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I have fit time series data to two models using SPSS. Their BIC values are as follows:

Normalised BIC,        Winters: -.111,   ARIMA: .048

I understand I must pick the lowest BIC value as this tells us the best model.

I am wondering how to interpret positive vs negative values:

I have read that the "lowest BIC value" is the best, but this usually compares two positive values, or two negative values. In this case is -.111 BIC value lower than 0.48? Or should I treat these differently as they are positive and negative?

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AIC, BIC, and all of the xIC family are likelihood-based measures. Meaning they are functions of the negated sums of a series of likelihoods. Near the mode of the distribution, the likelihood can be > 1, which means that the log-likelihood is > 0, which means that the negative log-likelihood can be truly negative. So what you are seeing is reasonable. And yes, a negative number is lower in magnitude than a positive number and is thus the "better" model in the information criteria framework.

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