ABSTRACT
The characteristics of time series can be concisely described using time series models. Further, the time series model can be used for prediction, signal extraction and decision making for the time series. This chapter considers methods for obtaining the impulse response function, the autocovariance function, the partial autocorrelation (PARCOR), the power spectrum and the roots of the characteristic equation from the univariate autoregressive moving average mode (ARMA) model. The relations between the autoregressive (AR) coefficients and the PARCOR’s are also shown. Further, for multivariate time series, the cross-spectrum and the relative power contribution are derived from the multivariate AR model. The function armachar of the package Time Series Analysis with State Space Model computes and draw graphs of the impulse response function, the autocovariance function, the PARCORs, power spectrum and the characteristic roots of the AR operator and the MA operator of an ARMA mod.
