When you are analyzing time series data using ARIMA model, you get AIC value, sigma squared value and log likelihood value. Normally if the value of AIC is smaller than BIC value the model fit well the data. What can you say about log likelihood value? Thank you.
See these links:
https://medium.com/analytics-vidhya/interpreting-arma-model-results-in-statsmodels-for-absolute-beginners-a4d22253ad1c
https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/time-series/how-to/arima/interpret-the-results/key-results/?SID=117600
https://otexts.com/fpp2/arima-estimation.html
https://www.researchgate.net/topic/ARIMA
Who cares? The AIC OR BIC TELLS YOU ABOUT PREDICTION QUALITY OF YOUR MODEL. That's what you usually want in a time series right. The LL GIVES YOU LOG OF THE LIKELIHOOD FUNCTION. This helps you optimize the likelihood function see a math statistics book. Does that help? Best wishes, David Booth
Sometimes, the log-likelihood value is seen as a simpler illustration of the maximum likelihood estimation. This is because it is determined by taking logs of the previous value. Although, it is well noted that the higher the log-likelihood, the better the model. However, log-likelihood is not the only guiding metric for comparing or call it model selection technique. In terms of AIC, the only difference is that as the number of variables gets bigger, it is more unlikely that the AIC ends up overparametrizing( Gonzalo and Pitarakis, 2002). Also, AIC balances this by penalizing for the number of parameters, hence searching for models with few parameters but fitting the data well. Looking at the models with the lowest AIC is a good way to select to better model
Exact maximum likelihood estimation for extended ARIMA model
10.1007/978-1-4899-4515-0_9
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