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Published: 18 November 2022
Last updated: 21 December 2022

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1

Priestly, M. B. Non-linear and non-stationary time series. London: Academic Press, 1988.

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2

Segal, Mordechai. Time delay estimation in stationary and non-stationary environments. Woods Hole, Mass: Woods Hole Oceanographic Institution, 1988.

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3

Priestley, M. B. Non-linear and non-stationary time series analysis. London: Academic Press, 1988.

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4

Hunter, John, Simon P. Burke, and Alessandra Canepa. Multivariate Modelling of Non-Stationary Economic Time Series. London: Palgrave Macmillan UK, 2017. http://dx.doi.org/10.1057/978-1-137-31303-4.

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5

Wong, W. K. Some contributions to multivariate stationary non-linear time series. Manchester: UMIST, 1993.

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6

Moukadem, Ali, Djaffar Ould Abdeslam, and Alain Dieterlen. Time-Frequency Domain for Segmentation and Classification of Non-Stationary Signals. Hoboken, USA: John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781118908686.

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7

Qian, Ying. Optimal hedging strategy re-visited: Acknowledging the existence of non-stationary economic time series. [Washington, DC]: World Bank, International Economics Dept., International Trade Division, 1994.

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8

Bergstrom, A. R. The estimation of parameters in non-stationary higher order continuous time dynamic models. [Colchester]: Department of Economics, University of Essex, 1985.

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9

Priestly, M. B. Non-linear and non-stationary time series analysis. Academic, 1988.

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10

Priestly. Non-linear and Stationary Time Series Analysis. Elsevier, 1991.

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11

Burke, Simon P., and Hunter John. Modelling Non-Stationary Economic Time Series: A Multivariate Approach. Palgrave Macmillan, 2005.

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12

Hunter, J., and S. Burke. Modelling Non-Stationary Economic Time Series: A Multivariate Approach. Palgrave Macmillan Limited, 2005.

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13

Burke, Simon P., Hunter John, and Alessandra Canepa. Multivariate Modelling of Non-Stationary Economic Time Series. Palgrave Macmillan, 2016.

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14

Champagne, Benoit. Optimum space-time processing in non-stationary environments. 1990.

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15

Clements, Michael P., and David F. Hendry. Forecasting Non-Stationary Economic Time Series (Zeuthen Lectures). The MIT Press, 2001.

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16

Clements, Michael P., and David F. Hendry. Forecasting Non-Stationary Economic Time Series (Zeuthen Lectures). The MIT Press, 1999.

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17

Burke, Simon P., Hunter John, and Alessandra Canepa. Multivariate Modelling of Non-Stationary Economic Time Series. Palgrave Macmillan, 2017.

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18

Hinderer, K. Foundations of Non-Stationary Dynamic Programming with Discrete Time Parameter. Springer London, Limited, 2012.

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19

Hunter, John, and Simon P. Burke. Modelling Non-Stationary Economic Time Series: A Multivariate Approach (Palgrave Texts in Econometrics). Palgrave Macmillan, 2005.

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20

Hargreaves, Colin. Non-Stationary Time Series Analysis and Cointegration (Advanced Texts in Econometrics). Oxford University Press, 1994.

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21

Hunter, John, and Simon P. Burke. Modelling Non-Stationary Economic Time Series: A Multivariate Approach (Palgrave Texts in Econometrics). Palgrave Macmillan, 2005.

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22

Coolen, A. C. C., A. Annibale, and E. S. Roberts. Random graph ensembles. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0003.

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Abstract:
This chapter presents some theoretical tools for defining random graph ensembles systematically via soft or hard topological constraints including working through some properties of the Erdös-Rényi random graph ensemble, which is the simplest non-trivial random graph ensemble where links appear between two nodes with a fixed probability p. The chapter sets out the central representation of graph generation as the result of a discrete-time Markovian stochastic process. This unites the two flavours of graph generation approaches – because they can be viewed as simply moving forwards or backwards through this representation. It is possible to define a random graph by an algorithm, and then calculate the associated stationary probability. The alternative approach is to specify sampling weights and then to construct an algorithm that will have these weights as the stationary probabilities upon convergence.
23

McCleary, Richard, David McDowall, and Bradley J. Bartos. Noise Modeling. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780190661557.003.0003.

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Chapter 3 introduces the Box-Jenkins AutoRegressive Integrated Moving Average (ARIMA) noise modeling strategy. The strategy begins with a test of the Normality assumption using a Kolomogov-Smirnov (KS) statistic. Non-Normal time series are transformed with a Box-Cox procedure is applied. A tentative ARIMA noise model is then identified from a sample AutoCorrelation function (ACF). If the sample ACF identifies a nonstationary model, the time series is differenced. Integer orders p and q of the underlying autoregressive and moving average structures are then identified from the ACF and partial autocorrelation function (PACF). Parameters of the tentative ARIMA noise model are estimated with maximum likelihood methods. If the estimates lie within the stationary-invertible bounds and are statistically significant, the residuals of the tentative model are diagnosed to determine whether the model’s residuals are not different than white noise. If the tentative model’s residuals satisfy this assumption, the statistically adequate model is accepted. Otherwise, the identification-estimation-diagnosis ARIMA noise model-building strategy continues iteratively until it yields a statistically adequate model. The Box-Jenkins ARIMA noise modeling strategy is illustrated with detailed analyses of twelve time series. The example analyses include non-Normal time series, stationary white noise, autoregressive and moving average time series, nonstationary time series, and seasonal time series. The time series models built in Chapter 3 are re-introduced in later chapters. Chapter 3 concludes with a discussion and demonstration of auxiliary modeling procedures that are not part of the Box-Jenkins strategy. These auxiliary procedures include the use of information criteria to compare models, unit root tests of stationarity, and co-integration.
24

Moukadem, Ali, Djaffar Ould Abdeslam, and Alain Dieterlen. Time-Frequency Domain for Segmentation and Classification of Non-Stationary Signals: The Stockwell Transform Applied on Bio-Signals and Electric Signals. Wiley & Sons, Incorporated, John, 2014.

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25

Moukadem, Ali, Djaffar Ould Abdeslam, and Alain Dieterlen. Time-Frequency Domain for Segmentation and Classification of Non-Stationary Signals: The Stockwell Transform Applied on Bio-Signals and Electric Signals. Wiley & Sons, Incorporated, John, 2014.

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26

Moukadem, Ali, Djaffar Ould Abdeslam, and Alain Dieterlen. Time-Frequency Domain for Segmentation and Classification of Non-Stationary Signals: The Stockwell Transform Applied on Bio-Signals and Electric Signals. Wiley & Sons, Incorporated, John, 2014.

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27

Moukadem, Ali, Djaffar Ould Abdeslam, and Alain Dieterlen. Time-Frequency Domain for Segmentation and Classification of Non-Stationary Signals: The Stockwell Transform Applied on Bio-Signals and Electric Signals. Wiley & Sons, Incorporated, John, 2014.

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28

Moukadem, Ali, Djaffar Ould Abdeslam, and Alain Dieterlen. Time-Frequency Domain for Segmentation and Classification of Non-stationary Signals: The Stockwell Transform Applied on Bio-signals and Electric Signals. Wiley-Interscience, 2014.

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29

Wendling, Fabrice, Marco Congendo, and Fernando H. Lopes da Silva. EEG Analysis. Edited by Donald L. Schomer and Fernando H. Lopes da Silva. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780190228484.003.0044.

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This chapter addresses the analysis and quantification of electroencephalographic (EEG) and magnetoencephalographic (MEG) signals. Topics include characteristics of these signals and practical issues such as sampling, filtering, and artifact rejection. Basic concepts of analysis in time and frequency domains are presented, with attention to non-stationary signals focusing on time-frequency signal decomposition, analytic signal and Hilbert transform, wavelet transform, matching pursuit, blind source separation and independent component analysis, canonical correlation analysis, and empirical model decomposition. The behavior of these methods in denoising EEG signals is illustrated. Concepts of functional and effective connectivity are developed with emphasis on methods to estimate causality and phase and time delays using linear and nonlinear methods. Attention is given to Granger causality and methods inspired by this concept. A concrete example is provided to show how information processing methods can be combined in the detection and classification of transient events in EEG/MEG signals.
30

Tibaldi, Stefano, and Franco Molteni. Atmospheric Blocking in Observation and Models. Oxford University Press, 2018. http://dx.doi.org/10.1093/acrefore/9780190228620.013.611.

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The atmospheric circulation in the mid-latitudes of both hemispheres is usually dominated by westerly winds and by planetary-scale and shorter-scale synoptic waves, moving mostly from west to east. A remarkable and frequent exception to this “usual” behavior is atmospheric blocking. Blocking occurs when the usual zonal flow is hindered by the establishment of a large-amplitude, quasi-stationary, high-pressure meridional circulation structure which “blocks” the flow of the westerlies and the progression of the atmospheric waves and disturbances embedded in them. Such blocking structures can have lifetimes varying from a few days to several weeks in the most extreme cases. Their presence can strongly affect the weather of large portions of the mid-latitudes, leading to the establishment of anomalous meteorological conditions. These can take the form of strong precipitation episodes or persistent anticyclonic regimes, leading in turn to floods, extreme cold spells, heat waves, or short-lived droughts. Even air quality can be strongly influenced by the establishment of atmospheric blocking, with episodes of high concentrations of low-level ozone in summer and of particulate matter and other air pollutants in winter, particularly in highly populated urban areas.Atmospheric blocking has the tendency to occur more often in winter and in certain longitudinal quadrants, notably the Euro-Atlantic and the Pacific sectors of the Northern Hemisphere. In the Southern Hemisphere, blocking episodes are generally less frequent, and the longitudinal localization is less pronounced than in the Northern Hemisphere.Blocking has aroused the interest of atmospheric scientists since the middle of the last century, with the pioneering observational works of Berggren, Bolin, Rossby, and Rex, and has become the subject of innumerable observational and theoretical studies. The purpose of such studies was originally to find a commonly accepted structural and phenomenological definition of atmospheric blocking. The investigations went on to study blocking climatology in terms of the geographical distribution of its frequency of occurrence and the associated seasonal and inter-annual variability. Well into the second half of the 20th century, a large number of theoretical dynamic works on blocking formation and maintenance started appearing in the literature. Such theoretical studies explored a wide range of possible dynamic mechanisms, including large-amplitude planetary-scale wave dynamics, including Rossby wave breaking, multiple equilibria circulation regimes, large-scale forcing of anticyclones by synoptic-scale eddies, finite-amplitude non-linear instability theory, and influence of sea surface temperature anomalies, to name but a few. However, to date no unique theoretical model of atmospheric blocking has been formulated that can account for all of its observational characteristics.When numerical, global short- and medium-range weather predictions started being produced operationally, and with the establishment, in the late 1970s and early 1980s, of the European Centre for Medium-Range Weather Forecasts, it quickly became of relevance to assess the capability of numerical models to predict blocking with the correct space-time characteristics (e.g., location, time of onset, life span, and decay). Early studies showed that models had difficulties in correctly representing blocking as well as in connection with their large systematic (mean) errors.Despite enormous improvements in the ability of numerical models to represent atmospheric dynamics, blocking remains a challenge for global weather prediction and climate simulation models. Such modeling deficiencies have negative consequences not only for our ability to represent the observed climate but also for the possibility of producing high-quality seasonal-to-decadal predictions. For such predictions, representing the correct space-time statistics of blocking occurrence is, especially for certain geographical areas, extremely important.
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