SOA ATPAAdvanced Topics in Predictive Analytics

Before running k-means on variables with very different scales (e.g., premium in dollars and age in years), the analyst should:

List the key elements ASOP 56 expects an actuary to address when relying on a predictive model built by others.

Simple exponential smoothing uses $\hat y_{t+1}=\alpha y_t+(1-\alpha)\hat y_t$ with $\alpha=0.3$. Given $y_t=100$ and the prior forecast $\hat y_t=90$, calculate the updated forecast $\hat y_{t+1}$.

A time series shows a clearly increasing trend and its sample ACF decays very slowly. The appropriate first step before fitting an ARMA model is to:

Explain what it means for a time series to be (weakly) stationary, and describe two diagnostic tools used to check whether differencing has achieved stationarity.

In a scree plot of PCA eigenvalues, the recommended number of components to retain by the 'elbow' rule is the point where:

A clustered point has average within-cluster distance $a_i=2$ and average distance to the nearest other cluster $b_i=5$. Calculate its silhouette coefficient.

A categorical rating variable (vehicle make/model) has over 500 levels. Explain the risk of using simple target-mean encoding for this variable and propose a safer alternative.

A model selects 40% of applicants in demographic group A and 50% in group B for a favorable outcome. Calculate the disparate-impact ratio and state whether it passes the commonly cited 80% rule.

Outline the key stages of a model risk management framework (such as SR 11-7 style guidance) that an actuary relying on a third-party predictive model should expect to see documented.