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Journal articles on the topic 'Stationarity'

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Author: Grafiati

Published: 4 June 2021

Last updated: 10 June 2023

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1

Yilmaz, A. G., I. Hossain, and B. J. C. Perera. "Effect of climate change and variability on extreme rainfall intensity–frequency–duration relationships: a case study of Melbourne." Hydrology and Earth System Sciences 18, no. 10 (October 15, 2014): 4065–76. http://dx.doi.org/10.5194/hess-18-4065-2014.

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Abstract. The increased frequency and magnitude of extreme rainfall events due to anthropogenic climate change, and decadal and multi-decadal climate variability question the stationary climate assumption. The possible violation of stationarity in climate can cause erroneous estimation of design rainfalls derived from extreme rainfall frequency analysis. This may result in significant consequences for infrastructure and flood protection projects since design rainfalls are essential input for design of these projects. Therefore, there is a need to conduct frequency analysis of extreme rainfall events in the context of non-stationarity, when non-stationarity is present in extreme rainfall events. A methodology consisting of threshold selection, extreme rainfall data (peaks over threshold data) construction, trend and non-stationarity analysis, and stationary and non-stationary generalised Pareto distribution (GPD) models was developed in this paper to investigate trends and non-stationarity in extreme rainfall events, and potential impacts of climate change and variability on intensity–frequency–duration (IFD) relationships. The methodology developed was successfully implemented using rainfall data from an observation station in Melbourne (Australia) for storm durations ranging from 6 min to 72 h. Although statistically significant trends were detected in extreme rainfall data for storm durations of 30 min, 3 h and 48 h, statistical non-stationarity tests and non-stationary GPD models did not indicate non-stationarity for these storm durations and other storm durations. It was also found that the stationary GPD models were capable of fitting extreme rainfall data for all storm durations. Furthermore, the IFD analysis showed that urban flash flood producing hourly rainfall intensities have increased over time.

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2

Yilmaz, A. G., I. Hossain, and B. J. C. Perera. "Effect of climate change and variability on extreme rainfall intensity–frequency–duration relationships: a case study of Melbourne." Hydrology and Earth System Sciences Discussions 11, no. 6 (June 16, 2014): 6311–42. http://dx.doi.org/10.5194/hessd-11-6311-2014.

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Abstract. The increased frequency and magnitude of extreme rainfall events due to anthropogenic climate change, and decadal and multi-decadal climate variability question the stationary climate assumption. The possible violation of stationarity in climate can cause erroneous estimation of design rainfalls derived from extreme rainfall frequency analysis. This may result in significant consequences for infrastructure and flood protection projects since design rainfalls are essential input for design of these projects. Therefore, there is a need to conduct frequency analysis of extreme rainfall events in the context of non-stationarity, when non-stationarity is present in extreme rainfall events. A methodology consisting of, threshold selection, extreme rainfall data (peaks over threshold data) construction, trend and non-stationarity analysis, and stationary and non-stationary Generalized Pareto Distribution (GPD) models was developed in this paper to investigate trends and non-stationarity in extreme rainfall events, and potential impacts of climate change and variability on Intensity–Frequency–Duration (IFD) relationships. The developed methodology was successfully implemented using rainfall data from an observation station in Melbourne (Australia) for storm durations ranging from 6 min to 72 h. Although statistically significant trends were detected in extreme rainfall data for storm durations of 30 min, and 3 and 48 h, statistical non-stationarity tests and non-stationary GPD models did not indicate non-stationarity for these storm durations and other storm durations. It was also found that the stationary GPD models were capable of fitting extreme rainfall data for all storm durations. Furthermore, the IFD analysis showed that urban flash flood producing hourly rainfall intensities have increased over time.

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3

Fan, Gai Ling, and Zhi Hua Huang. "Stationarity of the EEG Segment with Event-Related Potentials." Applied Mechanics and Materials 148-149 (December 2011): 30–33. http://dx.doi.org/10.4028/www.scientific.net/amm.148-149.30.

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EEG (electroencephalography), as a noninvasive and inexpensive method, is widely used to measure brain function and make inferences about regional brain activity. The stationarity of EEG has been investigated by many researchers, while the stationarity of EEG segment with ERPs (Event-related Potentials) has hardly been concerned about. It is necessary to analyze the stationarity of this kind of EEG. In this paper, we concentrate on the stationarity of the EEG with ERPs by testing the stationarity of 500ms EEG segments with ERPs recorded from six subjects in two types of experiments. The results suggest that selected EEG segment whose length is larger than 190ms remains to be stationarity and all epochs duration less than 40ms is considered to be stationary, whichever channel the data is from and whatever type of cognitive task is performed in the experiment. This is an obvious difference between the stationarity of EEG with ERPs and that of EEG, which is reported to be stationary as long as its length is less than 12s.

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4

Shen, Yi, and Tony S. Wirjanto. "Stationarity as a path property." Probability and Mathematical Statistics 39, no. 2 (December 19, 2019): 403–22. http://dx.doi.org/10.19195/0208-4147.39.2.9.

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Traditionally, stationarity refers to shift invariance of the distribution of a stochastic process. In this paper, we rediscover stationarity as a path property instead of a distributional property. More precisely, we characterize a set of paths, denoted by A, which corresponds to the notion of stationarity. On one hand, the set A is shown to be large enough, so that for any stationary process, almost all of its paths are in A. On the other hand, we prove that any path in A will behave in the optimal way under any stationarity test satisfying some mild conditions.

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5

Valera, Harold Glenn A., Mark J. Holmes, and Gazi M. Hassan. "Does inflation targeting matter for the behavior of inflation and output growth? Some regime-based evidence for Asian economies." Journal of Economic Studies 45, no. 5 (October 8, 2018): 932–55. http://dx.doi.org/10.1108/jes-01-2017-0023.

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PurposeThe purpose of this paper is to consider whether or not the introduction of inflation targeting (IT) impacts on the mean-reversion properties of inflation and output growth.Design/methodology/approachFocusing on eight Asian countries of which four are inflation-targeters, the authors employ a two-state Markov-switching model which characterizes the behavior of inflation and output growth as regime-dependent based on periods of stationarity or non-stationarity.FindingsIn contrast to a literature that offers mixed findings, the authors find the presence of stationary inflation and output growth in one regime for all IT countries, except for South Korea which is characterized by stationary output growth in both regimes. In the cases of South Korea and Thailand, IT reduces the probability of inflation remaining in a non-stationary regime. IT increases the probability of South Korea remaining in a regime of low persistence output growth. While IT is important in understanding behavior, so are other considerations such as exchange rate volatility, as well as the Asian and global financial crises.Originality/valueIn contrast to other unit root tests of inflation and output growth, a novelty of the approach is that the authors obtain new insights in terms of two concepts of stationarity that allow for inflation and output growth to switch between stationary and non-stationary regimes (partial stationarity), or between stationary regimes of differing degrees of persistence (varied stationarity).

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6

Česnik, Martin, Janko Slavič, Lorenzo Capponi, Massimiliano Palmieri, Filippo Cianetti, and Miha Boltežar. "The relevance of non-stationarities and non-Gaussianities in vibration fatigue." MATEC Web of Conferences 165 (2018): 10011. http://dx.doi.org/10.1051/matecconf/201816510011.

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In classical fatigue of materials, the frequency contents of dynamic loading are well below the natural frequencies of the observed structure or test specimen. However, when dealing with vibration fatigue the frequency contents of dynamic loading and structure's dynamic response overlap, resulting in amplified stress loads of the structure. For such cases, frequency counting methods are especially convenient. Gaussianity and stationarity assumptions are applied in frequency-domain methods for obtaining dynamic structure's response and frequency-domain methods for calculating damage accumulation rate. Since it is common in real environments for the structure to be excited with non-Gaussian and non-stationary loads, this study addresses the effects of such dynamic excitation to experimental time-to-failure of a structure. Initially, the influence of non-Gaussian stationary excitation is experimentally studied via excitation signals with equal power density spectrum and different values of kurtosis. Since no relevant changes of structure's time-to-failure were observed, the study focused on non-stationary excitation signals that are also inherently non-Gaussian. The non-stationarity of excitation was achieved by amplitude modulation and significantly shorter times-to-failure were observed when compared to experiments with stationary non-Gaussian excitation. Additionally, the structure's time-to-failure varied with the rate of the amplitude modulation. To oversee this phenomenon the presented study proposes a non-stationarity index which can be obtained from the excitation time history. The non-stationarity index was experimentally confirmed as a reliable estimator for severity of non-stationary excitation. The non-stationarity index is used to determine if the frequencydomain methods can safely be applied for time-to-failure calculation.

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7

Lu, Zhiping, Ming Li, and Wei Zhao. "Stationarity Testing of Accumulated Ethernet Traffic." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/217213.

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We investigate the stationarity property of the accumulated Ethernet traffic series. We applied several widely used stationarity and unit root tests, such as Dickey-Fuller test and its augmented version, Phillips-Perron test, as well as the Kwiatkowski-Phillips-Schmidt-Shin test and some of its generalizations, to the assessment of the stationarity of the traffic traces at the different time scales. The quantitative results in this research provide evidence that when the time scale increases, the accumulated traffic series are more stationary.

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8

Tan, Yi, Jesper Ødum Nielsen, and Gert Frølund Pedersen. "Spatial Stationarity of Ultrawideband and Millimeter Wave Radio Channels." International Journal of Antennas and Propagation 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/3212864.

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For radio channels with broad bandwidth resource, such as those often used for ultrawideband (UWB) and millimeter wave (mmwave) systems, the Wide-Sense Stationary Uncorrelated Scattering (WSSUS) and spatial stationary assumptions are more critical than typical cellular channels with very limited bandwidth resource. This paper studies spatial stationarity and bandwidth dependency of the Multipath Component (MPC) parameters, and the concept of local region of stationarity (LRS) is used as the measure of the physical stationarity region. LRS calculation results based on channel measurements show that the size of LRS is bandwidth dependent in all measured bands, 2–4 GHz, 14–16 GHz, and 28–30 GHz. The results in this paper point out that an inappropriate choice of bandwidth in channel parameter estimation could violate spatial stationary assumptions. The paper indicates LRS sizes for different bandwidths in the three bands.

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9

Arrieta-Pastrana, Alfonso, Manuel Saba, and Adriana Puello Alcázar. "Analysis of Climate Variability in a Time Series of Precipitation and Temperature Data: A Case Study in Cartagena de Indias, Colombia." Water 14, no. 9 (April 24, 2022): 1378. http://dx.doi.org/10.3390/w14091378.

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Anthropogenic climate change is a global trend, hitherto incontrovertible, causing immense social and economic damage. Although the this is evident at the global level, at the local level, there is still debate about the most appropriate analyses to support this fact. This debate is particularly relevant in developing countries, such as Colombia, where there is a significant lack of data at the local level that require analysis and interpretation. Consequently, studies are often superficially conducted to support climate change theory at the local level. However, such studies are then used to design hydraulic infrastructure, with potential catastrophic errors for human and environmental health. In this study, we sought evidence of climate change through an analysis of a series of data on temperature (maximum, mean and minimum), as well as total annual and maximum rainfall in 24 h registered at the Rafael Nuñez Airport station in the city of Cartagena, Colombia, from 1941 to 2015. The hypotheses of homogeneity, trend, stationarity and non-stationarity were analyzed. Problems of non-homogeneity and the presence of periodicity in the analyzed series were found, showing a trend and apparent non-stationarity in the original series. This could be associated with the effects of climate change. In this case, no correlation was found between temperatures and rainfall. Spectral analysis was performed for all series, and residual series were generated by extracting the harmonics of greatest significance. It was found that the series data generated from the third harmonic are generally stationary and without trend. Therefore, the trend and non-stationarity of the original series are due to problems of non-homogeneity and periodicity in the series. In the results of the stationarity test conducted according to the Phillips–Perron criterion, all series were non-stationary. For the two additional criteria of stationarity tests, 40% were shown to be stationary, and 60% were non-stationary. Specifically, non-homogeneity problems and apparent trends associated with climate change could have negative implications for the design of drainage systems.

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10

Arrieta-Pastrana, Alfonso, Manuel Saba, and Adriana Puello Alcázar. "Analysis of Climate Variability in a Time Series of Precipitation and Temperature Data: A Case Study in Cartagena de Indias, Colombia." Water 14, no. 9 (April 24, 2022): 1378. http://dx.doi.org/10.3390/w14091378.

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Anthropogenic climate change is a global trend, hitherto incontrovertible, causing immense social and economic damage. Although the this is evident at the global level, at the local level, there is still debate about the most appropriate analyses to support this fact. This debate is particularly relevant in developing countries, such as Colombia, where there is a significant lack of data at the local level that require analysis and interpretation. Consequently, studies are often superficially conducted to support climate change theory at the local level. However, such studies are then used to design hydraulic infrastructure, with potential catastrophic errors for human and environmental health. In this study, we sought evidence of climate change through an analysis of a series of data on temperature (maximum, mean and minimum), as well as total annual and maximum rainfall in 24 h registered at the Rafael Nuñez Airport station in the city of Cartagena, Colombia, from 1941 to 2015. The hypotheses of homogeneity, trend, stationarity and non-stationarity were analyzed. Problems of non-homogeneity and the presence of periodicity in the analyzed series were found, showing a trend and apparent non-stationarity in the original series. This could be associated with the effects of climate change. In this case, no correlation was found between temperatures and rainfall. Spectral analysis was performed for all series, and residual series were generated by extracting the harmonics of greatest significance. It was found that the series data generated from the third harmonic are generally stationary and without trend. Therefore, the trend and non-stationarity of the original series are due to problems of non-homogeneity and periodicity in the series. In the results of the stationarity test conducted according to the Phillips–Perron criterion, all series were non-stationary. For the two additional criteria of stationarity tests, 40% were shown to be stationary, and 60% were non-stationary. Specifically, non-homogeneity problems and apparent trends associated with climate change could have negative implications for the design of drainage systems.

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11

Ren, Huiying, Z. Jason Hou, Mark Wigmosta, Ying Liu, and L. Ruby Leung. "Impacts of Spatial Heterogeneity and Temporal Non-Stationarity on Intensity-Duration-Frequency Estimates—A Case Study in a Mountainous California-Nevada Watershed." Water 11, no. 6 (June 21, 2019): 1296. http://dx.doi.org/10.3390/w11061296.

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Changes in extreme precipitation events may require revisions of civil engineering standards to prevent water infrastructures from performing below the designated guidelines. Climate change may invalidate the intensity-duration-frequency (IDF) computation that is based on the assumption of data stationarity. Efforts in evaluating non-stationarity in the annual maxima series are inadequate, mostly due to the lack of long data records and convenient methods for detecting trends in the higher moments. In this study, using downscaled high resolution climate simulations of the historical and future periods under different carbon emission scenarios, we tested two solutions to obtain reliable IDFs under non-stationarity: (1) identify quasi-stationary time windows from the time series of interest to compute the IDF curves using data for the corresponding time windows; (2) introduce a parameter representing the trend in the means of the extreme value distributions. Focusing on a mountainous site, the Walker Watershed, the spatial heterogeneity and variability of IDFs or extremes are evaluated, particularly in terms of the terrain and elevation impacts. We compared observations-based IDFs that use the stationarity assumption with the two approaches that consider non-stationarity. The IDFs directly estimated based on the traditional stationarity assumption may underestimate the 100-year 24-h events by 10% to 60% towards the end of the century at most grids, resulting in significant under-designing of the engineering infrastructure at the study site. Strong spatial heterogeneity and variability in the IDF estimates suggest a preference for using high resolution simulation data for the reliable estimation of exceedance probability over data from sparsely distributed weather stations. Discrepancies among the three IDFs analyses due to non-stationarity are comparable to the spatial variability of the IDFs, underscoring a need to use an ensemble of non-stationary approaches to achieve unbiased and comprehensive IDF estimates.

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12

Wang, Zuo-Cai, Feng Wu, and Wei-Xin Ren. "Stationarity test of vibration signals with surrogate data and time–frequency analysis." Advances in Structural Engineering 20, no. 8 (November 21, 2016): 1143–54. http://dx.doi.org/10.1177/1369433216677602.

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The stationarity test of vibration signals is critical for the extraction of the signal features. In this article, the surrogate data with various time–frequency analysis methods are proposed for stationary test of vibration signals. The surrogate data are first generated from the Fourier spectrum of the original signal with keeping the magnitude of the spectrum unchanged and replacing its phase by a random sequence. The local and global spectra of the original signal and the surrogate data are then estimated by four time–frequency analysis methods, which are short-time Fourier transform, multitaper spectrograms, wavelet transform, and S-transform methods. The index of nonstationarity is then defined based on the distances between the local and global spectra. Three kinds of synthetic signals, which are stationary signals, frequency-modulated signals, and amplitude-modulated signals, are tested to compare the efficiency of the four time–frequency analysis methods as mentioned. The results show that with a certain observation scale value, the index of nonstationarity based on the short-time Fourier transform or wavelet transform method may fail to test the stationarity of the signal. The parametric studies and sensitivity analysis of the observation scale and noise-level effect are also extensively conducted. The results show that the index of nonstationarity calculated using the multitaper spectrograms’ method is more suitable for stationarity test of frequency-modulated signals, while the index of nonstationarity calculated using the S-transform method is more suitable for stationarity test of amplitude-modulated signals. The results also show that the noise has a significant effect on the stationarity test results. Finally, the stationarity of a real vibration signal measured from a cable is tested, and the results show that the proposed index of nonstationarity can effectively test the stationarity of real vibration signals.

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13

Arellano, Consuelo, and Sastry G. Pantula. "TESTING FOR TREND STATIONARITY VERSUS DIFFERENCE STATIONARITY." Journal of Time Series Analysis 16, no. 2 (March 1995): 147–64. http://dx.doi.org/10.1111/j.1467-9892.1995.tb00227.x.

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14

Puchstein, Ruprecht, and Philip Preuß. "Testing for Stationarity in Multivariate Locally Stationary Processes." Journal of Time Series Analysis 37, no. 1 (May 14, 2015): 3–29. http://dx.doi.org/10.1111/jtsa.12133.

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15

Kalamkar, V. A. "Minification processes with discrete marginals." Journal of Applied Probability 32, no. 3 (September 1995): 692–706. http://dx.doi.org/10.2307/3215123.

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We investigate the stationarity of minification processes when the marginal is a discrete distribution. There is a close relationship between the problem considered by Arnold and Isaacson (1976) and the stationarity in minification processes. We give a necessary and sufficient condition for a discrete distribution to be the marginal of a stationary minification process. Members of the Poisson and negative binomial families can be the marginals of stationary minification processes. The geometric minification process is studied in detail, and two characterizations of it based on the structure of the innovation process are given.

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16

Kalamkar, V. A. "Minification processes with discrete marginals." Journal of Applied Probability 32, no. 03 (September 1995): 692–706. http://dx.doi.org/10.1017/s0021900200103146.

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We investigate the stationarity of minification processes when the marginal is a discrete distribution. There is a close relationship between the problem considered by Arnold and Isaacson (1976) and the stationarity in minification processes. We give a necessary and sufficient condition for a discrete distribution to be the marginal of a stationary minification process. Members of the Poisson and negative binomial families can be the marginals of stationary minification processes. The geometric minification process is studied in detail, and two characterizations of it based on the structure of the innovation process are given.

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17

Genton, Marc G., and Olivier Perrin. "On a time deformation reducing nonstationary stochastic processes to local stationarity." Journal of Applied Probability 41, no. 1 (March 2004): 236–49. http://dx.doi.org/10.1239/jap/1077134681.

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A stochastic process is locally stationary if its covariance function can be expressed as the product of a positive function multiplied by a stationary covariance. In this paper, we characterize nonstationary stochastic processes that can be reduced to local stationarity via a bijective deformation of the time index, and we give the form of this deformation under smoothness assumptions. This is an extension of the notion of stationary reducibility. We present several examples of nonstationary covariances that can be reduced to local stationarity. We also investigate the particular situation of exponentially convex reducibility, which can always be achieved for a certain class of separable nonstationary covariances.

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Genton, Marc G., and Olivier Perrin. "On a time deformation reducing nonstationary stochastic processes to local stationarity." Journal of Applied Probability 41, no. 01 (March 2004): 236–49. http://dx.doi.org/10.1017/s0021900200014170.

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A stochastic process is locally stationary if its covariance function can be expressed as the product of a positive function multiplied by a stationary covariance. In this paper, we characterize nonstationary stochastic processes that can be reduced to local stationarity via a bijective deformation of the time index, and we give the form of this deformation under smoothness assumptions. This is an extension of the notion of stationary reducibility. We present several examples of nonstationary covariances that can be reduced to local stationarity. We also investigate the particular situation of exponentially convex reducibility, which can always be achieved for a certain class of separable nonstationary covariances.

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19

Benoit, Lionel, Mathieu Vrac, and Gregoire Mariethoz. "Dealing with non-stationarity in sub-daily stochastic rainfall models." Hydrology and Earth System Sciences 22, no. 11 (November 19, 2018): 5919–33. http://dx.doi.org/10.5194/hess-22-5919-2018.

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Abstract. Understanding the stationarity properties of rainfall is critical when using stochastic weather generators. Rainfall stationarity means that the statistics being accounted for remain constant over a given period, which is required for both inferring model parameters and simulating synthetic rainfall. Despite its critical importance, the stationarity of precipitation statistics is often regarded as a subjective choice whose examination is left to the judgement of the modeller. It is therefore desirable to establish quantitative and objective criteria for defining stationary rain periods. To this end, we propose a methodology that automatically identifies rain types with homogeneous statistics. It is based on an unsupervised classification of the space–time–intensity structure of weather radar images. The transitions between rain types are interpreted as non-stationarities. Our method is particularly suited to deal with non-stationarity in the context of sub-daily stochastic rainfall models. Results of a synthetic case study show that the proposed approach is able to reliably identify synthetically generated rain types. The application of rain typing to real data indicates that non-stationarity can be significant within meteorological seasons, and even within a single storm. This highlights the need for a careful examination of the temporal stationarity of precipitation statistics when modelling rainfall at high resolution.

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20

Muhammadullah, Sara, Amena Urooj, and Faridoon Khan. "A revisit of the unemployment rate, interest rate, GDP growth and Inflation of Pakistan: Whether Structural break or unit root?" iRASD Journal of Economics 3, no. 2 (September 25, 2021): 80–92. http://dx.doi.org/10.52131/joe.2021.0302.0027.

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The study investigates the query of structural break or unit root considering four macroeconomic indicators; unemployment rate, interest rate, GDP growth, and inflation rate of Pakistan. The previous studies create ambiguity regarding the stationarity and non-stationarity of these variables. We employ Zivot & Andrews (1992) unit root test and Step Indicator Saturation (SIS) method for multiple break detection in mean. GDP growth and inflation rate are stationary at level whereas unit root tests fail to reject the null hypothesis of the unemployment rate and interest rate at level. However, Zivot and Andrew unit root test with a single endogenous break indicates that the unemployment rate and interest rate are stationary at level with a single endogenous break. On the other hand, the SIS method reveals that the series are stationary with multiple structural breaks. It is inferred that it is inappropriate to take the first difference of the unemployment rate and interest rate to attain stationarity. The results of this study confirmed that there exist multiple breaks in the macroeconomic variables considered in the context of Pakistan.

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Li, Fang, Wei Chen, and Yishui Shui. "Analysis of Non-Stationarity for 5.9 GHz Channel in Multiple Vehicle-to-Vehicle Scenarios." Sensors 21, no. 11 (May 23, 2021): 3626. http://dx.doi.org/10.3390/s21113626.

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The vehicle-to-vehicle (V2V) radio channel is non-stationary due to the rapid movement of vehicles. However, the stationarity of the V2V channels is an important indicator of the V2V channel characteristics. Therefore, we analyzed the non-stationarity of V2V radio channels using the local region of stationarity (LRS). We selected seven scenarios, including three directions of travel, i.e., in the same, vertical, and opposite directions, and different speeds and environments in a similar driving direction. The power delay profile (PDP) and LRS were estimated from the measured channel impulse responses. The results show that the most important influences on the stationary times are the direction and the speed of the vehicles. The average stationary times for driving in the same direction range from 0.3207 to 1.9419 s, the average stationary times for driving in the vertical direction are 0.0359–0.1348 s, and those for driving in the opposite direction are 0.0041–0.0103 s. These results are meaningful for the analysis of the statistical characteristics of the V2V channel, such as the delay spread and Doppler spread. Small-scale fading based on the stationary times affects the quality of signals transmitted in the V2V channel, including the information transmission rate and the information error code rate.

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22

Pareek, Vishakha, Santanu Chaudhury, and Sanjay Singh. "Handling non-stationarity in E-nose design: a review." Sensor Review 42, no. 1 (November 1, 2021): 39–61. http://dx.doi.org/10.1108/sr-02-2021-0038.

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Purpose The electronic nose is an array of chemical or gas sensors and associated with a pattern-recognition framework competent in identifying and classifying odorant or non-odorant and simple or complex gases. Despite more than 30 years of research, the robust e-nose device is still limited. Most of the challenges towards reliable e-nose devices are associated with the non-stationary environment and non-stationary sensor behaviour. Data distribution of sensor array response evolves with time, referred to as non-stationarity. The purpose of this paper is to provide a comprehensive introduction to challenges related to non-stationarity in e-nose design and to review the existing literature from an application, system and algorithm perspective to provide an integrated and practical view. Design/methodology/approach The authors discuss the non-stationary data in general and the challenges related to the non-stationarity environment in e-nose design or non-stationary sensor behaviour. The challenges are categorised and discussed with the perspective of learning with data obtained from the sensor systems. Later, the e-nose technology is reviewed with the system, application and algorithmic point of view to discuss the current status. Findings The discussed challenges in e-nose design will be beneficial for researchers, as well as practitioners as it presents a comprehensive view on multiple aspects of non-stationary learning, system, algorithms and applications for e-nose. The paper presents a review of the pattern-recognition techniques, public data sets that are commonly referred to as olfactory research. Generic techniques for learning in the non-stationary environment are also presented. The authors discuss the future direction of research and major open problems related to handling non-stationarity in e-nose design. Originality/value The authors first time review the existing literature related to learning with e-nose in a non-stationary environment and existing generic pattern-recognition algorithms for learning in the non-stationary environment to bridge the gap between these two. The authors also present details of publicly available sensor array data sets, which will benefit the upcoming researchers in this field. The authors further emphasise several open problems and future directions, which should be considered to provide efficient solutions that can handle non-stationarity to make e-nose the next everyday device.

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23

Yonghua, Mao. "Stationarity and quasi-stationarity for birth-death processes." SCIENTIA SINICA Mathematica 49, no. 3 (March 1, 2019): 467. http://dx.doi.org/10.1360/n012018-00047.

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24

Mohd Lokoman, Rahmah, Fadhilah Yusof, Nor Eliza Alias, and Zulkifli Yusop. "Construction of Dependence Structure for Rainfall Stations by Joining Time Series Models with Copula Method." Malaysian Journal of Fundamental and Applied Sciences 17, no. 4 (August 31, 2021): 306–20. http://dx.doi.org/10.11113/mjfas.v17n4.2345.

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Copula model has applied in various hydrologic studies, however, most analyses conducted does not considering the non-stationary conditions that may exist in the time series. To investigate the dependence structure between two rainfall stations at Johor Bahru, two methods have been applied. The first method considers the non-stationary condition that exists in the data, while the second method assumes stationarity in the time series data. Through goodness-off-fit (GOF) and simulation tests, performance of both methods are compared in this study. The results obtained in this study highlight the importance of considering non-stationarity conditions in the hydrological data.

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Conni, Michele, and Hilda Deborah. "Texture Stationarity Evaluation with Local Wavelet Spectrum." London Imaging Meeting 2020, no. 1 (September 29, 2020): 24–27. http://dx.doi.org/10.2352/issn.2694-118x.2020.lim-20.

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In texture analysis, stationarity is a fundamental property. There are various ways to evaluate if a texture image is stationary or not. One of the most recent and effective of these is a standard test based on non-decimated stationary wavelet transform. This method permits to evaluate how stationary is an image depending on the scale considered. We propose to use this feature to characterize an image and we discuss the implication of such approach.

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ISLIKER, HEINZ, and JÜRGEN KURTHS. "A TEST FOR STATIONARITY: FINDING PARTS IN TIME SERIES APT FOR CORRELATION DIMENSION ESTIMATES." International Journal of Bifurcation and Chaos 03, no. 06 (December 1993): 1573–79. http://dx.doi.org/10.1142/s0218127493001227.

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We propose a method to identify stationary phases in time series. Stationarity is a necessary condition for many concepts in dynamical systems theory, e.g. deterministic chaos. Therefore, testing for stationarity should necessarily be the first step in any data analysis. Above all, this testing is highly important whenever one deals with systems for which stationarity is not guaranteed by the data acquisition procedure: if only short and unique time series are accessible and if the experimental situation is not or only restrictedly controllable, as for instance in astronomy, economy, or medicine. The proposed stationarity test is easily workable and easy to implement in the form of a systematically searching loop. It singles out the parts of a time series which are a reasonable input to a dimension estimate algorithm. Thereby, it can ascertain finite correlation dimensions which are not indicative of deterministic behavior; this kind of dimensions can occur in stochastic processes which are nonstationary, e.g. self-affine.

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Marques, Julian M. E., Denis Benasciutti, Jan Papuga, and Milan Růžička. "Uncertainty of Estimated Rainflow Damage in Stationary Random Loadings and in Those Stationary per partes." Applied Sciences 13, no. 5 (February 22, 2023): 2808. http://dx.doi.org/10.3390/app13052808.

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The uncertainty of rainflow fatigue damage is evaluated for stationary loadings and for non-stationary switching loadings with a finite number of stationary states. The approach is based on confidence intervals constructed after direct analysis of stress-time histories. The accuracy of confidence intervals is verified first by numerical simulations, and then by experimental data measured in a mountain bike traveling under various driving and road surface conditions, yielding stationary and non-stationary switching loadings. Stationarity and non-stationarity of loading records is checked by a statistical method (run test). In experiments, a small set of records (validation set) is also collected and used to approximate the expected damage, which serves for verification purposes. Not only do numerical and experimental results confirm the correctness of the proposed confidence interval for damage, but they also emphasize its usefulness in real engineering applications.

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Tovstik, T. M. "Vector autoregression process. Stationarity and simulation." Journal of Physics: Conference Series 2099, no. 1 (November 1, 2021): 012068. http://dx.doi.org/10.1088/1742-6596/2099/1/012068.

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Abstract For vector discrete-parameter random autoregressive processes and for a mixed autoregression/moving-average model, we obtain conditions which should be satisfied by the correlation functions or the model coefficients in order that the process be weakly stationary. Fairly simple tests are used. Algorithms for modeling such vector stationary processes are given. Examples are presented clarifying testing criteria for stationarity of models defned in terms of the coefficients or the correlation functions of the process.

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Last, Günter, and Hermann Thorisson. "Invariant transports of stationary random measures and mass-stationarity." Annals of Probability 37, no. 2 (March 2009): 790–813. http://dx.doi.org/10.1214/08-aop420.

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Shang, Shang, Kangning He, Zhaobin Wang, and Xuguang Yang. "Stationary Time Statistical Property of Ionospheric Clutter in High-Frequency Surface-Wave Radar." Journal of Electrical and Computer Engineering 2019 (November 3, 2019): 1–6. http://dx.doi.org/10.1155/2019/2450191.

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In HFSWR (high-frequency surface-wave radar) system, the detection performance is impacted seriously by ionospheric clutter. Frequency selection is an effective method to avoid the effect of ionospheric clutter. The key to the method is the stationarity of ionospheric clutter over a period of time. This paper mainly researches the stationary time statistical property of the ionospheric clutter. A large number of real data including ionospheric clutter in HFSWR are processed and analyzed. It shows that ionospheric clutter in HFSWR has the characteristics of approximate stationarity within a period of time.

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Wang, Hong, and Fubao Sun. "On the Stationarity of Annual Precipitation over China (1959–2018)." Journal of Hydrometeorology 21, no. 5 (May 2020): 881–90. http://dx.doi.org/10.1175/jhm-d-19-0195.1.

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AbstractStationarity is an assumption that permeates training and practice in water-resource engineering. However, with global change, the validity of stationarity as well as uncertainty of nonstationarity in water-resource planning are being questioned; thus, it is critical to evaluate the stationarity of climate variables, especially precipitation. Based on the continuous observation data of precipitation from 1427 stations across China, 593 efficient grid cells (1° × 1°) are constructed, and the annual precipitation stationarities from 1959 to 2018 are analyzed. The evaluated autocorrelation stationarity indicates that 92.24%–96.12% of the grid cells for an autocorrelation coefficient of lag 1–8 years of precipitation are indistinguishable from 0 [90% confidence level (CL)]. The mean stationarity indicates that 97.47% of the grid cells have a stable mean for 30 years (90% CL); beyond the confidence limits, they are mainly located in the northwest of China, where annual precipitation is less, and the average exceeding range is ±3.78 mm. The long-term observation of annual precipitation in Beijing (1819–2018) and Shanghai (1879–2018) also yields autocorrelation and mean stationarities. There is no significant difference in the annual precipitations between the past 20 years (1999–2018) and the past 60 years (1959–2018) over China. Therefore, the annual precipitation in China exhibits a weak stationary behavior that is indistinguishable from the stationary stochastic process. The average variation in precipitation is ±9.55% between 30 successive years and 16.53% between 10 successive years. Therefore, it is valuable and feasible to utilize the historical data of annual precipitation as the basis of water-resources application.

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Xiao, Zhijie, and Luiz Renato Lima. "Testing Covariance Stationarity." Econometric Reviews 26, no. 6 (November 29, 2007): 643–67. http://dx.doi.org/10.1080/07474930701639080.

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33

Kemppainen, Antti. "Stationarity of SLE." Journal of Statistical Physics 139, no. 1 (February 19, 2010): 108–21. http://dx.doi.org/10.1007/s10955-010-9929-4.

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34

Kremer, Erhard. "Credibility for stationarity." Blätter der DGVFM 22, no. 4 (October 1996): 755–64. http://dx.doi.org/10.1007/bf02808406.

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Kremer, Erhard. "Credibility for stationarity." Blätter der DGVFM 23, no. 1 (April 1997): 100. http://dx.doi.org/10.1007/bf02808716.

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36

Kremer, E. "Credibility for stationarity." Insurance: Mathematics and Economics 17, no. 3 (April 1996): 238. http://dx.doi.org/10.1016/0167-6687(96)82382-1.

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Rahimullaily, Rahimullaily, and Amalina Amalina. "Kestasioneran Kurs Dolar Amerika dan Harga Saham Pada Masa Pandemi Covid 19 Tahun 2020." JOSTECH: Journal of Science and Technology 1, no. 1 (March 31, 2021): 83–91. http://dx.doi.org/10.15548/jostech.v1i1.2439.

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This study aims to determine the stationarity of the US dollar exchange rate and stock prices during the Covid 19 pandemic. One of the interesting stocks to study is the stock price of PT Telecommunications Indonesia Tbk. The augmented Dickey-Fuller test was used to determine the stationarity of the two variables. The research data is sourced from secondary data through the official website of Bank Indonesia to view the US Dollar Exchange Rate and through the website investing to see the stock price of PT. Telekomunikasi Indonesia Tbk during the Covid 19 pandemic period in Indonesia occurred from March to December 2020. The results showed that the check of the stationary stock price of PT. Telekomunikasi Indonesia Tbk and the US Dollar exchange rate at level I (0) was not stationary. While the two variables are stationary in the first differencing conditions I (1).

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Bierens, Herman J., and Shingyi Guo. "Testing stationarity and trend stationarity against the unit root hypothesis." Econometric Reviews 12, no. 1 (January 1993): 1–32. http://dx.doi.org/10.1080/07474939308800252.

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BEN-NERIA, OMER. "ON SINGULAR STATIONARITY II (TIGHT STATIONARITY AND EXTENDERS-BASED METHODS)." Journal of Symbolic Logic 84, no. 1 (March 2019): 320–42. http://dx.doi.org/10.1017/jsl.2018.46.

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AbstractWe study the notion of tightly stationary sets which was introduced by Foreman and Magidor in [8]. We obtain two consistency results showing that certain sequences of regular cardinals ${\langle {\kappa _n}\rangle _{n < \omega }}$ can have the property that in some generic extension, every ground-model sequence of fixed-cofinality stationary sets ${S_n} \subseteq {\kappa _n}$ is tightly stationary. The results are obtained using variations of the short-extenders forcing method.

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Ben-Neria, Omer. "On singular stationarity I (mutual stationarity and ideal-based methods)." Advances in Mathematics 356 (November 2019): 106790. http://dx.doi.org/10.1016/j.aim.2019.106790.

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41

Squartini, T., and D. Garlaschelli. "Stationarity, non-stationarity and early warning signals in economic networks." Journal of Complex Networks 3, no. 1 (May 5, 2014): 1–21. http://dx.doi.org/10.1093/comnet/cnu012.

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Horváth, Lajos, Zhenya Liu, Gregory Rice, and Shixuan Wang. "Sequential monitoring for changes from stationarity to mild non-stationarity." Journal of Econometrics 215, no. 1 (March 2020): 209–38. http://dx.doi.org/10.1016/j.jeconom.2019.08.010.

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43

Ribeiro, Maria Eduarda, Taison Anderson Bortolin, Ludmilson Abritta Mendes, and Leonardo de Carvalho Souza Santa Rita. "Análise de Séries Hidrológicas na Bacia Hidrográfica afluente à Usina Hidrelétrica Castro Alves, RS." Revista Brasileira de Geografia Física 14, no. 4 (2021): 2042–58. http://dx.doi.org/10.26848/rbgf.v14.4.p2042-2058.

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This study aims to analyze the stationariety and homogeneity of rainfall and streamflow series of the contribution basin of Castro Alves Hydroeletric Power Plant, in Southern Brazil. The rainfall data were acquired from the Agência Nacional de Águas, and the average rainfall series was calculated for the period from 1945 to 2017. The streamflow data were acquired from the Operador Nacional do Sistema Elétrico covering a period from 1945 to 2017. The analysis were performed in the complete series and in two periods obtained from the same, referring to the period before and after 1970. Six statistical tests were used to check the stationarity: t-Student, F-Snedecor, Spearman Correlation Coefficent, Cox-Stuart, Mann-Whitney and Mann-Kendall. The verification of the point of change in the series of total annual precipitations, monthly totals and monthly average flows was performed using Pettitt’s test. The analysis results made it possible to conclude that the hydrological series are non-stationary. The period prior to 1970 was characterized as non-stationary. The period after 1970 showed significant signs of stationarity and homogeneity for both variables. Using the Pettitt test, a trend change was identified in the year 1971 and 1970 for the series of annual total precipitations and monthly mean flows, respectively. In the monthly analyzes of the series, it was found that the increase in the precipitated total was more accentuated in the dry months of May and November. This corroborates the more pronounced increase in the average monthly streamflow observed in those same months.

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Fill, James Allen. "Time to Stationarity for a Continuous-Time Markov Chain." Probability in the Engineering and Informational Sciences 5, no. 1 (January 1991): 61–76. http://dx.doi.org/10.1017/s0269964800001893.

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Separation is one measure of distance from stationarity for Markov chains. Strong stationary times provide bounds on separation and so aid in the analysis of mixing rates. The precise connection between separation and strong stationary times was drawn by Aldous and Diaconis (1987) (Advances in Applied Mathematics8: 69−97) for discrete time chains. We develop the corresponding foundational theory for continuous time chains; several new and interesting mathematical issues arise.

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Ferreira, Isabela Arantes, Mariana Borges Albuquerque, Bruno Henrique Toná Juliani, Sandro Lautenschlager, Cristhiane Michiko Passos Okawa, and Antonio Carlos Zuffo. "Stationarity of pluviometric series of the state of Ceará, Brazil." Ciência e Natura 44 (April 20, 2022): e22. http://dx.doi.org/10.5902/2179460x68824.

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This paper aims to investigate stationarity in the pluviometric historical series of the state of Ceará, Brazil. After selection, the gaps were filled using linear regression. The Mann-Kendall and Pettitt tests were conducted with the help of the package “trend”, in R programming language. After applying the tests, it was noted that most of the selected stations presented stationary behavior, except for Chorozinho, which presented a p-value of 0,018 for the Mann-Kendall test, i.e., rejecting the null hypothesis of stationarity at 5% significance and presenting a positive monotone trend. For the Pettitt test, the station presented a p-value of 0,022, thus rejecting the null hypothesis of lack of change point at 5% significance, the change point being in the year of 1982. It is concluded that it was possible to analyze the stationarity of historic pluviometric series and have a better understanding of the hydrological regime of the region.

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HILFER, R. "FOUNDATIONS OF FRACTIONAL DYNAMICS." Fractals 03, no. 03 (September 1995): 549–56. http://dx.doi.org/10.1142/s0218348x95000485.

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Time flow in dynamical systems is reconsidered in the ultralong time limit. The ultralong time limit is a limit in which a discretized time flow is iterated infinitely often and the discretization time step is infinite. The new limit is used to study induced flows in ergodic theory, in particular for subsets of measure zero. Induced flows on subsets of measure zero require an infinite renormalization of time in the ultralong time limit. It is found that induced flows are given generically by stable convolution semigroups and not by the conventional translation groups. This could give new insight into the origin of macroscopic irreversibility. Moreover, the induced semigroups are generated by fractional time derivatives of orders less than unity, and not by a first order time derivative. Invariance under the induced semiflows therefore leads to a new form of stationarity, called fractional stationarity. Fractionally stationary states are dissipative. Fractional stationarity also provides the dynamical foundation for a previously proposed generalized equilibrium concept.

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Oruc, Sertac. "Non-stationary Investigation of Extreme Rainfall." Civil Engineering Journal 7, no. 9 (September 1, 2021): 1620–33. http://dx.doi.org/10.28991/cej-2021-03091748.

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Natural or human-induced variability emerged from investigation of the traditional stationary assumption regarding extreme precipitation analyses. The frequency of extreme rainfall occurrence is expected to increase in the future and neglecting these changes will result in the underestimation of extreme events. However, applications of extremes accept the stationarity that assumes no change over time. Thus, non-stationarity of extreme precipitation of 5, 10, 15, and 30 minutes and 1-, 3-, 6-, and 24-hour data of 17 station in the Black Sea region were investigated in this study. Using one stationary and three non-stationary models for every station and storm duration, 136 stationary and 408 non-stationary models were constructed and compared. The results are presented as non-stationarity impact maps across the Black Sea Region to visualize the results, providing information about the spatial variability and the magnitude of impact as a percentage difference. Results revealed that nonstationary (NST) models outperformed the stationary model for almost all precipitation series at the 17 stations. The model in which time dependent location and scale parameter used (Model 1), performed better among the three different time variant non-stationary models (Model 1 as time variant location and scale parameters, Model 2 as time variant location parameter, and Model 3 as time variant scale parameter). Furthermore, non-stationary impacts exhibited site-specific behavior: Higher magnitudes of non-stationary impacts were observed for the eastern Black Sea region and the coastal line. Moreover, the non-stationary impacts were more explicit for the sub-hourly data, such as 5 minutes or 15 minutes, which can be one of the reasons for severe and frequent flooding events across the region. The results of this study indicate the importance of the selected covariate and the inclusion of it for the reliability of the model development. Spatial and temporal distribution of the nonstationary impacts and their magnitude also urges to further investigation of the impact on precipitation regime, intensification, severity. Doi: 10.28991/cej-2021-03091748 Full Text: PDF

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48

Deléamont, P. Y., and D. La Vecchia. "Semiparametric segment M-estimation for locally stationary diffusions." Biometrika 106, no. 4 (September 16, 2019): 941–56. http://dx.doi.org/10.1093/biomet/asz042.

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Summary We develop and implement a novel M-estimation method for locally stationary diffusions observed at discrete time-points. We give sufficient conditions for the local stationarity of general time-inhomogeneous diffusions. Then we focus on locally stationary diffusions with time-varying parameters, for which we define our M-estimators and derive their limit theory.

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Gonzalez, Jesus D. Terrazas, and Witold Kinsner. "Evaluating the Security Level of a Cryptosystem based on Chaos." International Journal of Software Science and Computational Intelligence 4, no. 3 (July 2012): 80–120. http://dx.doi.org/10.4018/jssci.2012070105.

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This paper presents tests specially-designed for a cryptosystem based on chaotic continuous cellular automata (CCA). The degree of the cryptosystem security is assessed by evaluating its (i) stationarity, (ii) spectral fractal dimension, and (iii) surrogate data. These tools are verified with known signals before applying them to test the cryptosystem. This paper introduces (i) a robust method to determine the minimum stationary window in a given time series, and (ii) a technique to conceal a chaotic attractor based on surrogate data. These new ideas are relevant because the stationarity of a signal can be determined rapidly, and the chaotic attractor concealment enhances the cryptosystem to increase its security degree.

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Van Achter, Guillian, Leandro Ponsoni, François Massonnet, Thierry Fichefet, and Vincent Legat. "Brief communication: Arctic sea ice thickness internal variability and its changes under historical and anthropogenic forcing." Cryosphere 14, no. 10 (October 21, 2020): 3479–86. http://dx.doi.org/10.5194/tc-14-3479-2020.

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Abstract. We use model simulations from the CESM1-CAM5-BGC-LE dataset to characterise the Arctic sea ice thickness internal variability both spatially and temporally. These properties, and their stationarity, are investigated in three different contexts: (1) constant pre-industrial, (2) historical and (3) projected conditions. Spatial modes of variability show highly stationary patterns regardless of the forcing and mean state. A temporal analysis reveals two peaks of significant variability, and despite a non-stationarity on short timescales, they remain more or less stable until the first half of the 21st century, where they start to change once summer ice-free events occur, after 2050.

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