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AIRLINE_CHECK (Pro)
Examines the model's parameters for stability constraints (e.g. stationary, 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.
) of the ARMAi model's residuals should be greater than zero. - The Airline model is a special case of multiplicative seasonal ARMA model.
- The Airline model is a special case of multiplicative seasonal ARIMAi model, and it assumes independent and normally distributed residuals with constant variance.
Examples
Example 1:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Date | Data | ||
| 2 | 1/1/2008 | -0.300 |
ARMA |
|
| 3 | 1/2/2008 | -1.278 | Mean | -0.00258 |
| 4 | 1/3/2008 | 0.244 | Sigma | 0.14 |
| 5 | 1/4/2008 | 1.276 | Phi_1 | -0.236 |
| 6 | 1/6/2008 | 1.733 | Theta_1 | -5.60E-05 |
| 7 | 1/7/2008 | -2.184 | ||
| 8 | 1/8/2008 | -0.234 | ||
| 9 | 1/9/2008 | 1.095 | ||
| 10 | 1/10/2008 | -1.087 | ||
| 11 | 1/11/2008 | -0.690 | ||
| 12 | 1/12/2008 | -1.690 | ||
| 13 | 1/13/2008 | -1.847 | ||
| 14 | 1/14/2008 | -0.978 | ||
| 15 | 1/15/2008 | -0.774 |
| Formula | Description (Result) | ||
|---|---|---|---|
| =ARMA_AICi($B$2:$B$15,1,$D$3,$D$4,$D$5,$D$6) | 1046.59 | Akaike's information criterion (AIC) | |
| =ARMA_LLFi($B$2:$B$15,1,$D$3,$D$4,$D$5,$D$6) | -519.095 | Log-Likelihood Function | |
| =ARMA_CHECK($D$3,$D$4,$D$5,$D$6) | 1 | Is ARMA model stable? |
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
