VARselect {vars} | R Documentation |
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.
VARselect(y, lag.max = 10, type = c("const", "trend", "both", "none"), season = NULL, exogen = NULL)
y |
Data item containing the endogenous variables |
lag.max |
Integer for the highest lag order (default is
lag.max = 10 ). |
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:
y_t = A_1 y_{t-1} + ... + A_p y_{t-p} + CD_t + u_t
where 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} sum_{t=1}^T hat{u}_t 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
lag.max . |
Bernhard Pfaff
Akaike, H. (1969), Fitting autoregressive models for prediction, Annals of the Institute of Statistical Mathematics, 21: 243-247.
Akaike, H. (1971), Autoregressive model fitting for control, Annals of the Institute of Statistical Mathematics, 23: 163-180.
Akaike, H. (1973), Information theory and an extension of the maximum likelihood principle, in B. N. Petrov and F. Csáki (eds.), 2nd International Symposium on Information Theory, Académia Kiadó, Budapest, pp. 267-281.
Akaike, H. (1974), A new look at the statistical model identification, IEEE Transactions on Automatic Control, AC-19: 716-723.
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: 190-195.
Lütkepohl, 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: 182-185.
Schwarz, G. (1978), Estimating the dimension of a model, Annals of Statistics, 6: 461-464.
data(Canada) VARselect(Canada, lag.max = 5, type="const")