what is meant by biased and unbiased Autocovariance sequence estimate? In nonparametric spectral estimation method what is meant by biased and unbiased Autocovariance sequence estimate and why most commonly biased one is used? 
I have the answer to the second question from Peter Stoica (SPECTRAL ANALYSIS OF SIGNALS)but not getting what he wants to say.
In spectral estimation, one estimates "spectra" and other values. And one is interested in knowing whether the estimate $\hat{x}$ converge to the "true" but unknown value  $x$. It is unknown, for instance because one has only access to a finite quantity $N$ of samples to compute with, a limited number of realization, because ergodicity is not assured, etc. So we want to know whether  $\hat{x}_N\to x$ as $N\to \infty$. The convergence can be thought in different ways, and the most common is the mean square sense: does

$$\lim_{N\to \infty} E(|\hat{x}_N-x|^2)=0$$
where $E$ is the expectation? This can be really complicated to prove in practice. Thus, often people are satisfied when simpler conditions are met. And there are two necessary conditions for the above: 

$$\lim_{N\to \infty} E(\hat{x}_N)=x$$

$$\lim_{N\to \infty} E(|\hat{x}_N|^2)=0$$

The first is the asymptotic unbiasedness, the second the vanishing variance. Together, they define consistent estimators. So, a biased autocorrelation estimate won't converge to the true autocorrelation. And derived estimators (like periodograms) are unlikely to converge as well.