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We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…

Different disciplines pursue the aim to develop models which characterize certain phenomena as accurately as possible. Climatology is a prime example, where the temporal evolution of the climate is modeled. In order to compare and improve…

In complex systems, crucial parameters are often subject to unpredictable changes in time. Climate, biological evolution and networks provide numerous examples for such non-stationarities. In many cases, improved statistical models are…

Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…

For earthquake-resistant design, engineering seismologists employ time-history analysis for nonlinear simulations. The nonstationary stochastic method previously developed by Pousse et al. (2006) has been updated. This method has the…

Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null…

All too often measuring statistical dependencies between financial time series is reduced to a linear correlation coefficient. However this may not capture all facets of reality. We study empirical dependencies of daily stock returns by…

We propose a new nonparametric procedure for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second- order) piecewise stationary process, which also identifies the components of…

This paper explores the identification and estimation of nonseparable panel data models. We show that the structural function is nonparametrically identified when it is strictly increasing in a scalar unobservable variable, the conditional…

In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are…

A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for…

Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly…

Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…

Long-run covariance matrix estimation is the building block of time series inference. The corresponding difference-based estimator, which avoids detrending, has attracted considerable interest due to its robustness to both smooth and abrupt…

Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…

Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…

A stationary spatial model is an idealization and we expect that the true dependence structures of physical phenomena are spatially varying, but how should we handle this non-stationarity in practice? We study the challenges involved in…

Time series measured from real-world systems are generally noisy, complex and display statistical properties that evolve continuously over time. Here, we present a method that combines wavelet analysis and non-stationary surrogates to…

In this paper, we investigate time-varying nonlinear time series regression for a broad class of locally stationary time series. First, we propose sieve nonparametric estimators for the time-varying regression functions that achieve uniform…

It is commonplace to encounter nonstationary data, of which the underlying generating process may change over time or across domains. The nonstationarity presents both challenges and opportunities for causal discovery. In this paper we…