ECON 174 Lecture Notes - Lecture 17: Autoregressive Integrated Moving Average, Exponential Decay, Exponential Smoothing
28 Feb 2020
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Document Summary
The seasonal part of an ar or ma model will be seen in the seasonal lags of the pacf and acf. A spike at lag 12 in the acf but no other significant spikes. The pacf will show exponential decay in the seasonal lags; that is, at lags 12, 24, Exponential decay in the seasonal lags of the acf. A single significant spike at lag 12 in the pacf. Euretail %>% diff(lag=4) %>% diff() %>% ggtsdisplay() D = 1 and d = 1 seems necessary. Significant spike at lag 1 in acf suggests non-seasonal ma(1) component. Significant spike at lag 4 in acf suggests seasonal ma(1) component. We could also have started with arima(1,1,0)(1,1,0)4. Acf and pacf of residuals show significant spikes at lag 2, and maybe lag 3. Relative widespread but outdated view that exponential smoothing is less general than. Linear exponential smoothing models all special cases ofarima models. Non-linear exponential smoothing models have no equivalent arima counterparts.
