GetCharPolyRoots {FCVAR}

Roots of the Characteristic Polynomial

Description

GetCharPolyRoots calculates the roots of the characteristic polynomial and plots them with the unit circle transformed for the fractional model, see Johansen (2008). summary.FCVAR_roots prints the output of GetCharPolyRoots to screen.

Usage

GetCharPolyRoots(coeffs, opt, k, r, p)

Arguments

coeffs

A list of coefficients for the FCVAR model. An element of the list of estimation results output from FCVARestn.

opt

An S3 object of class FCVAR_opt that stores the chosen estimation options, generated from FCVARoptions().

k

The number of lags in the system.

r

The cointegrating rank.

p

The number of variables in the system.

Value

An S3 object of type FCVAR_roots with the following elements:

cPolyRoots

A vector of the roots of the characteristic polynomial. It is an element of the list of estimation results output from FCVARestn.

b

A numeric value of the fractional cointegration parameter.

Note

The roots are calculated from the companion form of the VAR, where the roots are given as the inverse eigenvalues of the coefficient matrix.

References

Johansen, S. (2008). "A representation theory for a class of vector autoregressive models for fractional processes," Econometric Theory 24, 651-676.

See Also

FCVARoptions to set default estimation options. FCVARestn to estimate the model for which to calculate the roots of the characteristic polynomial. summary.FCVAR_roots prints the output of GetCharPolyRoots to screen.

Other FCVAR postestimation functions: FCVARboot(), FCVARhypoTest(), MVWNtest(), plot.FCVAR_roots(), summary.FCVAR_roots(), summary.MVWN_stats()

Examples

opt <- FCVARoptions()
opt$gridSearch   <- 0 # Disable grid search in optimization.
opt$dbMin        <- c(0.01, 0.01) # Set lower bound for d,b.
opt$dbMax        <- c(2.00, 2.00) # Set upper bound for d,b.
opt$constrained  <- 0 # Impose restriction dbMax >= d >= b >= dbMin ? 1 <- yes, 0 <- no.
x <- votingJNP2014[, c("lib", "ir_can", "un_can")]
results <- FCVARestn(x, k = 2, r = 1, opt)
FCVAR_CharPoly <- GetCharPolyRoots(results$coeffs, opt, k = 2, r = 1, p = 3)