AIRLINE_AIC - Akaike's Information Criterion (AIC) of an Airline Model

Jacquie Nesbitt

October 20, 2016 19:19

Calculates the Akaike's information criterion (AIC) of the given airline model (with correction to small sample sizes).

Syntax

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

[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).

Warning

AIRLINE_AIC(.) function is deprecated as of version 1.63: use AIRLINE_GOF(.) function instead.

The underlying model is described here.
Akaike's Information Criterion (AIC) is described here.
The time series is homogeneous or equally spaced.
The time series may include missing values (e.g., #N/A) at either end.
The airline model with order $s$ has 4 parameters: $\mu\,,\sigma\,\,,\theta\,,\mathit{and} \: \Theta$.
The Airline model is a special case of the multiplicative seasonal ARIMA model, and it assumes independent and normally distributed residuals with constant variance.

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.