# AIRLINE_LLF - Log Likelihood Function of an Airline Model

Returns an array of cells for the initial/quick guess of the model's parameters

## Syntax

AIRLINE_GUESS(X, Order, s)

X is the univariate time series data (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)

s is the length of seasonality (expressed in terms of lags, where s > 1).

## Remarks

1. The underlying model is described here.
2. Warning: AIRLINE_LLF() function is deprecated as of version 1.63: use AIRLINE_GOF function instead.
3. The time series is homogeneous or equally spaced.
4. The time series may include missing values (e.g. #N/A) at either end.
5. AIRLINE_GUESS returns the model's parameters in the following order:
1. $\mu$
2. $\theta$
3. $\Theta$
4. $\sigma$
6. 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 $\Theta=0$

## Examples

Example 1:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
A B C D
Date Data
1/1/2008 -0.300 AIRLINE
1/2/2008 -1.278 Mean 0.0481
1/3/2008 0.244 theta(1) 0.14
1/4/2008 1.276 theta(2) 0.30
1/6/2008 1.733 Sigma 2.74127
1/7/2008 -2.184 s 2
1/8/2008 -0.234
1/9/2008 1.095
1/10/2008 -1.087
1/11/2008 -0.690
1/12/2008 -1.690
1/13/2008 -1.847
1/14/2008 -0.978
1/15/2008 -0.774

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?

## References

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