Calculates the Akaike's information criterion (AIC) of the given estimated ARMA model (with correction to small sample sizes).
ARMA_AIC(X, Order, mean, sigma, phi, theta)
- is the univariate time series data (one dimensional array of cells (e.g. rows or columns)).
- is the time order in the data series (i.e. the first data point's corresponding date (earliest date=1 (default), latest date=0)).
Order Description 1 ascending (the first data point corresponds to the earliest date) (default) 0 descending (the first data point corresponds to the latest date)
- is the ARMA model mean (i.e. mu).
- is the standard deviation of the model's residuals/innovations.
- are the parameters of the AR(p) component model (starting with the lowest lag).
- are the parameters of the MA(q) component model (starting with the lowest lag).
- The underlying model is described here.
- Akaike's Information Criterion (AIC) is described here.
Warning: ARMA_AIC() function is deprecated as of version 1.63: use ARMA_GOF function instead.
- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g. #N/A) at either end.
- The standard deviation (i.e. $\sigma$) of the ARMA model's residuals should be greater than zero.
- Given a fixed data set, several competing models may be ranked according to their AIC, the model with the lowest AIC being the best.
- The ARMA model has p+q+2 parameters, and it has independent and normally distributed residuals with constant variance.
- Maximizing for the log-likelihood function, the AICc function for an ARMA model becomes:
- $T$ is the number of non-missing values in the time series.
- $p$ is the order of the AR component model.
- $q$ os the order of the MA component model.
- $\hat\sigma$ is the standard deviation of the residuals.
- The number of parameters in the input argument - phi - determines the order of the AR component.
- The number of parameters in the input argument - theta - determines the order of the MA component.
|=ARMA_AIC($B$2:$B$15,1,$D$3,$D$4,$D$5,$D$6)||Akaike's Information Criterion (1046.59)|
|=ARMA_LLF($B$2:$B$15,1,$D$3,$D$4,$D$5,$D$6)||Log-Likelihood Function (-519.095)|
|=ARMA_CHECK($D$3,$D$4,$D$5,$D$6)||Is ARMA model stable? (1)|
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