# Correct formula for converting the ARIMA MA(1) coefficient to the exponential smoothing $\alpha$ parameter?

Two crucial sources for time series analysis differ in a critical formula for equivalence between simple exponential smoothing (SES) and ARIMA(0, 1, 1).

From Hyndman's F:PP:

$\theta_1 = \alpha - 1$

and from R. Nau's Statistical Forecasting:

$\theta_1 = 1- \alpha$

Can someone help me understand the apparent discrepancy?

• The ETS model formulation is not the same as simple exponential smoothing. SES relies on a $-$ sign in front of the term involving the error but ETS has a $+$ sign in front, hence the relationship between the two (different) $\theta_1$s. Feb 27, 2018 at 21:25