Hello Please explain how to fit the parameter in the model as given in part iv). I couldn't comprehend the examiner's report solution at all.
Hello If alpha = 1, then the process is not stationary. However, we do get a stationary model after differencing three times (after differencing three times we just get left with the white noise term). Let this process be Yt. We therefore fit white noise to Yt. Assuming we fit white noise with mean 0, the only parameter to fit is the variance of the white noise terms, which we can estimate using the sample variance of Yt. Hope this helps Andy
Hi In your answer above, "However, we do get a stationary model after differencing three times" does this apply to all AR(p)? Meaning if its AR(4) then 4 times differencing will lead to a stationary series? Thanks in advance
Hello This doesn't apply to all AR(p). Some AR(p) models are already stationary. Checking stationarity of a particular model is covered in Section 3 of Chapter 13. Whether differencing creates a stationary series from a non-stationary ARMA(p,q) process depends on the roots of the characteristic equation of the process terms. For a series to be stationary, we require all roots to be larger than 1 in magnitude. However, in the special case where there is one or more unit roots (ie a root of 1), these can be removed via differencing. As long as the remaining roots are larger than 1 in magnitude, the resultant series, after differencing to remove the unit roots, will be stationary. This is the idea behind ARIMA processes also covered in Section 3 of Chapter 13. Hope this helps! Andy
