cointBootTest: Bootstrap Determination of Cointegration Rank in VAR Models In VARtests: Tests for Error Autocorrelation, ARCH Errors, and Cointegration in Vector Autoregressive Models

Description

This function uses the bootstrap and wild bootstrap to test the cointegration rank of a VAR model. The test is an implementation of Cavaliere, Rahbek & Taylor (2012, 2014), and is used in Ahlgren & Catani (2018).

Usage

 ```1 2 3 4``` ```cointBootTest(y, r = "sequence", p, model = 1, signif = 0.05, dummies = NULL, B = 999, boot_type = c("B", "WB"), WB_dist = c("rademacher", "normal", "mammen")) ## S3 method for class 'cointBootTest' print(x, ...) ```

Arguments

 `y` a T x K matrix containing the time series. `r` either `"sequence"` or a vector of integers (0 <= r <= K - 1, where K is the number of columns in `y`). If a vector of integers, `r` is the cointegration rank being tested. If `r = "sequence"`, the bootstrap sequential algorithm will be used (see 'details'). `p` the lag order of the model. `model` either 1 (no deterministic terms), 2 (restricted constant), or 3 (restricted linear trend). See 'details' below. `signif` if `r = "sequence"` is used, `signif` sets the significance level of the tests in the sequential algorithm. `dummies` (optional) dummy variables. Must have the same number of rows as `y`. The models will then be estimated with the dummy variables, but the dummy variables are not used in the bootstrap DGP. In the `boot_type = "B"` version, the residuals used to draw the bootstrap errors do not include rows corresponding to observations where any of the dummies are equal to 1. `B` the number of bootstrap replications. `boot_type` either "B", "WB", or both. "B" uses the iid bootstrap algorithm, while "WB" uses the wild bootstrap algorithm. `WB_dist` The distribution used for the wild bootstrap. Either "rademacher", "normal", or "mammen". `x` Object with class attribute ‘cointBootTest’. `...` further arguments passed to or from other methods.

Details

Please see the pdf version of the manual at the package's CRAN page for mathematical details of the test.

Value

a list of class `"cointBootTest"`.

 `eigen_val` the eigenvalues. `eigen_vec` the eigenvectors. `alpha` a matrix with the estimated alpha parameters for the model with `r = K` (for other values of `r`, the alpha parameters are the first `r` columns of this matrix). `beta` a matrix with the estimated beta parameters for the model with `r = K` (for other values of `r`, the beta parameters are the first `r` columns of this matrix). `gamma` a list of matrices with the estimated gamma parameters. Each parameter matrix corresponds to the model estimated under the null hypothesis in `r` (0:(K-1) if `r = "sequence"`), in the same order. `rho` a matrix with the estimated rho parameters for the model with `r = K` (for other values of `r`, the rho parameters are the first `r` columns of this matrix). `phi` a list of matrices with the estimated phi parameters. Each parameter matrix corresponds to the model estimated under the null hypothesis in `r` (0:(K-1) if `r = "sequence"`), in the same order. `dummy_coefs` a list of matrices with the estimated dummy parameters. Each parameter matrix corresponds to the model estimated under the null hypothesis in `r` (0:(K-1) if `r = "sequence"`), in the same order. `residuals` a list of residual matrices, one for each model estimated under the null hypothesis in `r` (0:(K-1) if `r = "sequence"`), in that order. `Q` a vector with the Q test statistics. If `r = "sequence"`, then the first element is for the null hypothesis r = 0, and the last is for r = K - 1. Otherwise, the order corresponds to the `r` argument. `B.Q` a matrix of the iid bootstrap Q statistics. Each column represent the null hypothesis in the order of `r` (0:(K-1) if `r = "sequence"`). `WB.Q` a matrix of the wild bootstrap Q statistics. Each column represent the null hypothesis in the order of `r` (0:(K-1) if `r = "sequence"`). `B.r` the selected cointegration rank from the iid bootstrap test, if `r = "sequence"`) were used. `WB.r` the selected cointegration rank from the wild bootstrap test, if `r = "sequence"`) were used. `B.pv` a vector with the bootstrap P.values, in the order of `r` (0:(K-1) if `r = "sequence"`). `WB.pv` a vector with the wild bootstrap P.values, in the order of `r` (0:(K-1) if `r = "sequence"`). `B.errors` the number of times the bootstrap simulations had to be resimulated due to errors. `WB.errors` the number of times the wild bootstrap simulations had to be resimulated due to errors. `companion_eigen` a list of matrices with the eigenvalues of the companion matrix. The inverse of the eigenvalues are the roots in step 2 of the boostrap algorithm (see the .pdf version of this help file).

References

Ahlgren, N. & Catani, P. (2018). Practical Problems with Tests of Cointegration Rank with Strong Persistence and Heavy-Tailed Errors. In Corazza, M., Durábn, M., Grané, A., Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance, Cham, Springer.

Cavaliere, G., Rahbek, A., & Taylor, A. M. R. (2012). Bootstrap determination of the co-integration rank in vector autoregressive models, Econometrica, 80, 1721-1740.

Cavaliere, G., Rahbek, A., & Taylor, A. M. R. (2014). Bootstrap determination of the co-integration rank in heteroskedastic VAR models, Econometric Reviews, 33, 606-650.

Johansen, S. (1996). Likelihood-based inference in cointegrated vector autoregressive models, Oxford, Oxford University Press.

Examples

 ```1 2 3 4 5 6 7``` ```## Not run: test <- cointBootTest(y = VodafoneCDS, r = "sequence", p = 2, model = 3, signif = 0.05, dummies = NULL, B = 999, boot_type = c("B", "WB"), WB_dist = "rademacher") test ## End(Not run) ```

VARtests documentation built on May 2, 2019, 5:03 a.m.