AIRLINE_SIM - Simulated Values of an Airline Model

Calculates the out-of-sample conditional simulated values.

Syntax

AIRLINE_SIM ([x], order, µ, σ, s, θ, θ_s, t, seed)

[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).

T

Required. Is the forecast time/horizon (expressed in terms of steps beyond the end of the time series).

Seed

Required. Is an unsigned integer for setting up the random number generator(s).

Remarks

1. The underlying model is described here.
2. ARMA_SIM returns an array of one simulation path starting from the end of the input data.
3. The input data argument (i.e., latest observations) is optional. If omitted, an array of zeroes is assumed.
4. The time series is homogeneous or equally spaced.
5. The time series may include missing values (e.g., #N/A) at either end.
6. The long-run mean argument (mean) can take any value or be omitted, in which case a zero value is assumed.
7. The value of the residuals/innovations standard deviation (sigma) must be positive.
8. The season length must be greater than one.
9. The input argument for the non-seasonal MA parameter - θ - is optional and can be omitted, in which case no non-seasonal MA component is included.
10. The input argument for the seasonal MA parameter - θ_s - is optional and can be omitted, in which case no seasonal MA component is included.
11. 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.