Have a Question?
Phone: +1 (888) 427-9486
+1 (312) 324-0367
Fax: +1 (312) 238-9092
Contact Us
AIRLINE_MEAN (Pro)
Returns an array of cells for the fitted values of the conditional mean.
Syntax
AIRLINE_MEAN(X, Order, mean, sigma, s, theta, theta2)
X
is the univariate time series data (one dimensional array of cells (e.g. rows or columns)).
Order
is the time order of the data series (i.e. whether the first data point corresponds to the earliest or latest date (earliest date=1 (default), latest date=0)).
| Order | Description |
|---|---|
| 1 | ascending (the first data point corresponds to the earliest date) |
| 0 | descending (the first data point corresponds to the latest date) |
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 time series is homogeneous or equally spaced.
- The time series may include missing values (e.g. #N/A) at either end.
- The standard deviation (i.e.
) of the ARMAi model's residuals should be greater than zero. - The AICi is not a test on the model in the sense of hypothesis testing, rather it is a test between models - a tool for model selection.
- Given a fixed data set, several competing models may be ranked according to their AIC, the model with the lowest AIC being the best.
- The Airline model is a special case of multiplicative seasonal ARMA model.
- The Airline model is a special (but often-used) 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_AIC($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
