Estimate ARIMA as equivalent exponential smoothing

[ac_1]

Hi Tom,

An ARIMA(1,1,2) with no constant is equivalent to linear exponential smoothing with damped trend,
Gardner, E. S., & McKenzie, E. (1985) Forecasting trends in time series. Management Science, 31(10), 1237–1246.

An ARIMA(1,1,2) with no constant can be estimated using BOXJENK, is there a way to estimate with ESMOOTH?

thanks,
Amarjit

[TomDoan]

The TREND=LINEAR,SEASONAL=NONE exponential smoothing model is equivalent to an ARIMA(0,2,2) model. I assume their result is that if you change the trend rate from I(1) to AR(1) process, that it creates an ARIMA(1,1,2) process instead. The only "point" would be that the exponential smoothing representation would generate estimates of the local trend rate and local smoothed value. However, if you really want to estimate the unobserved components, it would make more sense to use a state-space model (which weren't as commonly used back in the 1980's).