A Likelihood Approximation for Locally Stationary Processes

By Rainer Dahlhaus. 2000

238 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5422e76db735cbf7b35637770e2e9a7775d75673

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Citations in the corpus

Empirical spectral processes for locally stationary time series (2009, methodology): “In Dahlhaus (2000), it has been shown that Ln(θ) := 1 4π 1 n n∑ t=1 ∫ π −π { log 4π2fθ ( t n ,λ ) + Jn(t/n,λ) fθ(t/n,λ) } dλ (31) is an approximation to −log Gaussian likelihood of a locally stationary process.”
Fitting dynamic factor models to non-stationary time series (2009, background): “…cases of locally stationary processes (Dahlhaus 2000, Remark 2.2) the process Y NT (t) as defined above is not locally stationary in the strict sense of Dahlhaus (1996, 2000) as it does not have a time-varying moving average represenation in terms of an N–dimensional white noise process ε̃N(t).”
Validating Stationarity Assumptions in Time Series Analysis by Rolling Local Periodograms (2010, methodology): “…grateful to the Editor, the Associate Editor, and two referees for their valuable and insightful comments leading to a considerable improvement of the paper. a meaningful setup for investigating asymptotic properties of statistical inference procedures can be developed; see Dahlhaus (1997, 2000).”
Quantile spectral analysis for locally stationary time series (2014, methodology): “1 below shows that, under relatively mild assumptions (which are required for the comparison to make sense), processes that are locally stationary in the sense of Dahlhaus (1996) are also locally strictly stationary in the sense of our definition.”
LOCALLY STATIONARY FACTOR MODELS: IDENTIFICATION AND NONPARAMETRIC ESTIMATION (2011, methodology): “1 of Dahlhaus (1997). The rescaled time principle is a tool for local estimation: We get more and more observations for the local structure of the loadings N ( t T ) at each time point. Our estimation target has to be defined properly, which is not the case if we do not rescale in time. A process wi”
Locally stationary long memory estimation (2009, background): “One prominent approach, that we adopt in this paper, too, is the model of local stationarity, introduced by a series of papers by R. Dahlhaus ([4, 5, 6]): in a non-parametric set-up, the spectral structure of the underlying stochastic process is allowed to be smoothly varying over time.”
A Measure of Stationarity in Locally Stationary Processes With Applications to Testing (2011, background): “7 of Dahlhaus (2009), the calculation of the limiting distribution of a corresponding Kolmogorov-Smirnov statistic is an unsolved task, because the limiting process depends in a complicated way on certain features of the data generating process.”
Locally Stationary Processes (2011, background): “ere˙2(u) istheonesteppredictionerrorattimeu. Themathematicalcoreoftheaboveresultsconsistsofthederivationofpropertiesofproducts of matrices T(A;B), T(A;A) 1 and U T(˚). These properties are derived in Dahlhaus (2000)inLemmaA.1,A.5,A.7andA.8. Theseresultsaregeneralizationsofcorresponding resultsinthes”
SLEX Analysis of Multivariate Nonstationary Time Series (2005, methodology): “In particular, ORvSG (2002) showed the asymptotic equivalence between the univariate SLEX and univariate Dahlhaus model of local stationarity. A similar consideration is possible for the multivariate models. Once the best adapted segmentation is chosen, one can develop asymptotic theory of consisten”
Local inference for locally stationary time series based on the empirical spectral measure (2009, methodology): “¤ Example 3.6 (Curve estimation by local Whittle-estimates) Whittle estimates were introduced by Whittle (1953) for stationary processes and were generalized by Dahlhaus (2000) to locally stationary processes.”
Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets (2008, background): “A similar idea motivates the covariance tapering approach that we explore in this article.”
Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes (2006, background): “nU n 1 2π φ (61) X , where Un(φ)jk= φˆ(1 n⌊ j+k 2 ⌋,j− k) and ⌊x⌋ denotes the largest integer less than or equal to x. The properties of Un(φ) have been investigated under diﬀerent assumptions in [10]. In this paper, we only need the following result on kUn(φ)kspec and kUn(φ)k2, where kAk2 :=tr(AH”