SOA ATPAAdvanced Topics in Predictive Analytics

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.