Some Interesting Things

At least to me.

A timeseries (X_n)_{n\ge 0} is determined by all finite joint distributions.

To have a chance to apply statistics to observed sample paths we need to assume (strict) stationarity: (X_n) and (X_{n+k}) have the same law for any k > 0.

Kolmogorov showed there exists a positive spectral measure dF on the boundary of the unit disk D = \{z\mid |z| < 1\}. \Cov(X_n, X_{n + k}) = \int_{\partial D} z^k dF(t).

Parameterize by Bernolli series?