Constructs a time_series_model representing a stationary power-law
process with parameters kappa and sigma2.
In the frequency domain, a power-law process is often described by a
spectrum \(P(f) = P_0 f^{\kappa}\) (Bos et al., 2008), where \(f\) is the frequency, \(P_0\) is a constant and \(\kappa\) is the spectral index.
Note that we use the convention that the power spectral density satisfies
\(P(f) \propto |f|^{\kappa}\), where \(\kappa > -1\) ensures second-order
stationarity. This corresponds to the alternative notation
\(P(f) \propto |f|^{-\alpha}\) with \(\alpha = -\kappa\).
The autocovariance used here (Hosking, 1981) is
\(\gamma(0) = \sigma^{2} \frac{\Gamma(1+\kappa)}{\Gamma\left(1+\kappa/2\right)^2}\),
and for \(h > 0\)
\(\gamma(h) =\mathrm{cov}(X_t, X_{t+h}) = \frac{-\kappa/2 + h - 1}{\kappa/2 + h}\,\gamma(h-1)\).