SARIMAX_FIT - SARIMAX In-Sample Fitted Values

Returns an array of cells for the in-sample model fitted values of the conditional mean, volatility or residuals.

 

Syntax

SARIMAX_FIT(Y, X, Order, Beta, mean, sigma, d, phi, theta, period, sd, sPhi, sTheta, Type)

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 SARIMA model mean (i.e. long-run of the differenced time series). If missing, mean is assumed zero.

sigma is the standard deviation value of the model's residuals/innovations.

d is the non-seasonal difference order.

phi are the parameters of the non-seasonal AR model component AR(p) (starting with the lowest lag).

theta are the parameters of the non-seasonal 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 output type: (1=Mean (default), 2=Volatility, 3=Raw Residuals, 4=Standardized Residuals)

Order Description
1 Fitted mean (default)
2 Fitted standard deviation or volatility
3 Raw (non-standardized) residuals
4 Standardized residuals
 

Remarks

  1. The underlying model is described here.
  2. The Log-Likelihood Function (LLF) is described here.
  3. Each column in the explanatory factors input matrix (i.e. X) corresponds to a separate variable.
  4. Each row in the explanatory factors input matrix (i.e. X) corresponds to an observation.
  5. Observations (i.e. rows) with missing values in X or Y are assumed missing.
  6. The number of rows of the explanatory variable (X) must be at equal to the number of rows of the response variable (Y).
  7. The time series is homogeneous or equally spaced.
  8. The time series may include missing values (e.g. #N/A) at either end.
  9. The intercept or the regression constant term input argument is optional. If omitted, a zero value is assumed.
  10. For the input argument - Beta:
    • The input argument is optional and can be ommitted, in which case no regression component is included (i.e. plain SARIMA).
    • The order of the parameters defines how the exogneous factor input arguments are passed.
    • One or more parameters may have missing value or an error code(i.e. #NUM!, #VALUE!, etc.).
  11. The long-run mean argumen (mean) of the differenced regression residuals can take any value. If ommitted, a zero value is assumed.
  12. The residuals/innovations standard deviation (sigma) must greater than zero.
  13. For the input argument - phi (parameters of the non-seasonal AR component):
    • The input argument is optional and can be ommitted, in which case no non-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 non-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).
  14. For the input argument - theta (parameters of the non-seasonal MA component):
    • The input argument is optional and can be ommitted, in which case no non-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 non-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).
  15. For the input argument - sPhi (parameters of the seasonal AR component):
    • The input argument is optional and can be ommitted, 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).
  16. For the input argument - sTheta (parameters of the seasonal MA component):
    • The input argument is optional and can be ommitted, 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).
  17. The non-seasonal integration order - d - is optional and can be ommitted, in which case d is assumed zero.
  18. The seasonal integration order - sD - is optional and can be ommitted, in which case sD is assumed zero.
  19. The season length - s - is optional and can be ommitted, in which case s is assumed zero (i.e. Plain ARIMA).
  20. The function was added in version 1.63 SHAMROCK.

Files Examples

References

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