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SARIMA_GOF
Computes the goodness of fit measure (e.g. loglikelihood function (LLF^{i}), AIC^{i}, etc.) of the estimated SARIMA^{i} model.
Syntax
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^{i} model mean (i.e. mu). If missing, mean is assumed to be zero.
sigma
is the standard deviation value of the model's residuals/innovations.
d
is the nonseasonal difference order.
phi
are the parameters of the nonseasonal AR model component AR(p) (starting with the lowest lag^{i}).
theta
are the parameters of the nonseasonal MA model component (i.e. MA(q)) (starting with the lowest lag).
period
is the the number of observations per one period (e.g. 12=Annual, 4=Quarter).
sd
is the seasonal difference order.
sPhi
are the parameters of the seasonal AR model component AR(p) (starting with the lowest lag).
sTheta
are the parameters of the seasonal MA model component (i.e. MA(q)) (starting with the lowest lag).
Type
is an integer switch to select the goodness of fitness measure: (1=LLF (default), 2=AIC, 3=BIC^{i}, 4=HQC^{i}).
Order  Description 

1  LogLikelihood Function (LLF) (default) 
2  Akaike Information Criterion (AIC) 
3  Schwarz/Bayesian Information Criterion (SIC^{i}/BIC^{i}) 
4  HannanQuinn information criterion (HQC) 
Remarks
 The underlying model is described here.
 The LogLikelihood Function (LLF) is described here.
 The time series is homogeneous or equally spaced.
 The time series may include missing values (e.g. #N/A) at either end.
 The residuals/innovations standard deviation (i.e. ) should be greater than zero.

The ARMA model has independent and normally distributed residuals with constant variance. The ARMA loglikelihood function becomes:
Where:
 is the standard deviation of the residuals.
 The value of the input argument  period  must be greater than one, or the function returns #VALUE!.
 The value of the seasonal difference argument  sD  must be greater than one, or the function returns #VALUE!.
 The maximum likelihood estimation (MLE) is a statistical method for fitting a model to the data and provides estimates for the model's parameters.
 The longrun mean argument (mean) can take any value or be omitted, in which case a zero value is assumed.
 The residuals/innovations standard deviation (sigma) must be greater than zero.
 For the input argument  phi (parameters of the nonseasonal AR component):
 The input argument is optional and can be omitted, in which case no nonseasonal AR component is included.
 The order of the parameters starts with the lowest lag.
 One or more parameters may have missing values or error codes (i.e. #NUM!, #VALUE!, etc.).
 The order of the nonseasonal AR component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
 For the input argument  theta (parameters of the nonseasonal MA component):
 The input argument is optional and can be omitted, in which case no nonseasonal 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 nonseasonal MA component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
 For the input argument  sPhi (parameters of the seasonal AR component):
 The input argument is optional and can be omitted, in which case no seasonal AR component is included.
 The order of the parameters starts with the lowest lag.
 One or more parameters may have missing values or error codes (i.e. #NUM!, #VALUE!, etc.).
 The order of the seasonal AR component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
 For the input argument  sTheta (parameters of the seasonal MA component):
 The input argument is optional and can be omitted, in which case no seasonal 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 seasonal MA component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
 The nonseasonal integration order  d  is optional and can be omitted, in which case d is assumed to be zero.
 The seasonal integration order  sD  is optional and can be omitted, in which case sD is assumed to be zero.
 The season length  s  is optional and can be omitted, in which case s is assumed to be zero (i.e. plain ARIMA).
 The function was added in version 1.63 SHAMROCK.
Files Examples
References
 Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0691042896
 Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0471690740