vars (version 0.1.7)

VARselect: 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.

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.

encoding

latin1

concept

• VAR
• Vector autoregressive model
• Information criteria
• Final Prediction Error
• Akaike
• Hannan-Quinn
• Scharz

Details

Estimates a VAR by OLS per equation. The model is of the following form: $$\bold{y}_t = CD_t + A_1 \bold{y}_{t-1} + \ldots + A_p \bold{y}_{t-p} + \bold{u}_t$$ 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 $A_1, \ldots, A_p$ 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: $$AIC(n) = \ln \det(\tilde{\Sigma}_u(n)) + \frac{2}{T}n K^2 \quad,$$ $$HQ(n) = \ln \det(\tilde{\Sigma}_u(n)) + \frac{2 \ln(\ln(T))}{T}n K^2 \quad,$$ $$SC(n) = \ln \det(\tilde{\Sigma}_u(n)) + \frac{\ln(T)}{T}n K^2 \quad,$$ $$FPE(n) = \left ( \frac{T + n^*}{T - n^*} \right )^K \det(\tilde{\Sigma}_u(n)) \quad ,$$ with $\tilde{\Sigma}_u (n) = T^{-1} \sum_{t=1}^T \bold{\hat{u}}_t \bold{\hat{u}}_t'$ and $n^*$ is the total number of the parameters in each equation and $n$ assigns the lag order.

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. Cs�ki (eds.), 2nd International Symposium on Information Theory, Acad�mia Kiad�, 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. L�tkepohl, 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")