I have 6 years of data which has both a 3-month and a 12-month seasonality, it exhibits a trend and is very noisy. I implemented the triple exponential smoothing procedure and changed my seasonality, trend, and smoothing parameters until the difference between the forecasted data and the actual data was as low as possible. Yet the forecasted curve lags behind the actual curve by 1 month. Also, the 'shape' of the 12-month moving average of Forecast and Actual is similar but also offset. I found that the offset is caused and amplified by any actual data points that are outliers. Q1) Is there a time-series analysis algorithm/method/procedure which ignores data points which are outliers so that I may get a better match and a better prediction. Or is this something I am going to have to live with? Q2) I plotted the difference between the actual and the forecasted (a residuals plot) and found that the residuals follow an almost perfect sinusoidal pattern with a 12-month period. Why is this so? And more importantly, if I know my forecasted data mismatches the actual sinusoidally then surely there is something I can do to fix it. Perhaps my seasonality parameter is wrong?