VARselect {vars}R Documentation

Information criteria and FPE for different VAR(p)

Description

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.

Usage

VARselect(y, lag.max = 10, type = c("const", "trend", "both", "none"))

Arguments

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.

Details

Estimates a VAR by OLS per equation. The model is of the following form:

y_t = CD_t + A_1 y_{t-1} + ... + A_p y_{t-p} + 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 (term CD_T, by setting the type argument to the corresponding value. The default is const.
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.

Value

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.

Author(s)

Bernhard Pfaff

References

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.

See Also

VAR

Examples

data(Canada)
VARselect(Canada, lag.max = 5, type="const")

[Package vars version 0.1.9 Index]