Tobias Kley

• Dr. rer. nat.
• Lecturer at University of Bristol

Frequency domain methods form a ubiquitous part of the statistical toolbox for time series analysis. In recent years, considerable interest has been given to the development of new spectral methodology and tools capturing dynamics in the entire joint distributions and thus avoiding the limitations of classical, $L^2$-based spectral methods. Most of...

We propose a new sequential monitoring scheme for changes in the parameters of a multivariate time series. In contrast to procedures proposed in the literature which compare an estimator from the training sample with an estimator calculated from the remaining data, we suggest to divide the sample at each time point after the training sample. Estima...

We propose a new sequential monitoring scheme for changes in the parameters of a multivariate time series. In contrast to procedures proposed in the literature which compare an estimator from the training sample with an estimator calculated from the remaining data, we suggest to divide the sample at each time point after the training sample. Estima...

In this paper, we introduce quantile coherency to measure general dependence structures emerging in the joint distribution in the frequency domain and argue that this type of dependence is natural for economic time series but remains invisible when only the traditional analysis is employed. We define estimators which capture the general dependence...

Finding parametric models that accurately describe the dependence structure of observed data is a central task in the analysis of time series. Classical frequency domain methods provide a popular set of tools for fitting and diagnostics of time series models, but their applicability is seriously impacted by the limitations of covariances as a measu...

Finding parametric models that accurately describe the dependence structure of observed data is a central task in the analysis of time series. Classical frequency domain methods provide a popular set of tools for fitting and diagnostics of time series models, but their applicability is seriously impacted by the limitations of covariances as a measu...

The uniqueness of the time-varying copula-based spectrum recently proposed by the authors is established via an asymptotic representation result involving Wigner–Ville spectra.

Classical spectral methods are subject to two fundamental limitations: they can account only for covariance-related serial dependences, and they require second-order stationarity. Much attention has been devoted lately to quantile-based spectral methods that go beyond covariance-based serial dependence features. At the same time, covariance-based m...

The unicity of the time-varying quantile-based spectrum proposed in Birr et al. (2016) is established via an asymptotic representation result involving Wigner-Ville spectra.

The unicity of the time-varying quantile-based spectrum proposed in Birr et al. (2016) is established via an asymptotic representation result involving Wigner-Ville spectra.

In statistical research there usually exists a choice between structurally simpler or more complex models. We argue that, even if a more complex, locally stationary time series model were true, then a simple, stationary time series model may be advantageous to work with under parameter uncertainty. We present a new model choice methodology, where o...

In statistical research there usually exists a choice between structurally simpler or more complex models. We argue that, even if a more complex, locally stationary time series model were true, then a simple, stationary time series model may be advantageous to work with under parameter uncertainty. We present a new model choice methodology, where o...

In this paper we introduce quantile cross-spectral analysis of multiple time series which is designed to detect general dependence structures emerging in quantiles of the joint distribution in the frequency domain. We argue that this type of dependence is natural for economic time series but remains invisible when the traditional analysis is employ...

In this paper, we introduce quantile coherency to measure general dependence structures emerging in the joint distribution in the frequency domain and argue that this type of dependence is natural for economic time series but remains invisible when only the traditional analysis is employed. We define estimators which capture the general dependence...

In this paper we introduce quantile cross-spectral analysis of multiple time series which is designed to detect general dependence structures emerging in quantiles of the joint distribution in the frequency domain. We argue that this type of dependence is natural for economic time series but remains invisible when the traditional analysis is employ...

Quantile-based approaches to the spectral analysis of time series have recently attracted a lot of attention. Despite a growing literature that contains various estimation proposals, no systematic methods for computing the new estimators are available to date. This paper contains two main contributions. First, an extensible framework for quantileba...

Quantile-based approaches to the spectral analysis of time series have recently attracted a lot of attention. Despite a growing literature that contains various estimation proposals, no systematic methods for computing the new estimators are available to date. This paper contains two main contributions. First, an extensible framework for quantile-b...

Classical spectral methods are subject to two fundamental limitations: they only can ac- count for covariance-related serial dependencies, and they require second-order stationarity. Much attention has been devoted recently to quantile-based spectral methods that go beyond covariance-based serial dependence features. At the same time, methods relax...

Quantile- and copula-related spectral concepts recently have been considered by various authors. Those spectra, in their most general form, provide a full characterization of the copulas associated with the pairs (Xt;Xt-k) in a process (Xt)t2Z, and account for important dynamic features, such as changes in the conditional shape (skewness, kurtosis)...

Quantile- and copula-related spectral concepts recently have been considered by various authors. Those spectra, in their most general form, provide a full characterization of the copulas associated with the pairs (Xt;Xt-k) in a process (Xt)t2Z, and account for important dynamic features, such as changes in the conditional shape (skewness, kurtosis)...

In this paper we present an alternative method for the spectral analysis of a strictly stationary time series (Yt)eZ. We define a "new" spectrum as the Fourier transform of the differences between copulas of the pairs (Yt; Yt-k) and the independence copula. This object is called copula spectral density kernel and allows to separate marginal and ser...

In this paper we present an alternative method for the spectral analysis of a strictly stationary time series $\{Y_t\}_{t\in \Z}$. We define a "new" spectrum as the Fourier transform of the differences between copulas of the pairs $(Y_t,Y_{t-k})$ and the independence copula. This object is called {\it copula spectral density kernel} and allows to s...