Time Series Data Mining with an Application to the Measurement of Underwriting Cycles

Abstract

Underwriting cycles are believed to pose a risk management challenge to property-casualty insurers. The classical statistical methods that are used to model these cycles and to estimate their length assume linearity and give inconclusive results. Instead, we propose to use novel time series data Mining algorithms to detect and estimate periodicity on U.S. property-casualty insurance markets. These algorithms are in increasing use in data science and are applied to Big Data. We describe several such algorithms and focus on two periodicity detection schemes. Estimates of cycle periods on industry-wide loss ratios, for all lines combined and for four specific lines, are provided. One of the methods appears to be robust to trends and to outliers.

Notes

1 If insurers do not identify the severity and turning points of market cycles, they may misprice their products. Cutting prices in response to competition in a “soft” phase, when profitability and premiums are falling, may lead to steep losses in future years. Conversely, if insurers raise prices excessively in a “hard” phase, they may lose business and have to abandon certain product lines altogether.

2 We refer readers to the references cited above for further discussion of the economic theories of underwriting cycles and empirical results supporting these various theories.

3 The periodogram is smoothed with suitable Daniell filter weights to reduce the confidence interval on the spectral density estimate.

4 We also controlled for the outlier due to Hurricane Andrew by creating a dummy variable for 1992 in Equation (4)(4) $$\left(1-\sum _{j=0}^p{\varphi }_j{B}^j\right)(X_t-\mu )={\varphi }_{0}t+\left(1+\sum _{j=0}^q{\theta }_j{B}^j\right){ϵ}_t,$$(4) . The resulting AR(2) model then estimated a suspiciously long cycle of 21.4 years in the homeowners line.

5 No cycle is detected on the homeowners insurance line, irrespective of whether a dummy variable is used in 1992 to control for the outlier represented by Hurricane Andrew.

Additional information

Funding

I.O. is grateful to CKER, Society of Actuaries, for a research grant. The ideas in this article were initiated when I.O. was in receipt of a grant from the Bank of England, to which he also expresses thanks.

Discussions on this article can be submitted until April 1, 2020. The authors reserve the right to reply to any discussion. Please see the Instructions for Authors found online at http://www.tandfonline.com/uaaj for submission instructions.