Locally Stationary Processes

By Rainer Dahlhaus. 2011

223 citations recorded by the source corpus.

Abstract The article contains an overview over locally stationary processes. At the beginning, time varying autoregressive processes are discussed in detail – both as a deep example and an important class of locally stationary processes. In the next section, a general framework for time series with time varying finite dimensional parameters is discussed with special emphasis on nonlinear locally stationary processes. Then, the paper focuses on linear processes where a more general theory is possible. First, a general definition for linear processes is given and time varying spectral densities are discussed in detail. Then, the Gaussian likelihood theory is presented for locally stationary processes. In the next section, the relevance of empirical spectral processes for locally stationary time series is discussed. Empirical spectral processes play a major role in proving theoretical results and provide a deeper understanding of many techniques. The article concludes with an overview of other results for locally stationary processes.

Subfields: Control and Systems Engineering, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/c8bc2684b773244217145556b760dbbfab022887

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. S. Rao
2. Carsten Jentsch
3. Holger Dette
4. Stanislav Volgushev
5. Marc Hallin
6. Tobias Kley
7. Stefan Birr
8. Rainer Dahlhaus

In Economics and Econometrics

1. Carsten Jentsch
2. Holger Dette
3. S. Rao
4. Rainer Dahlhaus
5. Stefan Richter
6. Wei Biao Wu
7. Marc Hallin
8. Tobias Kley

In Finance

1. Holger Dette
2. Carsten Jentsch
3. Rainer Dahlhaus
4. S. Rao
5. Stanislav Volgushev
6. Marc Hallin
7. Stefan Richter
8. Tobias Kley

Citations in the corpus

• Towards a general theory for nonlinear locally stationary processes (2017, background): “Dahlhaus, R. (2012)), tvARCH models (cf. Dahlhaus, R., and Subba Rao, S. (2006)) and random coefficient models (cf.”
• A test for second order stationarity of a multivariate time series (2015, methodology): “In Section 2 we consider the covariance between the DFTs for stationary and nonstationary time series, focusing on the class of locally stationary time series defined in Dahlhaus (1997), Dahlhaus and Polonik (2006) (see Dahlhaus (2012) for a review).”
• Quantile spectral analysis for locally stationary time series (2014, methodology): “Those four approaches, as already mentioned, are not without overlaps: the original concept by Dahlhaus (1997) is based on time-varying (second-order) spectral representations, turned into time-domain linear MA(∞) ones by Dahlhaus and Polonik (2006); Dahlhaus and Subba Rao (2006) and Fryzlewicz et a”