Korn, Uri. 2021. “A Simple Method for Modeling Changes over Time.” Variance 14 (1): 1–13.
• Figure 1. Time as a categorical variable versus RSSM
• Figure 2. Bayesian model versus RSSM
• Figure 3. Additive model fit on the example data
• Figure 4. Issues with the additive model fit
• Table 1. Simulation results of various time series methods
• Table 2. Default dummy encodings for a year categorical variable
• Table 3. Initial dummy encodings for a random walk
• Figure 5. Elastic net and ridge regression comparison
• Figure 6. Comparison of a large change
• Figure 7. A segment moving away from the mean
• Figure 8. A segment moving toward the mean
• Table 4. Example dummy encodings for a random walk on the slope
• Table 5. Example dummy encodings with 25% mean reversion
• Figure 9. Random walk with momentum
• Figure 10. Trended, ultimate loss ratios by segment
• Figure 11. Fitted trended, ultimate loss ratios by segment

## Abstract

Properly modeling changes over time is essential for forecasting and important for any model or process with data that span multiple time periods. Despite this, most approaches used are ad hoc or lack a statistical framework for making accurate forecasts.

A method is presented to add time series components within a penalized regression framework so that these models are capable of handling everything a penalized generalized linear model can handle (distributional flexibility and credibility) as well as changes over time. Doing this, a subset of state space model functionality can be incorporated in a more familiar framework. The benefits of state space models in terms of their accuracy and intuitiveness are explained.

The method presented here lends itself well to presentation, which can help with understanding and delivering results. This makes it useful not only for pricing and other models but for improving and streamlining other types of actuarial processes such as reserving and profitability studies.

Accepted: March 12, 2019 EDT