This node calculates the moving average of a column. The moving average values are displayed in a new column appended at the end of the table or (if selected) replaces the original columns. For all window based methods (Backward/Center/Forward simple/Gaussian, Harmonic Mean) the cells that do not have a complete window (at the beginning and the end of the table) are filled with Missing Values.

- Columns containing Double Values
- Select the input column containing double values on which to perform the moving average.
- Window Length
- The number of samples to include in the moving average window. It has to be an odd number if a center based method was selected. Minimum value: 3 samples. Maximum Value: Time Series length.
- Remove original columns
- If selected the original columns are replaced with the moving average columns.
- Type of Moving Average
- Moving Average can be applied with various methods. Here the used formulas for every kind, where v_n is the value in the n-th row of the data table in the selected column and k is the window size.

- Backward simple
Backward_simple_n = 1/k * sum{v_n-(k-1) ... v_n}

- Center simple
Center_simple_n = 1/k * sum{v_n-(n-1)/2 ... v_n ... v_n+(n-1)/2}

- Forward simple
Forward_simple_n = 1/k * sum{v_n ... v_n+k-1}

- Backward Gaussian
Backward_gaussian_n = sum{i = 0 ... k-1} gauss(i,k-1,std_dev)*v_n-i

- Center Gaussian
Center_gaussian_n = sum{i = 0 ... k-1} gauss(i,(k-1)/2,std_dev)*v_n+(i-(k-1)/2)

- Forward Gaussian
Forward_gaussian_n = sum{i = 0 ... k-1} gauss(i,0,std_dev)*v_n+i

- Harmonic Mean Center
- The harmonic mean can only be used for strictly positive values.
Center_harmonic_n = n/{sum{i = 0 ... k-1} 1/v_n+(i-(k-1)/2)

- Cumulative simple
Cumulative_n= 1/n * sum{v_0 ... v_n-1}

- Simple exponential
Simple_exponential_0 = v_0

EMA(v,n) = Simple_exponential_n = alpha*v_n + (1-alpha)*Simple_exponential_n-1

- Double exponential
Double_exponential_n = 2 * EMA(v,n) - EMA(EMA(v,n),n)

- Triple exponential
Triple_exponential_n = 3 * EMA(v,n) - 3 * EMA(EMA(v,n),n) + EMA(EMA(EMA(v,n),n),n)

- Old Exponential
Exponential_n = alpha*v_n + (1-alpha) * Backward_simple_n-1

- Appendix: Gaussian
- For the Gaussian weighted moving average the individual values are
weighted based on the position in the window.
std_dev = (k - 1) / 4

and the weighting:gauss(i,mean,std_dev) = Math.exp((-0.5) * (i - mean) * (i - mean) / std_dev^2)

- Appendix: Exponential
alpha = 2/(k+1)

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v4.4

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