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 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.

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.

Detecting Stationarity and Nonlinearity in Propeller Singing Signal

<Abstract>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.

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.

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,∞).

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.

Cointegration of event-related potential (ERP) signals in experiments with different electromagnetic field (EMF) conditions

Due to their non-stationarity, ERP signals are difficult to study. The concept of cointegration might overcome this problem and allow for the study of the co-variability between whole ERP signals. In this context cointegration factor is defined as the ability of an ERP signal to co-vary with other ERP signals. The aim of the present study was to investigate whether the cointegration factor is dependent on different EMF conditions and gender, as well as the locations of the electrodes on the scalp. The findings revealed that women have a significantly higher cointegration factor than men, while all subjects have increased cointegration factors in the presence of EMF. The cointegration factor is location dependent, creating a distinct cluster of high coin- tegration capacity at the central and lateral electrodes of the scalp, in contrast to clusters of low cointegration capacity at the anterior and posterior electrodes There seem to be distinct similarities of the present findings with those from standard methodologies of the ERPs. In conclusion cointegration is a promising tool towards the study of functional interactions between different brain locations.

On the Use of Second and Third Moments for the Comparison of Linear Gaussian and Simple Bilinear White Noise Processes

The linear Gaussian white noise process (LGWNP) is an independent and identically distributed (iid) sequence with zero mean and finite variance with distribution . Some processes, such as the simple bilinear white noise process (SBWNP), have the same covariance structure like the LGWNP. How can these two processes be distinguished and/or compared? If is a realization of the SBWNP. This paper studies in detail the covariance structure of . It is shown from this study that;1) the covariance structure of is non-normal with distribution equivalent to the linear ARMA(2, 1) model;2) the covariance structure of is iid;3) the variance of can be used for comparison of SBWNP and LGWNP.

Unbalanced Regressions and Spurious Inference

Spurious regression has been extensively studied in time series econometrics since Granger and Newbold’s seminal paper. Recently, it has been advanced that this phenomenon is due to a mistreatment of short-range autocorrelation in the residuals of the regression when at least one of the variables in a bivariate regression is stationary. HAC errors, feasible GLS and Cochrane-Orcutt-type procedures are then proposed to draw correct inference. Such a proposal should be cautiously considered, since nonsense inference might also be due to deterministic trend mechanisms, structural breaks, and long range dependence. In these cases, standard autocorrelation correction procedures would not solve the problem of spurious regression. We aim to make the later argument clear.

Time Series Analysis on Reported Cases of Tuberculosis in Minna Niger State Nigeria

Predicting the trend of non-seasonal data is a difficult task in Social Science. In this research work, we used time series analysis of 144 observations on monthly basis for record of reported cases of tuberculosis patients in Minna General Hospital, Niger State from the period of 2007-2018. Exploratory Data Analysis (EDA: Time Plot and Descriptive Statistics), Stationarity Test (ADF), Trend estimation (Tt), Normality Test, and Forecast evaluation were carried out. The Augmented Dickey Fuller test for stationarity was conducted and the result revealed that the series are not stationary but became stationary after first difference. The correlogram established that the ARIMA (2, 1, 3) was the best model this was further confirmed from the result of L-jung Box. Equation for ARIMA (2, 1, 3) was given as Xt + 0.6867Xt-1 – 0.8859Xt-2 = Et + 1.3077Et-1 - 1.2328Et-2 + 0.5788Et-3. Which was used to predict five years likely cases of tuberculosis in Minna for the period of 2019-2023. It was clearly shown from the projection that the reported cases of tuberculosis reduce year by year by 7% over the period under consideration which could be as a result of intervention from government, health worker, and individuals. In line with these findings, we recommend that the management of general hospital to increase awareness campaign to the public on the causes and dangers of tuberculosis.

Tools to Estimate Groundwater Levels in the Presence of Changes of Precipitation and Pumping

Central Wisconsin has the greatest density of high capacity wells in the state, most of which are used for agricultural irrigation. Irrigated agriculture has been growing steadily in the region since the 1950’s, when irrigation systems and high capacity wells became inexpensive and easy to install. Recent low lake and river levels have increased concerns that unregulated groundwater pumping for irrigation will undermine the availability of groundwater to support surface waters and domestic uses. Some research has quantified the magnitude of groundwater level declines due to irrigation pumping, but no studies have identified its relation to climatic precipitation changes. Changes in precipitation can appear to exacerbate or mask the effect of groundwater pumping. In this study, four groundwater monitoring wells and five climate stations were examined for shifts in groundwater levels and precipitation changes. Through statistical analysis, significant precipitation increases were identified in the southern part of the study area which averaged 2.7 mm per year, but no significant change was determined for the northern portion. Bivariate analysis identified water level declines within the region in the years 1974, 1992 and 1999 for irrigated land covers. Multiple regression analysis explained, predicted and quantified the interaction between precipitation and pumping. Wells located in areas with many high capacity wells showed a decline in water levels of up to 1.28 meters. In the southern portion of the study area where increases in precipitation occurred, this decline was thought to be masked. Results for one region (Plover) agreed with a previously published calibrated groundwater model, which demonstrates that this statistical method may be used to separate the impact of groundwater pumping from changing precipitation, even where observation well data are not widely available.

Modeling and Forecasting of SARS CoV-2 Cases in Sierra Leone

Severe acute respiratory syndrome coronavirus-2 (SARS CoV-2) has been a global threat spreading in Sierra Leone, and many studies are being conducted using various Statistical models to predict the probable evolution of this pandemic. In this paper, we use the autoregressive integrated moving average (ARIMA) model with the aim of forecasting the cumulative confirmed cases of SARS CoV-2 in Sierra Leone. The Akaike Information Criterion (AIC) was applied to the training data as a criterion method to select the best model. In addition, the statistical measure RMSE and MAPE were utilized for testing this data, and the model with the minimum RMSE and MAPE was selected for future forecasting. ARIMA (3, 2, 1) was confirmed to be the optimal model based on the lowest AIC value. This model was then applied to study the trend of SARS CoV-2 from 1st February 2022 to 30th February 2022. The result shows that incidence of SARS CoV-2 from 1st February 2022 to 30th February 2022, increasing growth steep in Sierra Leone (7718.629, 95% confidence limit of 6785.985 - 8651.274).