Hello

By using the filter exponential moving average, you can choose the first EMA value based on the mean of the first n observations. The number is limited to 6. Why this limitation ? Sometimes I see people taking the first value being the mean of half of the time series.

Where do I see any information about the way it is calculated in the Gretl documentation ?

I have a time series with mean = 351.2917 and the first observation is y₁ = 362

Gretl gives me correctly the first forecast being S₀ = 351.2917 for y₁ which equals the mean of the whole time series.

The second forecast is given by Gretl as being 354.2625 with alpha = 0.1.

According to me you should get: S₁ = 0.1(351.2917) + 0.9(362) = 352.3625

How to find the optimal alpha minimizing the MSE ?

Thank you for your help

Raul