# ARMA_GOF - Goodness of fit of an ARMA Model

Computes the goodness of fit measure (e.g., log-likelihood function (LLF), AIC, etc.) of the estimated ARIMA model.

## Syntax

ARMA_GOF(X, Order, mean, sigma, phi, theta, Type)
X
is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).
Order
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)
mean
is the ARMA model long-run mean (i.e., mu).
sigma
is the standard deviation of the model's residuals/innovations.
phi
are the parameters of the AR(p) component model (starting with the lowest lag).
theta
are the parameters of the MA(q) component model (starting with the lowest lag).
Type
is an integer switch to select the goodness of fitness measure: (1=LLF (default), 2=AIC, 3=BIC, 4=HQC)
Order Description
1 Log-Likelihood Function (LLF) (default)
2 Akaike Information Criterion (AIC)
3 Schwarz/Bayesian Information Criterion (SIC/BIC)
4 Hannan-Quinn information criterion (HQC)

## Remarks

1. The underlying model is described here.
2. The Log-Likelihood Function (LLF) is described here.
3. The time series is homogeneous or equally spaced.
4. The time series may include missing values (e.g., #N/A) at either end.
5. The long-run mean can take any value or be omitted, in which a zero value is assumed.
6. The residuals/innovations standard deviation (sigma) must be greater than zero.
7. For the input argument - phi:
• The input argument is optional and can be omitted, so no AR component is included.
• The order of the parameters starts with the lowest lag.
• One or more parameters may have missing values or an error code (i.e., #NUM!, #VALUE!, etc.).
• The order of the last value solely determines the order of the AR component model in the array with a numeric value (vs. missing or error).
8. For the input argument - theta:
• The input argument is optional and can be omitted, so no MA component is included.
• The order of the parameters starts with the lowest lag.
• One or more values in the input argument can be missing or an error code (i.e., #NUM!, #VALUE!, etc.).
• The order of the last value solely determines the order of the MA component model in the array with a numeric value (vs. missing or error).
9. Missing parameters values reduce the model's actual number of overall parameters, thus improving the AIC, BIC, and HQC statistics.
10. The function was added in version 1.63 SHAMROCK.