Description Usage Arguments Details Value Author(s) References See Also Examples
The function returns infomation criteria and final prediction error for sequential increasing the lag order up to a VAR(p)proccess. which are based on the same sample size.
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y 
Data item containing the endogenous variables 
lag.max 
Integer for the highest lag order (default is

type 
Type of deterministic regressors to include. 
season 
Inlusion of centered seasonal dummy variables (integer value of frequency). 
exogen 
Inlusion of exogenous variables. 
Estimates a VAR by OLS per equation. The model is of the following form:
\bold{y}_t = A_1 \bold{y}_{t1} + … + A_p \bold{y}_{tp} + CD_t + \bold{u}_t
where \bold{y}_t is a K \times 1 vector of endogenous
variables and u_t assigns a spherical disturbance term of the
same dimension. The coefficient matrices A_1, …, A_p are of
dimension K \times K. In addition, either a constant and/or a
trend can be included as deterministic regressors as well as centered
seasonal dummy variables and/or exogenous variables (term CD_T, by
setting the type
argument to the corresponding value and/or
setting season
to the desired frequency (integer) and/or providing a
matrix object for exogen
, respectively. The default for type
is
const
and for season
and exogen
the default is
set to NULL
.
Based on the same sample size the following information criteria and
the final prediction error are computed:
AIC(n) = \ln \det(\tilde{Σ}_u(n)) + \frac{2}{T}n K^2 \quad,
HQ(n) = \ln \det(\tilde{Σ}_u(n)) + \frac{2 \ln(\ln(T))}{T}n K^2 \quad,
SC(n) = \ln \det(\tilde{Σ}_u(n)) + \frac{\ln(T)}{T}n K^2 \quad,
FPE(n) = ≤ft ( \frac{T + n^*}{T  n^*} \right )^K \det(\tilde{Σ}_u(n)) \quad ,
with \tilde{Σ}_u (n) = T^{1} ∑_{t=1}^T \bold{\hat{u}}_t \bold{\hat{u}}_t' and n^* is the total number of the parameters in each equation and n assigns the lag order.
A list with the following elements:
selection 
Vector with the optimal lag number according to each criterium. 
criteria 
A matrix containing the values of the criteria up to

Bernhard Pfaff
Akaike, H. (1969), Fitting autoregressive models for prediction, Annals of the Institute of Statistical Mathematics, 21: 243247.
Akaike, H. (1971), Autoregressive model fitting for control, Annals of the Institute of Statistical Mathematics, 23: 163180.
Akaike, H. (1973), Information theory and an extension of the maximum likelihood principle, in B. N. Petrov and F. CsÃ¡ki (eds.), 2nd International Symposium on Information Theory, AcadÃ©mia KiadÃ³, Budapest, pp. 267281.
Akaike, H. (1974), A new look at the statistical model identification, IEEE Transactions on Automatic Control, AC19: 716723.
Hamilton, J. (1994), Time Series Analysis, Princeton University Press, Princeton.
Hannan, E. J. and B. G. Quinn (1979), The determination of the order of an autoregression, Journal of the Royal Statistical Society, B41: 190195.
LÃ¼tkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.
Quinn, B. (1980), Order determination for a multivariate autoregression, Journal of the Royal Statistical Society, B42: 182185.
Schwarz, G. (1978), Estimating the dimension of a model, Annals of Statistics, 6: 461464.
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