Application of spectral and ARIMA analysis to combined‐ratio patterns

Purpose – This paper seeks to use spectral analysis as an alternative method to analyze whether underwriting results exhibit a cyclical behavior for the property‐liability insurance industry and by lines of business. In addition, aims to use the AR(2) process to obtain information about cyclical behavior and cycle lengths. Then, the results from the two methods are to be closely examined and compared. Design/methodology/approach – Spectral analysis and ARIMA are used to obtain cycle lengths, then to compare them to check the consistency of the two methods. Findings – The AR(2) produced more significant results than spectral analysis. Originality/value – This is the first article in insurance using significant levels for spectral analysis to decide appropriate cycle lengths. In addition, the consideration of multiple comparisons to get critical values for significance levels reduces false positive and produces more reliable results.