SARIMAX_CHECK - Check parameters' values for model stability

Examines the model's parameters for stability constraints (e.g., stationary, invertibility, causality, etc.).

Syntax

SARIMAX_CHECK(mean, sigma, d, phi, theta, period, sd, sPhi, sTheta, Beta)

mean

is the SARIMA model mean (i.e., long-run of the differenced time series). If missing, the 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 MA(q) (starting with the lowest lag).

period

is 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 MA(q) (starting with the lowest lag).

Beta

are the coefficients array of the exogenous factors.

Remarks

1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. SARIMA_CHECK checks if $\sigma\gt 0$ and if all the characteristic roots of the underlying ARMA model fall outside the unit circle.
4. Using the Solver Add-in in Excel, you can specify the return value of SARIMA_CHECK as a constraint to ensure a stationary ARMA model.
5. The intercept or the regression constant term input argument is optional. If omitted, a zero value is assumed.
6. 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 a missing value or an error code (i.e., #NUM!, #VALUE!, etc.).
7. The long-run mean argument (mean) of the differenced regression residuals can take any value. If omitted, a zero value is assumed.
8. The residuals/innovations standard deviation (sigma) must be greater than zero.
9. For the input argument - phi (parameters of the non-seasonal AR component):
   • The input argument is optional and can be omitted, 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 a 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).
10. For the input argument - theta (parameters of the non-seasonal MA component):
    • The input argument is optional and can be omitted, 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).
11. 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 a 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).
12. 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).
13. The non-seasonal integration order - d - is optional and can be omitted, in which case d is assumed zero.
14. The seasonal integration order - sD - is optional and can be omitted, in which case sD is assumed zero.
15. The season length - s - is optional and can be omitted, in which case s is assumed zero (i.e. Plain ARIMA).
16. The function was added in version 1.63 SHAMROCK.

Files Examples

Related Links

• Wikipedia - Likelihood function.
• Wikipedia - Likelihood principle.
• Wikipedia - Autoregressive moving average model.

References

• Hamilton, J.D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6.
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740.