AIRLINE_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, µ, σ, s, θ, θ_s, return, maxiter)

[X]

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

Order

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

Value	Order
1	Ascending (the first data point corresponds to the earliest date) (default).
0	Descending (the first data point corresponds to the latest date).

µ

Optional. Is the model mean (i.e., mu) or the long run mean of the differenced time series.

σ

Required. Is the standard deviation of the model's residuals/innovations.

S

Required. Is the length of seasonality (expressed in terms of lags, where s 1).

θ

Optional. Is the coefficient of the non-seasonal MA component (see model description).

θ_s

Optional. Is the coefficient of the seasonal MA component (see model description).

Return

Optional. Is an integer switch to select the output array: (1 = Quick Guess (default), 2 = Calibrated, 3 = Std. Errors).

Value	Return
1	Quick guess (non-optimal) of parameter values (default).
2	Calibrated (optimal) values for the model's parameters.
3	Standard error of the parameters' values.

MaxIter

Optional. 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_PARAM 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 $\theta = 0$ and $\Theta=0$.
6. The function was added in version 1.63 SHAMROCK.

Files Examples

Related Links

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

References

• James Douglas Hamilton; Time Series Analysis, Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896.
• Tsay, Ruey S.; Analysis of Financial Time Series, John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740.