# Time Series Analysis: 3x Exp. Smoothing

• Oxymoron
In summary, time series analysis is a statistical technique used to analyze and model data over a period of time. 3x exponential smoothing is a forecasting method that uses weighted averages to estimate future values and is different from other smoothing techniques as it takes into account the previous two data points. It is most useful for data with trends, seasonal, or cyclic patterns but may not perform well with sudden changes or high levels of noise.
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?

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.

## 1. What is time series analysis?

Time series analysis is a statistical technique used to analyze and model data that is collected over a period of time. It involves studying patterns, trends, and relationships in the data to make predictions and forecast future values.

## 2. What is 3x exponential smoothing?

3x exponential smoothing is a forecasting method that uses weighted averages to estimate future values in a time series. It is an extension of double exponential smoothing, where three weights are used instead of two to give more weight to recent data points.

## 3. How is 3x exponential smoothing different from other smoothing techniques?

3x exponential smoothing is different from other smoothing techniques because it takes into account not only the most recent data points, but also the previous two data points. This allows for a more accurate and stable forecast, especially when there are seasonal or cyclic patterns in the data.

## 4. When is 3x exponential smoothing most useful?

3x exponential smoothing is most useful when the data being analyzed has a trend, seasonal, or cyclic pattern. It can also be effective for data with random fluctuations, as it can smooth out any outliers or noise in the data.

## 5. What are the limitations of 3x exponential smoothing?

One limitation of 3x exponential smoothing is that it relies heavily on the assumption that the underlying patterns in the data will continue into the future. If there are sudden changes or shifts in the data, the forecast may not accurately reflect these changes. Additionally, 3x exponential smoothing may not perform well with data that has a high level of noise or irregular patterns.

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