Phone: +1 (888) 4279486
+1 (312) 2573777
Contact Us
SARIMAX_GOF
Computes the goodness of fit measure (e.g. loglikelihood function (LLF^{i}), AIC^{i}, etc.) of the estimated SARIMA^{i} model.
Syntax
Y
is the response or the dependent variable time series data array (one dimensional array of cells (e.g. rows or columns)).
X
is the independent variables (exogenous factors) time series data matrix, such that each column represents one variable.
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) 
Beta
are the coefficients array of the exogenous factors.
mean
is the ARMA^{i} model mean (i.e. mu). If missing, mean is assumed 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.
 Each column in the explanatory factors input matrix (i.e. X) corresponds to a separate variable.
 Each row in the explanatory factors input matrix (i.e. X) corresponds to an observation.
 Observations (i.e. rows) with missing values in X or Y are assumed missing.
 The number of rows of the explanatory variable (X) must be at equal to the number of rows of the response variable (Y).
 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.

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 intercept or the regression constant term input argument is optional. If omitted, a zero value is assumed.
 For the input argument  Beta:
 The input argument is optional and can be omitted, in which case no regression component is included (i.e. plain SARIMA).
 The order of the parameters defines how the exogenous factor input arguments are passed.
 One or more parameters may have missing value or an error code(i.e. #NUM!, #VALUE!, etc.).
 The longrun mean argumen (mean) of the differenced regression residuals can take any value. If ommitted, a zero value is assumed.
 The residuals/innovations standard deviation (sigma) must 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 value or an error code(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 value or an error code(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 zero.
 The seasonal integration order  sD  is optional and can be omitted, in which case sD is assumed zero.
 The season length  s  is optional and can be omitted, in which case s is assumed 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