ARMA.selec: Selection of ARMA models

In weakARMA: Tools for the Analysis of Weak ARMA Models

Selection of ARMA models

Description

Identifies the orders p and q of an ARMA model according to several information criteria.

Usage

ARMA.selec(data, P, Q, c = 2)

Arguments

data	Univariate time series.
P	Integer for the maximum lag order of autoregressive component.
Q	Integer for the maximum lag order of moving-average component.
c	Real number >1 needed to compute Hannan-Quinn information criterion.

Details

The fitted model which is favored is the one corresponding to the minimum value of the criterion. The most popular criterion is the Akaike information criterion (AIC). This was designed to be an approximately unbiased estimator of a fitted model. For small sample or when the number of fitted parameters is large, it is more appropriate to manipulate a corrected AIC version (AICc) which is more nearly unbiased. But these two criteria are inconsistent for model orders selection. If you want to use a consistent criterion, it is possible to take the Bayesian information criterion (BIC) or the Hannan-Quinn information criteria (HQ).

For the weak ARMA, i.e under the assumption that the errors are uncorrelated but not necessarily independant, modified criteria has been adapted : AICm, AICcm, BICm, HQm.

The criteria definitions are the following :

AIC = n\log(σ^{2}) + 2(p + q)

AICm = n\log(σ^{2}) + \frac{Tr(IJ^{-1})}{σ^2}

AICc = n\log(σ^{2}) + n + \frac{n}{(n-(p + q + 1))} 2(p + q)

AICcm = n\log(σ^{2}) + \frac{n^{2}}{(n-(p + q + 1))} + \frac{n}{(2(n-(p + q + 1)))} \frac{Tr(IJ^{-1})}{σ^2}

BIC = n\log(σ^{2}) + (p + q)log(n)

BICm = n\log(σ^{2}) + \frac{1}{2} \frac{Tr(IJ^{-1})}{σ^2}log(n)

HQ = n\log(σ^{2}) + 2c(p + q)log(log(n))

HQm = n\log(σ^{2}) + c\frac{Tr(IJ^{-1})}{σ^2}log(log(n))

Value

A list of the different criteria, each item contains the matrix of the computed value for the different model and the selected order with this criterion (corresponding to the minimum value in the previous matrix).

References

Boubacar Maïnassara, Y. 2012, Selection of weak VARMA models by modified Akaike's information criteria, Journal of Time Series Analysis, vol. 33, no. 1, pp. 121-130

Boubacar Maïnassara, Y. and Kokonendji, C. C. 2016, Modified Schwarz and Hannan-Quin information criteria for weak VARMA models, Stat Inference Stoch Process, vol. 19, no. 2, pp. 199-217

Examples

ARMA.selec (CAC40return.sq, P = 3, Q = 3)

weakARMA documentation built on April 5, 2022, 1:16 a.m.