Bayesian Model Search for Nonstationary Periodic Time Series

We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit oscillatory behaviour. We approximate the time series using a piecewise oscillatory model with unknown periodicities, where our goal is to estimate the change-points while simultaneously identifying the potentially changing periodicities in the data. Our proposed methodology is based on a trans-dimensional Markov chain Monte Carlo (MCMC) algorithm that simultaneously updates the change-points and the periodicities relevant to any segment between them. We show that the proposed methodology successfully identifies time changing oscillatory behaviour in two applications which are relevant to e-Health and sleep research, namely the occurrence of ultradian oscillations in human skin temperature during the time of night rest, and the detection of instances of sleep apnea in plethysmographic respiratory traces.Comment: Received 23 Oct 2018, Accepted 12 May 201

Inference of time-varying regression models

We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate processes. With a two-stage method, the parametric component can be estimated with a $n^{1/2}$-convergence rate. A simulation-assisted hypothesis testing procedure is proposed for testing significance and parameter constancy. We further propose an information criterion that can consistently select the true set of significant predictors. Our method is applied to autoregressive models with time-varying coefficients. Simulation results and a real data application are provided.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1010 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bayesian Lattice Filters for Time-Varying Autoregression and Time-Frequency Analysis

Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a wide range of processes is a subject of ongoing interest. We propose a novel approach to model-based time-frequency estimation using time-varying autoregressive models. In this context, we take a fully Bayesian approach and allow both the autoregressive coefficients and innovation variance to vary over time. Importantly, our estimation method uses the lattice filter and is cast within the partial autocorrelation domain. The marginal posterior distributions are of standard form and, as a convenient by-product of our estimation method, our approach avoids undesirable matrix inversions. As such, estimation is extremely computationally efficient and stable. To illustrate the effectiveness of our approach, we conduct a comprehensive simulation study that compares our method with other competing methods and find that, in most cases, our approach performs superior in terms of average squared error between the estimated and true time-varying spectral density. Lastly, we demonstrate our methodology through three modeling applications; namely, insect communication signals, environmental data (wind components), and macroeconomic data (US gross domestic product (GDP) and consumption).Comment: 49 pages, 16 figure

Time-series Econometrics: Cointegration and Autoregressive Conditional Heteroskedasticity

Advanced information on the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel, 2003. Empirical research in macroeconomics as well as in financial economics is largely based on time series. Ever since Economics Laureate Trygve Haavelmo's work it has been standard to view economic time series as realizations of stochastic processes. This approach allows the model builder to use statistical inference in constructing and testing equations that characterize relationships between economic variables. This year's Prize rewards two contributions that have deepened our understanding of two central properties of many economic time series - nonstationarity and time-varying volatility - and have led to a large number of applicationstime-series; cointegration

Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology

The detection and attribution of long-term patterns in hydrological time series have been important research topics for decades. A significant portion of the literature regards such patterns as ‘deterministic components’ or ‘trends’ even though the complexity of hydrological systems does not allow easy deterministic explanations and attributions. Consequently, trend estimation techniques have been developed to make and justify statements about tendencies in the historical data, which are often used to predict future events. Testing trend hypothesis on observed time series is widespread in the hydro-meteorological literature mainly due to the interest in detecting consequences of human activities on the hydrological cycle. This analysis usually relies on the application of some null hypothesis significance tests (NHSTs) for slowly-varying and/or abrupt changes, such as Mann-Kendall, Pettitt, or similar, to summary statistics of hydrological time series (e.g., annual averages, maxima, minima, etc.). However, the reliability of this application has seldom been explored in detail. This paper discusses misuse, misinterpretation, and logical flaws of NHST for trends in the analysis of hydrological data from three different points of view: historic-logical, semantic-epistemological, and practical. Based on a review of NHST rationale, and basic statistical definitions of stationarity, nonstationarity, and ergodicity, we show that even if the empirical estimation of trends in hydrological time series is always feasible from a numerical point of view, it is uninformative and does not allow the inference of nonstationarity without assuming a priori additional information on the underlying stochastic process, according to deductive reasoning. This prevents the use of trend NHST outcomes to support nonstationary frequency analysis and modeling. We also show that the correlation structures characterizing hydrological time series might easily be underestimated, further compromising the attempt to draw conclusions about trends spanning the period of records. Moreover, even though adjusting procedures accounting for correlation have been developed, some of them are insufficient or are applied only to some tests, while some others are theoretically flawed but still widely applied. In particular, using 250 unimpacted stream flow time series across the conterminous United States (CONUS), we show that the test results can dramatically change if the sequences of annual values are reproduced starting from daily stream flow records, whose larger sizes enable a more reliable assessment of the correlation structures

A stochastic approach to synthesizing response spectrum compatible seismic accelerograms

Regulatory agencies require the use of artificial accelerograms satisfying specific criteria of compatibility with a given design spectrum, as input for certain types of analyses for the aseismic design of critical facilities. Most of the numerical methods for simulating seismic motions compatible with a specified design (target) spectrum proposed by various researchers require that a number of real recorded seismic accelerograms of appropriate frequency content is available. To by-pass this requirement, a previously established in the literature probabilistic approach to yield simulated earthquake records whose response spectrum achieves on average a certain level of agreement with a target spectrum is employed in the present paper. At the core of the above method lies the adoption of an appropriate parametric power spectrum model capable of accounting for various site-specific soil conditions. In this regard, the potential of two different, commonly, used spectral forms is evaluated for this purpose in context with the design spectrum defined by the European Code provisions. Next, an iterative wavelet-based matching procedure is applied to the thus acquired records to enhance, individually, the agreement of the corresponding response spectra with the targeted one. Special attention is paid to ensure that the velocity and the displacement time histories associated with the finally obtained artificial accelerograms are physically sound by means of appropriate baseline correction techniques

A Conditionally Heteroskedastic Model with Time-varying Coefficients for Daily Gas Spot Prices.

This paper examines the relationship between gas spot prices at the Zeebrugge market, one-month ahead Brent prices and temperatures over the period 2000–2005. A cointegration analysis is carried out and it is discovered that a cointegration relationship exists between the three series. To take into account the influence of temperature on the gas volatility, a GARCH(1,1) model with temperature-dependent coefficients is considered. Stability and estimation properties are discussed. An empirical finding is the existence of distinct volatility regimes for the volatility of gas prices, depending on the temperature level.Quasi-Maximum Likelihood Estimation; Time-Varying Coefficients; Periodic models; GARCH; Nonstationary Models; Gas Prices;

Dynamics of Intra-EMS Interest Rate Linkages

interest rates, long memory, error correction