Machine learning methods dealing with the spatial auto-correlation of the response variable have garnered significant attention in the context of spatial prediction.Nonetheless,under these methods,the relationship bet...Machine learning methods dealing with the spatial auto-correlation of the response variable have garnered significant attention in the context of spatial prediction.Nonetheless,under these methods,the relationship between the response variable and explanatory variables is assumed to be homogeneous throughout the entire study area.This assumption,known as spatial stationarity,is very questionable in real-world situations due to the influence of contextual factors.Therefore,allowing the relationship between the target variable and predictor variables to vary spatially within the study region is more reasonable.However,existing machine learning techniques accounting for the spatially varying relationship between the dependent variable and the predictor variables do not capture the spatial auto-correlation of the dependent variable itself.Moreover,under these techniques,local machine learning models are effectively built using only fewer observations,which can lead to well-known issues such as over-fitting and the curse of dimensionality.This paper introduces a novel geostatistical machine learning approach where both the spatial auto-correlation of the response variable and the spatial non-stationarity of the regression relationship between the response and predictor variables are explicitly considered.The basic idea consists of relying on the local stationarity assumption to build a collection of local machine learning models while leveraging on the local spatial auto-correlation of the response variable to locally augment the training dataset.The proposed method’s effectiveness is showcased via experiments conducted on synthetic spatial data with known characteristics as well as real-world spatial data.In the synthetic(resp.real)case study,the proposed method’s predictive accuracy,as indicated by the Root Mean Square Error(RMSE)on the test set,is 17%(resp.7%)better than that of popular machine learning methods dealing with the response variable’s spatial auto-correlation.Additionally,this method is not only valuable for spatial prediction but also offers a deeper understanding of how the relationship between the target and predictor variables varies across space,and it can even be used to investigate the local significance of predictor variables.展开更多
This research focuses on identifying the damping ratio of bridges using nonstationary ambient vibration data. The damping ratios of bridges in service have generally been identified using operational modal analysis （...This research focuses on identifying the damping ratio of bridges using nonstationary ambient vibration data. The damping ratios of bridges in service have generally been identified using operational modal analysis （OMA） based on a stationary white noise assumption for input signals. However, most bridges are generally subjected to nonstationary excitations while in service, and this violation of the basic assumption can lead to uncertainties in damping identification. To deal with nonstationarity, an amplitude-modulating function was calculated from measured responses to eliminate global trends caused by nonstationary input. A natural excitation technique （NExT）-eigensystem realization algorithm （ERA） was applied to estimate the damping ratio for a stationarized process. To improve the accuracy of OMA-based damping estimates, a comparative analysis was performed between an extracted stationary process and nonstationary data to assess the effect of eliminating nonstationarity. The mean value and standard deviation of the damping ratio for the first vertical mode decreased after signal stationarization.展开更多
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 prop...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.展开更多
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...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.展开更多
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 Aut...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.展开更多
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...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.展开更多
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 Bollersl...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.展开更多
Linear theory of stationary response in systems at thermal equilibrium requires to find equilibrium correlation function of unperturbed responding system. Studies of the response of the systems exhibiting anomalously ...Linear theory of stationary response in systems at thermal equilibrium requires to find equilibrium correlation function of unperturbed responding system. Studies of the response of the systems exhibiting anomalously slow dynamics are often based on the continuous time random walk description(CTRW) with divergent mean waiting times.The bulk of the literature on anomalous response contains linear response functions like one by Cole-Cole calculated from such a CTRW theory and applied to systems at thermal equilibrium. Here we show within a fairly simple and general model that for the systems with divergent mean waiting times the stationary response at thermal equilibrium is absent,in accordance with some recent studies. The absence of such stationary response(or dying to zero non-stationary response in aging experiments) would confirm CTRW with divergent mean waiting times as underlying physical relaxation mechanism, but reject it otherwise. We show that the absence of stationary response is closely related to the breaking of ergodicity of the corresponding dynamical variable. As an important new result, we derive a generalized Cole-Cole response within ergodic CTRW dynamics with finite waiting time. Moreover, we provide a physically reasonable explanation of the origin and wide presence of 1/f noise in condensed matter for ergodic dynamics close to normal, rather than strongly deviating.展开更多
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 ...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.展开更多
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...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,∞).展开更多
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 app...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.展开更多
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 regi...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.展开更多
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 th...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.展开更多
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. Acco...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展开更多
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 ...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.展开更多
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,...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.展开更多
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 nu...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.展开更多
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 coin...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.展开更多
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...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.展开更多
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 noi...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.展开更多
文摘Machine learning methods dealing with the spatial auto-correlation of the response variable have garnered significant attention in the context of spatial prediction.Nonetheless,under these methods,the relationship between the response variable and explanatory variables is assumed to be homogeneous throughout the entire study area.This assumption,known as spatial stationarity,is very questionable in real-world situations due to the influence of contextual factors.Therefore,allowing the relationship between the target variable and predictor variables to vary spatially within the study region is more reasonable.However,existing machine learning techniques accounting for the spatially varying relationship between the dependent variable and the predictor variables do not capture the spatial auto-correlation of the dependent variable itself.Moreover,under these techniques,local machine learning models are effectively built using only fewer observations,which can lead to well-known issues such as over-fitting and the curse of dimensionality.This paper introduces a novel geostatistical machine learning approach where both the spatial auto-correlation of the response variable and the spatial non-stationarity of the regression relationship between the response and predictor variables are explicitly considered.The basic idea consists of relying on the local stationarity assumption to build a collection of local machine learning models while leveraging on the local spatial auto-correlation of the response variable to locally augment the training dataset.The proposed method’s effectiveness is showcased via experiments conducted on synthetic spatial data with known characteristics as well as real-world spatial data.In the synthetic(resp.real)case study,the proposed method’s predictive accuracy,as indicated by the Root Mean Square Error(RMSE)on the test set,is 17%(resp.7%)better than that of popular machine learning methods dealing with the response variable’s spatial auto-correlation.Additionally,this method is not only valuable for spatial prediction but also offers a deeper understanding of how the relationship between the target and predictor variables varies across space,and it can even be used to investigate the local significance of predictor variables.
基金supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (2017R1A2B4008973)supported by grants (17SCIPB119960-02) from the Ministry of Land+2 种基金 Infrastructure and Transport of the Korean Governmentpartially supported by the BK21 PLUS research program of the National Research Foundation of Koreathe New Technology Research Center for Bridges through the Institute of Engineering Research at Seoul National University
文摘This research focuses on identifying the damping ratio of bridges using nonstationary ambient vibration data. The damping ratios of bridges in service have generally been identified using operational modal analysis （OMA） based on a stationary white noise assumption for input signals. However, most bridges are generally subjected to nonstationary excitations while in service, and this violation of the basic assumption can lead to uncertainties in damping identification. To deal with nonstationarity, an amplitude-modulating function was calculated from measured responses to eliminate global trends caused by nonstationary input. A natural excitation technique （NExT）-eigensystem realization algorithm （ERA） was applied to estimate the damping ratio for a stationarized process. To improve the accuracy of OMA-based damping estimates, a comparative analysis was performed between an extracted stationary process and nonstationary data to assess the effect of eliminating nonstationarity. The mean value and standard deviation of the damping ratio for the first vertical mode decreased after signal stationarization.
基金The National Natural Science Foundation of China(No.60972130)
文摘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.
基金Acknowledgements This work was supported partially by the Beijing Natural Science Foundation under Crant No. 4112048 the Program for New Century Excellent Talents in University under Gant No. NCET-09-0206+4 种基金 the National Natural Science Foundation of China under Crant No. 60830001 the Key Project of State Key Laboratory of Rail Traffic Control and Safety under Crants No. RCS2008ZZ006, No. RCS2011ZZ008 the Program for Changjiang Scholars and Innovative Research Team in University under Crant No. IRT0949 the Project of State Key kab. of Rail Traffic Control and Safety under C~ants No. RCS2008ZT005, No. RCS2010ZT012 the Fundamental Research Funds for the Central Universities under Crants No. 2010JBZ（~8, No. 2011YJS010.
文摘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.
基金the financial support through the General Research Program under project number GRP-73-41.
文摘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.
基金Supported by the Post Graduate Research Fund from Federal Government of Nigeria under the BEA Scholarship Program （No.CSC2005566002）
文摘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.
文摘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.
基金Supported by the Deutsche Forschungsgemeinschaft(German Research Foundation),Grant GO 2052/1-2
文摘Linear theory of stationary response in systems at thermal equilibrium requires to find equilibrium correlation function of unperturbed responding system. Studies of the response of the systems exhibiting anomalously slow dynamics are often based on the continuous time random walk description(CTRW) with divergent mean waiting times.The bulk of the literature on anomalous response contains linear response functions like one by Cole-Cole calculated from such a CTRW theory and applied to systems at thermal equilibrium. Here we show within a fairly simple and general model that for the systems with divergent mean waiting times the stationary response at thermal equilibrium is absent,in accordance with some recent studies. The absence of such stationary response(or dying to zero non-stationary response in aging experiments) would confirm CTRW with divergent mean waiting times as underlying physical relaxation mechanism, but reject it otherwise. We show that the absence of stationary response is closely related to the breaking of ergodicity of the corresponding dynamical variable. As an important new result, we derive a generalized Cole-Cole response within ergodic CTRW dynamics with finite waiting time. Moreover, we provide a physically reasonable explanation of the origin and wide presence of 1/f noise in condensed matter for ergodic dynamics close to normal, rather than strongly deviating.
基金funded by the National Polytechnic Institute(IPN)project#SIP 20110943–CONACYT,and COFAA
文摘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.
基金partially supported by National Natural Science Foundation of China(11701070,71871046)Ronglian Scholarship Fund.
文摘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,∞).
文摘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.
文摘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.
文摘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.
文摘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
基金Funded by the Natural Science Foundation of China (No. 70471050).
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
