Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes

By Rainer Dahlhaus, Wolfgang Polonik. 2006

92 citations recorded by the source corpus.

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior of the resulting estimator is studied. The results depend on the richness of the class of functions. Both sieve estimation and global estimation are considered. Our results apply, in particular, to estimation under shape constraints. As an example, autoregressive model fitting with a monotonic variance function is discussed in detail, including algorithmic considerations. A key technical tool is the time-varying empirical spectral process indexed by functions. For this process, a Bernstein-type exponential inequality and a central limit theorem are derived. These results for empirical spectral processes are of independent interest.

Subfields: Control and Systems Engineering, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/241d95dab95e5764f23a310c193f272810317489

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. Holger Dette
2. S. Rao
3. Carsten Jentsch
4. Mathias Vetter
5. Philip Preuss
6. Fabienne Comte
7. Rainer Dahlhaus
8. Jan Johannes

In Finance

1. Holger Dette
2. S. Rao
3. Carsten Jentsch
4. Piotr Fryzlewicz
5. Rainer Dahlhaus
6. Philip Preuss
7. Mathias Vetter
8. Fabienne Comte

In Statistics and Probability

1. Holger Dette
2. Philip Preuss
3. S. Rao
4. Carsten Jentsch
5. Mathias Vetter
6. Jan Johannes
7. Fabienne Comte
8. Rainer Dahlhaus

Citations in the corpus

• Adaptive functional linear regression (2011, background): “From the estimate (C.1) given in Dahlhaus and Polonik [2006] (Proposition A.1) follows p The estimate (C.3) follows analogously and we omit the details. which implies (C.2).”
• A Measure of Stationarity in Locally Stationary Processes With Applications to Testing (2011, background): “More recent work in this field can be found in the articles by Dahlhaus and Polonik (2006, 2009) and Dahlhaus (2009) who discussed quasi maximum likelihood estimation, empirical process theory, and its application to statistical inference in locally stationary processes.”
• A test for second order stationarity of a multivariate time series (2015, methodology): “These include, Priestley and Subba Rao (1969), Loretan and Phillips (1994), von Sachs and Neumann (1999), Paparoditis (2009, 2010), Dahlhaus and Polonik (2009), Dwivedi and Subba Rao (2011), Dette, Preuss, and Vetter (2011), Dahlhaus (2012), Example 10, Jentsch (2012), Lei, Wang, and Wang (2012) and”
• Locally Stationary Processes (2011, methodology): “The nonparametric estimator (29) with ` ∗t,T ( θ ) is studied in Dahlhaus and Polonik (2006).”
• Mixing properties of ARCH and time-varying ARCH processes (2011, background): “It is worth mentioning that by using (7), one can establish mixing rates for timevarying linear processes (such as the tvMA(∞) process considered in [10]).”
• Local inference for locally stationary time series based on the empirical spectral measure (2009, methodology): “Van Bellegem, S. and R. Dahlhaus, 2006, Semiparametric estimation by model selection for locally stationary processes.”