AIRLINE_FORE - Forecasting for Airline Model

Calculates the out-of-sample conditional mean and error forecast

Syntax

AIRLINE_FORE ([x], order, µ, σ, s, θ, θs, t, return, α)

[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).
θs
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).
Return
Optional. Is an integer switch to select the forecast output type: (1 = Mean (default), 2 = Std. Error, 3 = Term Struct, 4 = LL, 5 = UL).
Value Return
1 Mean forecast value (default).
2 Forecast standard error (aka local volatility).
3 Volatility term structure.
4 Lower limit of the forecast confidence interval.
5 Upper limit of the forecast confidence interval.
α
Optional. Is the statistical significance level (i.e., alpha). If missing or omitted, an alpha value of 5% 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. The long-run mean argument µ can take any value or be omitted, in which case a zero value is assumed.
  5. The value of the residuals/innovations’ standard deviation σ must be positive.
  6. The season length must be greater than one.
  7. 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.
  8. The input argument for the seasonal MA parameter θs is optional and can be omitted, in which case no seasonal MA component is included.

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