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ARMA_CHECK
Examines the model's parameters for stability constraints (e.g. stationary, etc.).
Syntax
ARMAi_CHECK(mean, sigma, phi, theta)
mean
is the ARMA model 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
- The underlying model is described here.
- The time series is homogeneous or equally spaced.
-
ARMA_CHECK checks if
and if all characteristic roots fall outside the unit circle.
- 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.
- The number of parameters in the input argument - phi - determines the order of the AR component.
- The number of parameters in the input argument - theta - determines the order of the MA component.
Examples
Example 1:
| A | B | |
|---|---|---|
| 1 | ARMA | |
| 2 | Mean | -0.35 |
| 3 | Sigma | 1.3059 |
| 4 | Phi_1 | -0.4296 |
| 5 | Theta | 0.999897 |
| Formula | Description (Result) | |
|---|---|---|
| =ARMA_CHECK($B$2,$B$3,$B$4,$B$5) | Is the model stable? (1) |
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
