Overview • Chapter 1: What are time series? Types of data, examples, objectives. Definitions , stationarity and autocovariances.

Key-words: population dynamics, quasi-stationarity, Yaglom’s limit, birth and death process, logistic Feller diffusion.

This paper introduces various consistent tests for the null hypothesis of stationarity with possibly unknown multiple structural break points against the alternative of nonstationarity that can be applied to multiple as well as univariate time series. These tests can be applied to either partial or pure structural breaks. It is shown that tests for stationarity become divergent when structural ...

We present a complete Bayesian treatment of autoregressive model estimation incorporating choice of autoregressive order, enforcement of stationarity, treatment of outliers and allowance for missing values and multiplicative seasonality. The paper makes three distinct contributions. First, we enforce the stationarity conditions using a very eecient Metropolis-within-Gibbs algorithm to generate ...

We consider the distributed optimal control of the obstacle problem with control constraints. Since Mignot proved in 1976 the necessity of a system which is equivalent to strong stationarity, it has been an open problem whether such a system is still necessary in the presence of control constraints. Using moderate regularity of the optimal control and an assumption on the control bounds (which ...

A multivariate test for stationarity is proposed in this paper. We develop Lagrange Multiplier type tests based on using additional stationary covariates. We show that the tests can be used to determine the number of cointegrating vectors in a system, starting with the null hypothesis of r cointegrating vectors and testing for less than r cointegrating vectors. A Monte Carlo experiment shows th...

Most methods for inferring phylogenies from sequence data assume that patterns of substitution have been stationary over time. Changes in evolutionary constraint can result in nonstationary substitution patterns that are phylogenetically misleading unless modeled appropriately. Here we present a multiple-alignment-based method to identify regions that are likely to contain misleading phylogenet...

Intrinsic random functions (IRF) provide a versatile approach when the assumption of second-order stationarity is not met. Here, we develop the IRF theory on the circle with its universal kriging application. Unlike IRF in Euclidean spaces, where differential operations are used to achieve stationarity, our result shows that low-frequency truncation of the Fourier series representation of the I...