Time Series Analysis: 3x Exp. Smoothing

[Oxymoron]

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?

 

[mmwave]

I would recommend using a robust time series analysis algorithm that takes into account outliers. One such method is the robust exponential smoothing technique, which uses a weighting function to downweight the impact of outliers on the forecast. This can help to improve the match between the forecast and actual data, and reduce the lag between the two curves.

Additionally, it may be helpful to review your seasonality parameter and make sure it is accurately reflecting the underlying patterns in your data. If the seasonality is incorrect, it can lead to a mismatch between the forecast and actual data. You may also want to consider using a different smoothing parameter to see if that improves the match between the two curves.

The sinusoidal pattern in the residuals plot could be due to the presence of a seasonal component in your data. It is important to make sure that your model is capturing this seasonality accurately. If not, it may be contributing to the mismatch between the forecast and actual data. Again, reviewing and adjusting your seasonality parameter may help to improve the fit of your model.

In summary, I would recommend using a robust time series analysis algorithm and carefully reviewing and adjusting your seasonality and smoothing parameters to improve the match between your forecast and actual data. It may also be helpful to investigate any potential outliers in your data and consider removing or downweighting them in your analysis.