Stationarity Preservation Properties of the Active Flux Scheme on Cartesian Grids

Hyperbolic systems of conservation laws in multiple spatial dimensions display features absent in the one-dimensional case,such as involutions and non-trivial stationary states.These features need to be captured by numerical methods without excessive grid refine-ment.The active flux method is an extension of the finite volume scheme with additional point values distributed along the cell boundary.For the equations of linear acoustics,an exact evolution operator can be used for the update of these point values.It incorporates all multi-dimensional information.The active flux method is stationarity preserving,i.e.,it discretizes all the stationary states of the PDE.This paper demonstrates the experimental evidence for the discrete stationary states of the active flux method and shows the evolution of setups towards a discrete stationary state.

Stationarity Intervals of Time-Variant Channel in High Speed Railway Scenario

The non-stationary behavior, caused by the train rmverrent, is the rmin factor for the variation of high speed railway channel. To measure the tirce-variant effect, the parameter of stationarity interval, in which the channel keeps constant or has no great change, is adopted based on Zhengzfiou- Xi＇an （Zhengxi） passenger dedicated line measurement with different train speeds. The stationarity interval is calculated through the definition of Local Region of Stationarity （LRS） under three train ve- locities. Furthermore, the time non-stationary characteristic of high speed pared with five standard railway channel is corn- Multiple-Input MultipleOutput （MIMO） channel models, i.e. Spatial Channel Model （SCM）, extended version of SCM （SCME）, Wireless World Initiative New Radio Phase II （WINNERII）, International Mobile Teleconmnications-Advanced （IMT-Advanced） and WiMAX models which contain the high speed moving scenario. The stationarity interval of real channel is 9 ms in 80% of the cases, which is shorter than those of the standard models. Hence the real channel of high speed railway changes more rapidly. The stationarity intervals of standard models are different due to different modeling methods and scenario def- initions. And the compared results are instructive for wireless system design in high speed railway.

STATIONARITY OF A CLASS OF LARGE-SCALE DISCRETE-TIME STOCHASTIC SYSTEMS

Stationarity of a class of stochastically interconnecteil discrete-timesystems is analyzed by utilizins results from ergodic theory of general stateMarkov chains, incorporated with the so called large-scale system approach.

Influence of non-stationarity and auto-correlation of climatic records on spatio-temporal trend and seasonality analysis in a region with prevailing arid and semi-arid climate,Iran

Trend and stationarity analysis of climatic variables are essential for understanding climate variability and provide useful information about the vulnerability and future changes,especially in arid and semi-arid regions.In this study,various climatic zones of Iran were investigated to assess the relationship between the trend and the stationarity of the climatic variables.The Mann-Kendall test was considered to identify the trend,while the trend free pre-whitening approach was applied for eliminating serial correlation from the time-series.Meanwhile,time series stationarity was tested by Dickey-Fuller and Kwiatkowski-Phillips-Schmidt-Shin tests.The results indicated an increasing trend for mean air temperature series at most of the stations over various climatic zones,however,after eliminating the serial correlation factor,this increasing trend changes to an insignificant decreasing trend at a 95%confidence level.The seasonal mean air temperature trend suggested a significant increase in the majority of the stations.The mean air temperature increased more in northwest towards central parts of Iran that mostly located in arid and semiarid climatic zones.Precipitation trend reveals an insignificant downward trend in most of the series over various climatic zones;furthermore,most of the stations follow a decreasing trend for seasonal precipitation.Furthermore,spatial patterns of trend and seasonality of precipitation and mean air temperature showed that the northwest parts of Iran and margin areas of the Caspian Sea are more vulnerable to the changing climate with respect to the precipitation shortfalls and warming.Stationarity analysis indicated that the stationarity of climatic series influences on their trend;so that,the series which have significant trends are not static.The findings of this investigation can help planners and policy-makers in various fields related to climatic issues,implementing better management and planning strategies to adapt to climate change and variability over Iran.

CONDITIONS FOR FOURTH-ORDER STATIONARITY AND ERGODICITY OF A HARMONIC RANDOM PROCESS

The finite data estimates of the complex fourth-order moments of a signal consisting of random harmonics are analyzed. Conditions for the fourth-order stationarity and ergodicity are obtained. Explicit formulas for the estimation error and its variance, as well as their limiting large sample values are derived. Finally, a special case relevant to cubic phase coupling is considered, and these results are stated for this case, the variance is shown to comprise an ergodic and a nonergodic part.

Definition of Stationarity Based on Monitoring the Uncertainty at Real Measurement Conditions

In the statistical standard literature the stationarity of a time dependent process generally is defined by the invariance in time of the distribution of the variable, like a SPL （sound pressure level） fluctuating in time. However in reality there cannot exist constant distribution, respectively characteristics, in time in the strict mathematical sense because the time intervals of observation only can be finite due to practical reasons. Hence on every distribution and characteristics based on it a certain, but evaluable uncertainty is imposed. For monitoring these uncertainties the online-measurement technique, i.e. primarily appropriate software, is already available, also for customers. According to this state of the art the following expanded definition of the stationarity is proposed： Stationarity during a quality controlled measurement process becomes established, when the upper confidence limit of the interesting specific characteristic has no positive slope in time and correspondingly the lower confidence limit of the specific characteristic no negative slope and, as a third, a common condition, the interesting specific characteristic has adjusted itself to a constant position in time. From this a systematic criteria scheme is established and in examples applied on different in- and outdoor situations of sound impact.

Bootstrap Test for Stationarity of Heavy-Tailed Series with Structural Breaks

The paper proposes a statistic to test stationarity of series with κ-stable innovations and structural breaks,obtains the asymptotical distribution of the statistic,and proves the consistency of the test.To obtain critic values for the test without the estimation of the index κ,the paper proposes the bootstrap procedures to approximate the distribution,and proves the consistency of the procedures.The simulations demonstrate that the bootstrap test is practical and powerful.

Stationarity in the variability of arid precipitation:A case study of aridCentral Asia

Precipitation is particularly scarce in arid Central Asia(CA),and is expected to be severely impacted by future warming,and the assessmentof the stationarity of precipitation variability is important for managing surface water resources in this region.In this study,we investigated thestatistics of stationarity in the totals and extremes of precipitation in CA based on the longest observational records(1881e2006),tree-ringreconstructed records(1756e2012 and 1760e2015),and the Coupled Model Intercomparison Project 5(CMIP5)simulations,applying theautocorrelation function and testing criteria established based on the statistical definitions of stationarity.We analyzed the longest daily pre-cipitation record(Tashkent station,1881e2006)and found that the autocorrelation coefficient of the precipitation totals(PRCPTOT)and annualmaximum 1-day precipitation amount(Rx1day)were statistically insignificant for all lags,implying stationary behavior.Regionally,nearly allthe Global Historical Climatology Network-Daily Database(GHCN-D)observatory sites(1925e2005)indicated likely stationary behavior.Thereconstructed records were also indistinguishable from a random process.For the CMIP5 models,the simulated and projected PRCPTOT closelyapproximated a purely random process;however,the projected Rx1day maintained non-stationary means in most of the models under therepresentative concentration pathway(RCPs),implying that extreme events would increase in the future.The mean precipitation changes(DP)can be expressed as an exponential function depending on the length of the successive mean periods(m)and variance(s2).TheDPof the nextdecade is projected to be within±14.8%of the previous decades mean annual PRCPTOT over CA.The higher the RCPs,the higher theDP overCA.The results show that the detection and prediction of precipitation change will be challenging in arid CA.

The stationarity and invertibility of a class of nonlinear ARMA models

We investigate some probabilistic properties of a new class of nonlinear time series models. A sufficient condition for the existence of a unique causal, strictly and weakly stationary solution is derived. To understand the proposed models better, we further discuss the moment structure and obtain some Yule-Walker difference equations for the second and third order cumulants, which can also be used for identification purpose. A sufficient condition for invertibility is also provided.

Detecting Stationarity and Nonlinearity in Propeller Singing Signal

The propeller singing is such a complex fluid-structure coupling phenomenon that needs to study intensively. In this paper, the stationarity of propeller singing signal is tested by the recurrence plot technique. According to surrogate data, the singing time series has nonlinearity character. And the nonlinearity of time series is not caused by the static nonlinear measurement function but the intrinsic character itself based on further research. The results provide an objective basis for analyzing the propeller singing signal with the nonlinear time series technique

Analysis, Variability and Rainfall Prediction in Sub-Saharan Africa: The Case of the Lake Guiers in Senegal

The aim of this article is to predict the rainfall evolution of a sub-Saharan area in which one of the most important freshwater resources is located: Lake Guiers. Characterized by short seasonal rains of three months, it experienced a long period of drought in the 1970s. We begin by analyzing the temporal distribution of the rainfall including the variability of the data, with a view to predicting a possible return. For this reason, we present here univariate modeling results of rainfall series collected on three stations in the area. The challenge lies in the adequacy of the parameters for the monthly rainfall series, which generates more or less significant forecast errors on the learning bases because of the missing data. This later motivated their conversion to moving average series. On the other hand, the normality of the latter seems to be rejected by the D’Agostino test. Student’s and Mann-Whitney’s tests confirmed the homogeneity. The autocorlograms show the presence of autoregressive terms in the data. Dickey-Fuller and Mann-Kendall tests reveal both trend and seasonality. The stationarity tests of Dickey-Fuller, Phillips-Perron and KPSS have shown that they are non-stationary. As a result, we did an ARIMA modeling method using the Box-Jenkins [1] method with the R software, which involves estimating model parameters, tests of significance, analysis of residualss, selection according to information criteria and forecasts. The results obtained during the learning-test phase showed a quasi-similarity of the base-tests in all the series except for that of Louga.

Training image analysis for three-dimensional reconstruction of porous media

In order to obtain a better sandstone three-dimensional （3D） reconstruction result which is more similar to the original sample, an algorithm based on stationarity for a two-dimensional （2D） training image is proposed. The second-order statistics based on texture features are analyzed to evaluate the scale stationarity of the training image. The multiple-point statistics of the training image are applied to obtain the multiple-point statistics stationarity estimation by the multi-point density function. The results show that the reconstructed 3D structures are closer to reality when the training image has better scale stationarity and multiple-point statistics stationarity by the indications of local percolation probability and two-point probability. Moreover, training images with higher multiple-point statistics stationarity and lower scale stationarity are likely to obtain closer results to the real 3D structure, and vice versa. Thus, stationarity analysis of the training image has far-reaching significance in choosing a better 2D thin section image for the 3D reconstruction of porous media. Especially, high-order statistics perform better than low-order statistics.

Functional Causality between Oil Prices and GDP Based on Big Data

This paper examines the causal relationship between oil prices and the Gross Domestic Product(GDP)in the Kingdom of Saudi Arabia.The study is carried out by a data set collected quarterly,by Saudi Arabian Monetary Authority,over a period from 1974 to 2016.We seek how a change in real crude oil price affects the GDP of KSA.Based on a new technique,we treat this data in its continuous path.Precisely,we analyze the causality between these two variables,i.e.,oil prices and GDP,by using their yearly curves observed in the four quarters of each year.We discuss the causality in the sense of Granger,which requires the stationarity of the data.Thus,in the first Step,we test the stationarity by using the Monte Carlo test of a functional time series stationarity.Our main goal is treated in the second step,where we use the functional causality idea to model the co-variability between these variables.We show that the two series are not integrated;there is one causality between these two variables.All the statistical analyzes were performed using R software.

Analysis of stochastic characteristics of the Benue River flow process

Stochastic characteristics of the Benue River streamflow process are examined under conditions of data austerity. The streamflow process is investigated for trend, non-stationarity and seasonality for a time period of 26 years. Results of trend analyses with Mann-Kendall test show that there is no trend in the annual mean discharges. Monthly flow series examined with seasonal Kendall test indicate the presence of positive change in the trend for some months, especially the months of August, January, and February. For the stationarity test, daily and monthly flow series appear to be stationary whereas at 1%, 5%, and 10% significant levels, the stationarity alternative hypothesis is rejected for the annual flow series. Though monthly flow appears to be stationary going by this test, because of high seasonality, it could be said to exhibit periodic stationarity based on the seasonality analysis. The following conclusions are drawn： （1） There is seasonality in both the mean and variance with unimodal distribution. （2） Days with high mean also have high variance. （3） Skewness coefficients for the months within the dry season period are greater than those of the wet season period, and seasonal autocorrelations for streamflow during dry season are generally larger than those of the wet season. Precisely, they are significantly different for most of the months. （4） The autocorrelation functions estimated ＂over time＂ are greater in the absolute value for data that have not been deseasonalised but were initially normalised by logarithmic transformation only, while autocorrelation functions for i = 1, 2 365 estimated ＂over realisations＂ have their coefficients significantly different from other coefficients.

Multivariate Generalized Autoregressive Conditional Heteroscedastic Model

In this paper, by making use of the Hadamard product of matrices, a natural and reasonable generalization of the univariate GARCH (Generalized Autoregressive Conditional heteroscedastic) process introduced by Bollerslev (J. Econometrics 31(1986), 307-327) to the multivariate case is proposed. The conditions for the existence of strictly stationary and ergodic solutions and the existence of higher-order moments for this class of parametric models are derived.

Spatial heterogeneity of factors influencing forest fires size in northern Mexico

In Mexico, forest fires are strongly influenced by environmental, topographic, and anthropogenic factors. A government-based database covering the period 2000-2011 was used to analyze the spatial heterogeneity of the factors influencing forest fire size in the state of Durango, Mexico. Ordinary least squares and geographically weighted regression models were fit to identify the main factors as well as their spatial influence on fire size. Results indicate that fire size is greatly affected by distance to roads, distance to towns, precipitation, temperature, and a population gravity index. The geographically weighted model was better than the ordinary least squares model. The improvement of the former is due to the influence of factors that were found to be non-stationary. These results suggest that geographic location determines the influence of a factor on fire size. While the models can be greatly improved with additional information, the study suggests the need to adopt fire management policies to more efficiently reduce the effect of anthropogenic factors. These policies may include more training for landowners who use fire for clearing, closure of roads, application of thinning, prescribed burning, and fire breaks in perimeters adjacent to roads.

EXTREMA OF A GAUSSIAN RANDOM FIELD:BERMAN'S SOJOURN TIME METHOD

In this paper we devote ourselves to extending Berman’s sojourn time method,which is thoroughly described in[1-3],to investigate the tail asymptotics of the extrema of a Gaussian random field over[0,T]^(d) with T∈(0,∞).

Vector FIGARCH process, its persistence and co-persistence in variance

In this paper, the definition of the vector FIGARCH process is established, and the stationarity and some properties of the process are discussed. According to the stationarity and the results of Du and Zhang [1], we verify the persistence in variance of the vector FIGARCH process, and finally establish the sufficient and necessary condition for the co-persistence in the variance of the process and also discuss the constant related vector FIGARCH ( p , d , q ) process as a special case.

Market efficiency of gold exchange-traded funds in India

Background:Gold exchange-traded funds,since introduction,are primarily aimed at tracking the price of physical gold in the financial market.This,a category of exchange-traded funds,whose units represent physical gold,is traded on exchanges like any other financial instrument.In the Indian financial market,gold exchange traded funds were introduced a decade ago to facilitate ordinary households'participation in the bullion market.They were also designed to assist in the price discovery mechanism of the bullion market.Presentation of the hypothesis:In this paper,it is attempted to check if one of the constituents of price discovery mechanism,informational efficiency,has been achieved in gold exchange-traded funds’market.Information efficiency becomes evident only when all available information is reflected in the market price of the instrument.Testing the hypothesis:Therefore,in order to assess the weak-form efficiency of the gold exchange-traded funds market,the daily returns of five gold exchangetraded funds traded on the Indian Stock Exchange over the period March 22,2010,to August 28,2015,were used.The non-parametric runs test,the parametric serial correlation test,and the augmented Dickey-Fuller unit root test are employed.Implications of the hypothesis:The test results provide evidence that the efficient market hypothesis does not hold for the gold exchange-traded funds’market in India.Further,the test results address several underlying issues with respect to price discovery in the market under study and suggest that the Indian market for this derivative is not weak-form efficient.Hence,the factors affecting gold exchange traded-funds’market warrant the attention of the country’s regulatory bodies,as appropriate legislation in support of market efficiency is needed.

Some Applications of Higher Moments of the Linear Gaussian White Noise Process

The Linear Gaussian white noise process is an independent and identically distributed (iid) sequence with zero mean and finite variance with distribution N (0, σ2 ) . Hence, if X1, x2, …, Xn is a realization of such an iid sequence, this paper studies in detail the covariance structure of X1d, X2d, …, Xnd, d=1, 2, …. By this study, it is shown that: 1) all powers of a Linear Gaussian White Noise Process are iid but, not normally distributed and 2) the higher moments (variance and kurtosis) of Xtd, d=2, 3, … can be used to distinguish between the Linear Gaussian white noise process and other processes with similar covariance structure.