AIRLINE_FORESD - Forecasting Error of Airline Model

Calculates the estimated error/standard deviation of the conditional mean forecast.

Syntax

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

[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).

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.

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.