AIRLINE_LLF - Log Likelihood Function of an Airline Model

X

is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).

Order

is the time order in the data series (i.e., the first data point's corresponding date (earliest date=1 (default), latest date=0)).

Order	Description
1	ascending (the first data point corresponds to the earliest date) (default)
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).

1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. The time series may include missing values (e.g., #N/A) at either end.
4. AIRLINE_GUESS returns the model's parameters in the following order:
   
   1. $\mu$
   2. $\theta$
   3. $\Theta$
   4. $\sigma$
5. The AIRLINE_GUESS sets the $\mu$ and $\sigma$ equal to the differenced sample (i.e., $Z_t=(1-L)(1-L^s)Y_t$) average and standard deviation respectively, and it sets the $\theta = 0$ and $\Theta=0$

Example 1:

Files Examples

Related Links

• Wikipedia - Akaike's Information Criterion (AIC)
• Wikipedia - Autoregressive moving average model

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