Additional file 6: Annex 1. Right side: Autocorrelation (ACF) and partial autocorrelation (PACF) functions of the residuals from ARIMA model (1, 0, 1) Ă (1, 0, 1)12 on log-transformed, differenced data. Left side: ACF and PACF of the residuals from ARIMA model (4, 0, 1) Ă (1, 0, 1)12 on log-transformed, differenced data