ARMAX_CHECK - Check Parameters' Values for Model Stability

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

Syntax

ARMAX_CHECK (µ, σ, [φ], [θ])

µ

Optional. Is the ARMA model long-run mean (i.e., mu). If missing, the process mean is assumed to be zero.

σ

Required. Is the standard deviation value of the model's residuals/innovations.

[φ]

Optional. Are the parameters of the AR(p) component model: [φ1, φ2 … φp] (starting with the lowest lag).

[θ]

Optional. Are the parameters of the MA(q) component model: [θ1, θ2 … θq] (starting with the lowest lag).

Remarks

1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. ARMAX_CHECK examines the model for stability: stationarity, invertibility, and causality.
4. Using the Solver add-in in Excel, you can specify the return value of ARMAX_CHECK as a constraint to ensure a stationary ARMA model.
5. The long-run mean can take any value or be omitted, in which case a zero value is assumed.
6. The residuals/innovations standard deviation (σ) must be greater than zero.
7. For the AR(p) input argument - ([φ]):
• 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 error codes (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).
8. For the MA(q) input argument - ([θ]):
• 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).
9. 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

• James Douglas Hamilton; Time Series Analysis, Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896.
• Tsay, Ruey S.; Analysis of Financial Time Series, John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740.