  Spectral density estimation is a core problem of system identification, which
is an important research area of system control and signal processing. There
have been numerous results on the design of spectral density estimators.
However to our best knowledge, quantitative error analyses of the spectral
density estimation have not been proposed yet. In real practice, there are two
main factors which induce errors in the spectral density estimation, including
the external additive noise and the limited number of samples. In this paper,
which is a very preliminary version, we first consider a univariate spectral
density estimator using covariance lags. The estimation task is performed by a
convex optimization scheme, and the covariance lags of the estimated spectral
density are exactly as desired, which makes it possible for quantitative error
analyses such as to derive tight error upper bounds. We analyze the errors
induced by the two factors and propose upper and lower bounds for the errors.
Then the results of the univariate spectral estimator are generalized to the
multivariate one.
