Show that the point forecasts from an ETS(M,A,M) model are the same as those obtained using Holt-Winters’ multiplicative method. Show that the forecast variance for an ETS(A,N,N) model is given by...

Show that the point forecasts from an ETS(M,A,M) model are the same as those obtained using Holt-Winters’ multiplicative method.

Show that the forecast variance for an ETS(A,N,N) model is given by

Write down 95% prediction intervals for an ETS(A,N,N) model as a function of ℓ_T, α, h and σ, assuming Gaussian errors.