Examines the model's parameters for stability constraints (e.g. stationary, invertibility, causality, etc.).
Syntax
AIRLINE_CHECK(mean, sigma, s, theta, theta2)
- mean
- is the model mean (i.e. mu).
- sigma
- is the standard deviation of the model's residuals/innovations.
- s
- is the length of seasonality (expressed in terms of lags, where s > 1).
- theta
- is the coefficient of first-lagged innovation (see model description).
- theta2
- is the coefficient of s-lagged innovation (see model description).
Remarks
- The underlying model is described here.
- The standard deviation (i.e. $\sigma$) of the ARMA model's residuals should be greater than zero.
- The Airline model is a special case of multiplicative seasonal ARIMA model. The model assumes independent and normally distributed residuals with constant variance.
- The AIRLINE_CHECK examines the MA coefficients: $\theta, \Theta, \theta\times\Theta$ for process stability.
Examples
Example 1:
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| Formula | Description (Result) | |
|---|---|---|
| =AIRLINE_AIC(Sheet1!$B$2:$B$15,1,$D$3,$D$6,$D$7,$D$4,$D$5) | 65.6 | Akaike's information criterion (AIC) |
| =AIRLINE_LLF(Sheet1!$B$2:$B$15,1,$D$3,$D$6,$D$7,$D$4,$D$5) | -25.47 | Log-Likelihood Function |
| =AIRLINE_CHECK($D$3,$D$6,$D$7,$D$4,$D$5) | 1 | Is the AIRLINE model stable? |
Files Examples
Related Links
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
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