# ARMA_CHECK - Check parameters' values for model stability

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

## Syntax

ARMA_CHECK(mean, sigma, phi, theta)

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).

## Remarks

1. The underlying model is described here.
2. ARMA_CHECK checks the process for stability: stationarity, invertability, and causality.
3. Using the Solver add-in in Excel, you can specify the return value of ARMA_CHECK as a constraint to ensure a stationary ARMA model.
4. The long-run mean can take any value or be omitted, in which case a zero value is assumed.
5. The residuals/innovations standard deviation (sigma) must greater than zero.
6. For the input argument - phi:
• The input argument is optional and can be omitted, in which case 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 AR component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
7. For the input argument - theta:
• The input argument is optional and can be omitted, in which case 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 MA component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).

## Examples

Example 1:

 1 2 3 4 5
A B
ARMA
Mean -0.35
Sigma 1.3059
Phi_1 -0.4296
Theta 0.999897

Formula Description (Result)
=ARMA_CHECK($B$2,$B$3,$B$4,$B$5) Is the model stable? (1)

## References

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