I am calculating the Akaike Information Criterion (AIC) for a forecasting model. What should be the value of K for the data which is having a nonlinear behaviour? Usually, for the linear, it is taken as 3, while for polynomial it is taken as 4. So in my case do I need to keep it as 4?
Muhammad Ali Musarat K is the no of parameters. see
https://www.researchgate.net/post/How-to-count-parameters-K-to-calculate-AIC-Akaikes-Information-Criterion-value-by-using-formula-AIC-2k-n-LogRSS-n
According to Shukor K is the number of parameters. A version of AIC is given by AIC(p) = 2K + pln(sigma^2). The first term is the over parametrization penalty and the second term tends to decrease with increase in model order p. You choose K to be equal to the number of parameters on the model. AIC selects the model based on its minimum.
Yunus Shukor thank you for sharing the link, however, it is still confusing.
Ette Etuk thank you, sir, for providing the detailed answer. I need to run AIC on the self-developed model. I have 2 questions, i) Does the K value changes with the data behaviour .i.e. linear or nonlinear, ii) Incase I have 1 dependent and 1 independent variable, what value of K I need to take?
Muhammad Ali Musarat Do you have a specific example of forecasting model?
See example from here
https://otexts.com/fpp3/selecting-predictors.html
The Akaike information criterion (AIC) is a statistical method for evaluating how well a model fits the data it was generated from. In statistics, AIC is used to compare different possible models and determine which one is the best fit for the data. AIC is calculated from:the number of independent variables used to build the model.the maximum likelihood estimate of the model, how well the model reproduces the data.
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