Initial transient detection in simulations using the second-order cumulant spectrum

Procedures for detecting an initial transient in simulation output data are developed. The tests use the second-order cumulant spectrum which differs from the power spectrum in that the stationarity constraint is not required for the former. The second-order cumulant spectrum can be interpreted as the nonstationary power spectrum and is an orthogonal decomposition of the variance of a nonstationary process. The null hypothesis is that the simulation output data series is a covariance stationary process. Equivalently, all estimates of the second-order cumulant spectrum in the region which excludes the estimates of the power spectrum will have an expected value of zero. The test procedures are designed to detect initialization bias in the estimation of the mean and the variance. These procedures can be extended to detect bias in the moments of cumulants of ordern, wheren>2. Results are presented from the application of the test to simulated processes with superimposed mean and variance transients and anM/M/1 queue example.     

Clustering Nonlinear,Nonstationary Time Series Using BSLEX

Accurate clustering of time series is a challenging problem for data arising from areas such as financial markets, biomedical studies, and environmental sciences, especially when some, or all, of the series exhibit nonlinearity and nonstationarity. When a subset of the series exhibits nonlinear characteristics, frequency domain clustering methods based on higher-order spectral properties, such as the bispectra or trispectra are useful. While these methods address nonlinearity, they rely on the assumption of series stationarity. We propose the Bispectral Smooth Localized Complex EXponential (BSLEX) approach for clustering nonlinear and nonstationary time series. BSLEX is an extension of the SLEX approach for linear, nonstationary series, and overcomes the challenges of both nonlinearity and nonstationarity through smooth partitions of the nonstationary time series into stationary subsets in a dyadic fashion. The performance of the BSLEX approach is illustrated via simulation where several nonstationary or nonlinear time series are clustered, as well as via accurate clustering of the records of 16 seismic events, eight of which are earthquakes and eight are explosions. We illustrate the utility of the approach by clustering S&P 100 financial returns.     

Diagnosing and modeling extra‐binomial variation for time‐dependent counts

This article considers the modeling of count data time series with a finite range having extra‐binomial variation. We propose a beta‐binomial autoregressive model using the concept of random coefficient thinning. We discuss the stationarity conditions, derive the moments and autocovariance function and consider approaches for parameter estimation. Furthermore, we develop two new tests for detecting extra‐binomial variation, and we derive the asymptotic distributions of the test statistics under the null hypothesis of a binomial autoregressive model. The size and power performance of the two tests are analyzed under various alternatives taken from a beta‐binomial autoregressive model with Monte Carlo experiments. The article ends with a real‐data example about the Harmonised Index of Consumer Prices of the European Union. Copyright © 2013 John Wiley & Sons, Ltd.     

TEMPORAL AGGREGATION AND TESTING FOR TIMBER PRICE BEHAVIOR

ABSTRACT. Different harvest timing models make different assumptions about timber price behavior. Those seeking to optimize harvest timing are thus first faced with a decision regarding which assumption of price behavior is appropriate for their market, particularly regarding the presence of a unit root in the timber price time series. Unfortunately for landowners and investors, the literature provides conflicting guidance on this subject. One source for the ambiguous results of unit root tests of timber prices may involve data problems. We used Monte Carlo simulations to show that aggregating observations below their observed rate resulted in similar power reductions and empirical size distortions across three classes of unit root tests. Moving‐average error structures can also affect power and sizes of tests on period‐averaged data. Such error structures can also be created by the kind of temporal averaging common in reported timber prices. If we take timber prices at their face value and therefore ignore these sampling error and temporal aggregation complications, we find that unit root tests on southern timber prices support a unit root in 158 out of 208 product‐deflation combinations tested, random walks in 38 of the series found to be nonsta‐tionary, and stationarity in none. However, if we recognize temporal aggregation errors, unit root tests more commonly favor stationarity, especially for pulpwood stumpage. Because price trends for sawtimber and pulpwood products may behave differently even in the same region, stochastic harvest timing models must be developed that allow their multiple products to follow different price paths.     

Detecting abrupt changes in a piecewise locally stationary time series

Non-stationary time series arise in many settings, such as seismology, speech-processing, and finance. In many of these settings we are interested in points where a model of local stationarity is violated. We consider the problem of how to detect these change-points, which we identify by finding sharp changes in the time-varying power spectrum. Several different methods are considered, and we find that the symmetrized Kullback-Leibler information discrimination performs best in simulation studies. We derive asymptotic normality of our test statistic, and consistency of estimated change-point locations. We then demonstrate the technique on the problem of detecting arrival phases in earthquakes.     

Krigings over space and time based on latent low-dimensional structures

We propose a new nonparametric approach to represent the linear dependence structure of a spatiotemporal process in terms of latent common factors.Though it is formally similar to the existing reduced rank approximation methods,the fundamental difference is that the low-dimensional structure is completely unknown in our setting,which is learned from the data collected irregularly over space but regularly in time.Furthermore,a graph Laplacian is incorporated in the learning in order to take the advantage of the continuity over space,and a new aggregation method via randomly partitioning space is introduced to improve the efficiency.We do not impose any stationarity conditions over space either,as the learning is facilitated by the stationarity in time.Krigings over space and time are carried out based on the learned low-dimensional structure,which is scalable to the cases when the data are taken over a large number of locations and/or over a long time period.Asymptotic properties of the proposed methods are established.An illustration with both simulated and real data sets is also reported.     

Computer extension and analytic continuation of problems of porous thrust bearings

Summary In this paper we propose new type of series solution, the semi-analytical, semi-numerical technique for the steady flow of a viscous fluid between two parallel disks in which the fluid is injected through the lower porous disk. We develop a double series expansion of the solution function and sufficiently large number of terms (30 terms-universal coefficients) in the expansion are obtained by delegating routine complex algebra to computer. The expression obtained in the form of power series for the normalized lift is analysed by means of Padé approximants. The change of roles of dependent and independent variables and the use of bilinear Euler transformation increases the region of validity of the corresponding power series. The results obtained from double series expansion method for small as well as moderately large values of cross-flow Reynolds number,R are more accurate and the computing time required in this method is negligible compared with pure numerical methods [1]. Besides this, we find that the method proposed by Phan-Thien and Bush [2] has to be implemented for each value ofR separately, whereas the one proposed by us has advantage of yielding, at a stretch, the results for larger range ofR which agree with exact values and at the same time requires less computer time. It is of interest to note that the pure numerical results in respect of normalized lift coefficient agree closely with the analytic continuation of our findings. In addition various Padé approximants are found to bracket the numerical results.     

基于Bootstrap的厚尾相依序列持久性变点检验

基于修正方差比率函数给出一种检验厚尾序列持久性变点的统计量.在无变点的假设下得到了统计量的渐近分布.为避免检验渐近分布中的厚尾指数,构造Bootstrap抽样方法来确定渐近分布的经验临界值.数值模拟研究结果说明修正方差比率统计量及Bootstrap抽样方法的有效性.     

An exact formula for the move-to-front rule for self-organizing lists

A collection of items (e.g., books), each with an associated weight (or popularity), is arranged in a row. At each unit of time an item is removed with probability proportional to its weight and replaced at the left end of the row. Thismove-to-front rule gives a Markov chain on permutations often known as theTsetlin library. We derive an exact and tractable formula for the probability of any permutation after any number of moves. From the formula we read off previously studied quantities of interest associated with the chain, such as the stationary distribution and eigenvalues. Measuring discrepancy from stationarity by separation, we use the formula to find the initial arrangement giving the slowest convergence to stationarity. The time to stationarity in this case is a convolution of geometric random variables which we analyze for three natural choices of weights. We also assess the time required for an important functional, namely, expected search cost, to approach its stationary value.     

IS THERE UNIT ROOT IN THE NITROGEN OXIDES EMISSIONS: A MONTE CARLO INVESTIGATION?

Abstract Use of the time‐series econometric techniques to investigate issues about environmental regulation requires knowing whether air pollution emissions are trend stationary or difference stationary. It has been shown that results regarding trend stationarity of the pollution data are sensitive to the methods used. I conduct a Monte Carlo experiment to study the size and power of two unit root tests that allow for a structural change in the trend at a known time using the data‐generating process calibrated to the actual pollution series. I find that finite sample properties of the Perron test are better than the Park and Sung Phillips‐Perron (PP) type test. Severe size distortions in the Park and Sung PP type test can explain the rejection of a unit root in air pollution emissions reported in some environmental regulation analyses.     

TESTING THE ADEQUACY OF GARCH-TYPE MODELS IN TIME SERIES

In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enhance power performance. The choice of weight functions and the power properties of the tests are studied. For a large number of alternatives, asymptotically distribution-free maximin test is constructed. The tests are asymptotically chi-squared under the null hypothesis and easy to implement. Simulation results indicate that the tests perform well.     

Asymptotic Null Distributions of Stationarity and Nonstationarity Tests Under Local-to-finite Variance Errors

The purpose of this paper is to investigate the asymptotic null distribution of stationarity and nonstationarity tests when the distribution of the error term belongs to the normal domain of attraction of a stable law in any finite sample but the error term is an i.i.d. process with finite variance as . This local-to-finite variance setup is helpful to highlight the behavior of test statistics under the null hypothesis in the borderline or near borderline cases between finite and infinite variance and to assess the robustness of these test statistics to small departures from the standard finite variance context. From an empirical point of view, our analysis can be useful in settings where the (non)-existence of the (second) moments is not clear-cut, such as, for example, in the analysis of financial time series. A Monte Carlo simulation study is performed to improve our understanding of the practical implications of the limi theory we develop. The main purpose of the simulation experiment is to assess the size distortion of the unit root and stationarity tests under investigation.     

Characterization of welding defects by fractal analysis of ultrasonic signals

In this work we apply tools developed for the study of fractal properties of time series to the problem of classifying defects in welding joints probed by ultrasonic techniques. We employ the fractal tools in a preprocessing step, producing curves with a considerably smaller number of points than in the original signals. These curves are then used in the classification step, which is realized by applying an extension of the Karhunen–Loève linear transformation. We show that our approach leads to small error rates, comparable with those obtained by using more time-consuming methods based on non-linear classifiers.     

Efficiencies of tests and estimators forp-order autoregressive processes when the error distribution is nonnormal

Summary We considerpth order autoregressive time series where the shocks need not be normal. By employing the concept of contiguity, we obtain the sysmptotic power for tests of hypothesis concerning the autoregressive parameters. Our approach allows consideration of the double exponential and other thicker-tailed distributions for the shocks. We derive a new result in the contiguity framework that leads directly to an expression for the Pitman efficiencies of tests as well as estimators. The numerical values of the efficiencies suggest a lack of robustness for the normal theory least squares estimators when the shock distribution is thick tailed or an outlier prone mixed normal. An important alternative test statistic is proposed that competes with the normal theory tests. This research was supported by the Office of Naval Research under Grant No. N00014-78-C-0722 and by the Army Research Office.     

Introducing <Emphasis FontCategory="NonProportional" Type="Bold">libeemd</Emphasis>: a program package for performing the ensemble empirical mode decomposition

The ensemble empirical mode decomposition (EEMD) and its complete variant (CEEMDAN) are adaptive, noise-assisted data analysis methods that improve on the ordinary empirical mode decomposition (EMD). All these methods decompose possibly nonlinear and/or nonstationary time series data into a finite amount of components separated by instantaneous frequencies. This decomposition provides a powerful method to look into the different processes behind a given time series data, and provides a way to separate short time-scale events from a general trend. We present a free software implementation of EMD, EEMD and CEEMDAN and give an overview of the EMD methodology and the algorithms used in the decomposition. We release our implementation, libeemd, with the aim of providing a user-friendly, fast, stable, well-documented and easily extensible EEMD library for anyone interested in using (E)EMD in the analysis of time series data. While written in C for numerical efficiency, our implementation includes interfaces to the Python and R languages, and interfaces to other languages are straightforward.     

A marginal contribution coefficient for sequences of nonstationary continuous Markov chains

In this work, a set of sequences of information (time series), under nonstationary regime, with continuous space state, discrete time, and a Markovian dependence, is considered. A new model that expresses the marginal transition density function of one sequence as a linear combination of the marginal transition density functions of all sequences in the set is proposed. The coefficients of this combination are denominated marginal contribution coefficients and represent how much each transition density function contributes to the calculation of a chosen transition density function. The proposed coefficient is a marginal coefficient because it can be computed instantaneously, and it may change from one time to another time since all calculations are performed before stationarity is reached. This clearly differentiates the new coefficient from well‐known measures such as the cross‐correlation and the coherence. The idea behind the model is that if a specific sequence has a high marginal contribution for the transition density function from another sequence, the first may be replaced by the latter without losing much information that means that the knowledge of few densities should be enough to recover the overall behaviour. Simulations, considering 2 chains, are presented so as to check the sensitivity of the proposed model. The methodology is also applied to a real data originated from a wire‐drawing machine whose main function is to decrease the transverse diameter of metal wires. The behaviour of the level of acceleration of each bearing in relation to the other ones is then verified.     

Blockwise empirical likelihood for time series of counts

Time series of counts have a wide variety of applications in real life. Analyzing time series of counts requires accommodations for serial dependence, discreteness, and overdispersion of data. In this paper, we extend blockwise empirical likelihood (Kitamura, 1997 [15]) to the analysis of time series of counts under a regression setting. In particular, our contribution is the extension of Kitamura’s (1997) [15] method to the analysis of nonstationary time series. Serial dependence among observations is treated nonparametrically using a blocking technique; and overdispersion in count data is accommodated by the specification of a variance-mean relationship. We establish consistency and asymptotic normality of the maximum blockwise empirical likelihood estimator. Simulation studies show that our method has a good finite sample performance. The method is also illustrated by analyzing two real data sets: monthly counts of poliomyelitis cases in the USA and daily counts of non-accidental deaths in Toronto, Canada.     

Stationarizing two classes of nonstationary processes by wavelet

The main purpose of this paper is to discuss the stationarity of two classes of nonstationary processes after wavelet transformations. Owing to the fact that the wavelet transformation possesses localization and implicit differencing property, the authors show that after wavelet transformation, the fractionally differenced process and the harmonizable periodically correlated process may be changed into stationary processes. Selected from Acta Scientiarum Naturalium Universitatis Pekinensis, 2004, 40(1): 19–28. This project was supported by the National Nataral Science Foundations of China under grant number 10171005     

On estimating the regular normal cone to constraint systems and stationarity conditions

Estimating the regular normal cone to constraint systems plays an important role for the derivation of sharp necessary optimality conditions. We present two novel approaches and introduce a new stationarity concept which is stronger than M-stationarity. We apply our theory to three classes of mathematical programs frequently arising in the literature.