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)

Files Examples

References

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