Description Usage Arguments Details Value Author(s) Examples
An information criterion is calculated for different orders of an autoregressive-moving-average (ARMA) model.
1 2 3 4 5 6 7 | critMatrix(
X,
p.max = 5,
q.max = 5,
criterion = c("bic", "aic"),
include.mean = TRUE
)
|
X |
a numeric vector that contains the observed time series ordered from past to present; the series is assumed to follow an ARMA process. |
p.max |
an integer value >= 0 that defines the maximum
autoregressive order to calculate the criterion for; is set to |
q.max |
an integer value >= 0 that defines the maximum
moving-average order to to calculate the criterion for; is set to |
criterion |
a character value that defines the information criterion
that will be calculated; the Bayesian Information Criterion ( |
include.mean |
a logical value; this argument regulates whether to
estimate the mean of the series ( |
This function is part of the smoots
package and was implemented under
version 1.1.0. The series passed to X
is assumed to follow an
ARMA(p,q) model. A p.max + 1
by q.max + 1
matrix is
calculated for this series. More precisely, the criterion chosen via the
argument criterion
is calculated for all combinations of orders
p = 0, 1, ..., p_max and
q = 0, 1, ..., q_max.
Within the function, two information criteria are supported: the Bayesian Information Criterion (BIC) and Akaike's Information Criterion (AIC). The AIC is given by
AIC_[p,q] := ln(hat[sigma]^[2]_[p,q]) + {2(p + q)}/n,
where hat[sigma]^[2]_[p,q] is the estimated innovation variance, p and q are the ARMA orders and n is the number of observations.
The BIC, on the other hand, is defined by
BIC_[p,q] := k * ln(n) - 2ln(hat[L])
with k being the number of estimated parameters and hat[L] being the estimated Log-Likelihood. Since the parameter k only differs with respect to the orders p and q for all estimated models, the term k * ln(n) is reduced to (p + q) * ln(n) within the function. Exemplarily, if the mean of the series is estimated as well, it is usually considered within the parameter k when calculating the BIC. However, since the mean is estimated for all models, not considering this estimated parameter within the calculation of the BIC will reduce all BIC values by the same amount of ln(n). Therefore, the selection via this simplified criterion is still valid, if the number of the estimated parameters only differs with respect to p and q between the models that the BIC is obtained for.
The optimal orders are considered to be the ones which minimize either the BIC or the AIC. The use of the BIC is however recommended, because the BIC is consistent, whereas the AIC is not.
NOTE:
Within this function, the arima
function of the
stats
package with its method "CSS-ML"
is used throughout for
the estimation of ARMA models.
The function returns a p.max + 1
by q.max + 1
matrix, where the
rows represent the AR orders from p = 0 to p = p_max
and the columns represent the MA orders from q = 0 to
q = q_max. The values within the matrix are the values of
the previously selected information criterion for the different combinations
of p and q.
Dominik Schulz (Research Assistant) (Department of Economics, Paderborn
University),
Package Creator and Maintainer
1 2 3 4 5 6 7 8 9 10 |
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