 trillion in 2024 and ₦2.30 trillion in 2025, the last representing year-on-year growth of 47.3 per cent, with total industry assets reaching ₦4.79 trillion (National Insurance Commission [NAICOM], 2026). In the first half of 2025 alone the industry wrote ₦1.98 trillion, with every segment growing by at least twenty-five per cent and life business expanding by 70.3 per cent. Whether this represents genuine market deepening or the nominal repricing of existing exposures under inflation of thirty per cent and above is precisely the kind of question a properly specified forecasting model, fitted to deflated as well as nominal data, can help to answer.

Two further considerations make forecasting timely. The Nigerian Insurance Industry Reform Act, 2025 imposes new minimum capital requirements with a twelve-month compliance window, and insurers must project the premium volume that the new capital will support. Simultaneously, the risk-based capital regime requires forward-looking projections of underwriting volume as an input to capital adequacy assessment. This study responds by developing and validating time series models for Nigerian insurance premium revenue.

1.2 Statement of the Problem

Insurance premium projections in Nigeria are typically produced by extrapolating recent growth rates or by applying management targets, rather than by fitting and validating statistical models. Four problems follow.

First, naive extrapolation of a period of exceptional growth. Projecting forward a 47 per cent annual growth rate observed during a period of thirty per cent inflation and one-off regulatory enforcement will produce forecasts that cannot be realised, with consequences for capital planning, staffing and reinsurance purchase.

Second, failure to separate nominal from real growth. Nigerian premium series are published in nominal naira. Without deflation, a forecasting model cannot distinguish volume growth from price growth, and the resulting projections conflate two phenomena with entirely different strategic implications.

Third, structural breaks. The study period contains several: the 2007 consolidation, the 2020 COVID-19 disruption, the 2023 subsidy removal and exchange rate liberalisation, the introduction of IFRS 17, and the enactment of NIIRA 2025. Standard ARIMA specifications assume parameter stability, and fitting a single model across these breaks will produce unreliable forecasts unless the breaks are explicitly modelled.

Fourth, limited Nigerian model comparison evidence. Hafiz et al. (2021) established that ARIMA can forecast Nigerian insurance penetration with reasonable accuracy, but the comparative performance of ARIMA, exponential smoothing and other candidates on premium revenue specifically and at segment level has not been established.

The problem, therefore, is the absence of empirically validated time series models for Nigerian insurance premium revenue, and the consequent reliance on projection methods whose accuracy has never been tested.

1.3 Aim and Objectives of the Study

The aim of this study is to forecast insurance premium revenue in Nigeria using time series analysis.

The specific objectives are to:

1. examine the trend, seasonality and stationarity properties of the Nigerian insurance premium revenue series;

2. identify, estimate and validate an appropriate ARIMA model for insurance premium revenue in Nigeria;

3. compare the forecast performance of ARIMA against alternative methods including exponential smoothing;

4. generate forecasts of insurance premium revenue over a defined horizon, in both nominal and inflation-adjusted terms; and

5. evaluate the accuracy of the selected model using appropriate out-of-sample error measures.

1.4 Research Questions

1. What are the trend, seasonality and stationarity properties of the Nigerian insurance premium revenue series?

2. Which ARIMA specification best describes insurance premium revenue in Nigeria?

3. How does the forecast performance of ARIMA compare with that of alternative time series methods?

4. What premium revenue is forecast for the Nigerian insurance industry over the projection horizon, in nominal and real terms?

5. How accurate are the model forecasts when evaluated out of sample?

1.5 Research Hypotheses

The following null hypotheses will be tested at the 5% level of significance:

H₀₁: The Nigerian insurance premium revenue series is not stationary at levels.

H₀₂: The residuals of the fitted ARIMA model do not constitute white noise.

H₀₃: There is no significant difference in forecast accuracy between the ARIMA model and the exponential smoothing model.

H₀₄: There is no significant structural break in the Nigerian insurance premium revenue series over the study period.

1.6 Significance of the Study

For insurance companies, validated forecasts support budgeting, capital planning, reinsurance purchase and the sizing of distribution investment, and the separation of real from nominal growth clarifies whether market share is genuinely expanding. For NAICOM, forecasts of industry premium volume inform supervisory planning, the assessment of whether the NIIRA 2025 capital thresholds are proportionate to projected underwriting volume, and the monitoring of progress towards the insurance penetration targets the reform was designed to achieve. For investors and analysts, the study offers a transparent, reproducible basis for valuing insurance sector equities in place of management guidance. For policymakers, projected premium revenue is an indicator of financial sector deepening and of progress towards the national economic growth objectives to which the insurance reform was explicitly linked. For scholarship, the study extends the small Nigerian literature on insurance time series forecasting from penetration rates to premium revenue, and supplies a structural-break-aware treatment of a series that recent shocks have made non-stationary in a complicated way.

1.7 Scope of the Study

The study covers gross premium written by the Nigerian insurance industry. Where annual data are used, the study covers 1995 to 2025; where quarterly data from NAICOM's Market Performance Bulletins are available, the quarterly series is used to permit seasonality analysis, covering the period for which consistent quarterly reporting exists. The series is analysed both in aggregate and, where data permit, disaggregated into life and non-life business and into the principal non-life branches (oil and gas, fire, motor, marine, aviation, general accident and miscellaneous). Both nominal and inflation-adjusted series are modelled, with deflation by the Consumer Price Index. Methodologically the study covers stationarity testing, ARIMA and SARIMA identification and estimation, exponential smoothing, structural break testing, and out-of-sample forecast evaluation. Data are drawn from NAICOM Annual Reports and Market Performance Bulletins, the Nigeria Insurance Digest, the CBN Statistical Bulletin and National Bureau of Statistics publications.

1.8 Limitations of the Study

(i) Series length annual data give a limited number of observations for ARIMA identification, and consistent quarterly reporting by NAICOM covers a shorter span, constraining the complexity of models that can be reliably estimated. (ii) Definitional discontinuity the introduction of IFRS 17 in 2023 changed the measurement of insurance revenue, so pre- and post-2023 figures are not strictly comparable without adjustment. (iii) Structural breaks the 2023 macroeconomic reforms and the 2025 legislative change are recent, so few post-break observations are available to estimate the new regime's parameters. (iv) Univariate limitation ARIMA models exploit only the history of the series itself and cannot anticipate policy changes, regulatory enforcement actions or macroeconomic shocks; forecasts should be read as conditional on the continuation of prevailing conditions. (v) Deflation assumptions headline CPI may not accurately reflect the price dynamics relevant to insurance premiums, so real-terms results are sensitive to the choice of deflator. (vi) Revision risk NAICOM figures for recent quarters are provisional and subject to revision.

1.9 Operational Definition of Terms

Time series: A sequence of observations on a variable recorded at successive, regularly spaced points in time.

Gross premium written (GPW): The total premium on all policies written during a period, before deduction of reinsurance ceded.

Stationarity: The property of a time series whose mean, variance and autocovariance structure do not depend on time.

ARIMA(p,d,q): An autoregressive integrated moving average model with p autoregressive terms, d degrees of differencing and q moving average terms.

SARIMA: A seasonal extension of ARIMA incorporating seasonal autoregressive, differencing and moving average terms.

Augmented Dickey–Fuller (ADF) test: A test of the null hypothesis that a time series contains a unit root and is therefore non-stationary.

Ljung–Box test: A test of the null hypothesis that the residuals of a fitted model are independently distributed, used to confirm white-noise behaviour.

Mean absolute percentage error (MAPE): A scale-independent measure of forecast accuracy expressing the average absolute forecast error as a percentage of the actual value.

Structural break: A change in the parameters of the data-generating process at a point in time, rendering a single fitted model inappropriate across the full sample.

References

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

Federal Republic of Nigeria. (2025). Nigerian Insurance Industry Reform Act, 2025. Federal Government Press.

Hafiz, U. A., Salleh, F., Garba, M., & Rashid, N. (2021). Projecting insurance penetration rate in Nigeria: An ARIMA approach. Revista Gestão Inovação e Tecnologias, 11(3), 5232–5243.

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

National Bureau of Statistics. (2025). Consumer price index and inflation report. NBS.

National Insurance Commission. (2026). Bulletin of the insurance market performance: Fourth quarter 2025. NAICOM.

Nigerian Insurers Association. (2024). Nigeria insurance digest 2023. Nigerian Insurers Association.

Odunayo, A. F., Adebayo, A. E., & Oladipo, O. A. (2020). Time series prediction of under-five mortality rates for Nigeria: Comparative analysis of artificial neural networks, Holt-Winters exponential smoothing and autoregressive integrated moving average models. BMC Medical Research Methodology, 20(1), 292. https://doi.org/10.1186/s12874-020-01159-9

Outreville, J. F. (2013). The relationship between insurance and economic development: 85 empirical papers for a review of the literature. Risk Management and Insurance Review, 16(1), 71–122. https://doi.org/10.1111/j.1540-6296.2012.01219.x