Local inference for locally stationary time series based on the empirical spectral measure

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Locally Stationary Processes (2011, methodology): “The asymptotic normality of the estimate θ̂ GW T (u0) is derived in Dahlhaus (2009), Example 3.6.”
Locally stationary long memory estimation (2009, result): “Such results are somewhat similar to that for estimating the time varying parameter of a locally stationary short memory process, see [20], or, in a more general fashion, Example 3.6 in [7].”
A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics (2013, background): “The process Jn = (Jn(u, ν))u∈[0,1],ν∈[0,π] can be used in many contexts, ranging from testing the hypothesis of stationarity to estimation of model parameters; see Dahlhaus [8] for several examples.”
A Measure of Stationarity in Locally Stationary Processes With Applications to Testing (2011, background): “…Association Journal of the American Statistical Association September 2011, Vol. 106, No. 495, Theory and Methods DOI: 10.1198/jasa.2011.tm10811 1113 Dahlhaus (2009) proposed a test for stationarity by comparing estimates of the integrated time frequency spectral density under the null hypothesis…”