# ARIMA_PARAM - Values of the Model's Parameters

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

## Syntax

AIRLINE_PARAM(X, Order, mean, sigma, s, theta, theta2, Type, maxIter)
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)
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 non-seasonal MA component (see model description).
theta2
is the coefficient of seasonal MA component (see model description).
Type
is an integer switch to select the output array: (1=Quick Guess (default), 2= Calibrated , 3=Std. Errors)
Order Description
1 Quick guess (non-optimal) of parameters values (default)
2 Calibrated (optimal) values for the model's parameters
3 Standard error of the parameters' values.
maxIter
is the maximum number of iterations used to calibrate the model. If missing, the default maximum of 100 is assumed.

## Remarks

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_PARAM returns an array of the values (or errors) of 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 $\Theta=0$
6. The function was added in version 1.63 SHAMROCK.

## Examples

Example 1:

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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?