We give conditions for first and second order stationarity of mixture autoregressive processes and discuss related, sometimes confusing, results for such models. We obtain a simple condition for positive definiteness of the solution of a generalisation of the Stein’s equation with semidefinite right-hand side and apply it to second order stationarity. The said condition may be of independent in...

A test for stationarity in the presence of a structural break is proposed. An unknown break point is endogenously determined at the value minimizing the test statistic. The break point can be estimated reasonably well under the null hypothesis of stationarity, especially when the magnitude of the break is large.

Abstract Whether river flows remain stationary is of great concern to hydrologists, water engineers, and society in general, yet subject substantial debate. Here we provide the first comprehensive assessment long-term stationarity annual streamflow for 11 069 catchments globally. Our observation-based evidence shows that remains 79% with minimal human disturbance, indicating historical climate ...

There are two ways in which moving observers could judge whether threedimensional objects are stationary in an earth-fixed—rather than observerrelative—reference frame. An observer may determine the relative motion of an object as well as his or her own motion relative to an earth-fixed reference frame, and then compare the two: the extraretinal criterion. Alternatively, the observer could heur...

Tests of the null hypothesis of stationarity against the unit root alternative play an increasingly important role in empirical work in macroeconomics and in international finance. We show that the use of conventional asymptotic critical values for stationarity tests may cause extreme size distortions, if the model under the null hypothesis is highly persistent. This fact calls into question th...

We develop a test for stationarity of a time series against the alternative of a time-varying covariance structure. Using localized versions of the periodogram, we obtain empirical versions of a reasonable notion of a time-varying spectral density. Coeecients w.r.t. a Haar wavelet series expansion of such a time-varying periodogram are an indicator whether there is some deviation from covarianc...

The statistical properties of medical images are central in characterizing the performance of imaging systems. The noise in cone-beam CT (CBCT) is often characterized using Fourier-based metrics, such as the 3D noise-power spectrum (NPS). Under a stationarity assumption, the NPS provides a complete representation of the covariance of the images, since the covariance matrix of the Fourier transf...

Multi-stationarity in biological systems is a mechanism of cellular decision-making. In particular, signalling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological inputs. The features that lead to multi-stationarity are of particular interest to determine, as well as the stability, properties of the steady states. In this...