Ten weeks of data on the Commodity Futures Index are 7.35, 7.40, 7.55, 7.56, 7.60, 7.52, 7.52, 7.70, 7.62, and 7.55. Use trial and error to find a value of the exponential smoothing coefficient a results in a relatively small MSE.
Ten weeks of data on the Commodity Futures Index are 7.35, 7.40, 7.55, 7.56, 7.60, 7.52, 7.52, 7.70, 7.62, and 7.55.
- Use trial and error to find a value of the exponential smoothing coefficient a results in a relatively small MSE.
To find the exponential smoothing coefficient a that results in a relatively small Mean Squared Error (MSE), we can perform trial and error by testing different values of a and comparing the MSE for each value. Here is a basic outline of the steps:
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Initialize the first forecast: where is the first observation.
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For each time step t, calculate the forecast for the next time step using the exponential smoothing formula:
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Calculate the forecast error at each time step t :
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Calculate the MSE for the set of a values: .
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Repeat the above steps for different values of a and find the value of a that results in the lowest MSE.
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