VAR.spec:Allows Specifying a Bivariate VAR (Vector Autoregression) with Desired Spectral Characteristics

The spectral characteristics of a bivariate series (Marginal Spectra, Coherency- and Phase-Spectrum) determine whether there is a strong presence of short-, medium-, or long-term fluctuations (components of certain frequencies in the spectral representation of the series) in each one of them. These are induced by strong peaks of the marginal spectra of each series at the corresponding frequencies. The spectral characteristics also determine how strongly these short-, medium-, or long-term fluctuations of the two series are correlated between the two series. Information on this is provided by the Coherency spectrum at the corresponding frequencies. Finally, certain fluctuations of the two series may be lagged to each other. Information on this is provided by the Phase spectrum at the corresponding frequencies. The idea in this package is to define a VAR (Vector autoregression) model with desired spectral characteristics by specifying a number of polynomials, required to define the VAR. See Ioannidis(2007) <doi:10.1016/j.jspi.2005.12.013>. These are specified via their roots, instead of via their coefficients. This is an idea borrowed from the Time Series Library of R. Dahlhaus, where it is used for defining ARMA models for univariate time series. This way, one may e.g. specify a VAR inducing a strong presence of long-term fluctuations in series 1 and in series 2, which are weakly correlated, but lagged by a number of time units to each other, while short-term fluctuations in series 1 and in series 2, are strongly present only in one of the two series, while they are strongly correlated to each other between the two series. Simulation from such models allows studying the behavior of data-analysis tools, such as estimation of the spectra, under different circumstances, as e.g. peaks in the spectra, generating bias, induced by leakage.