Stationarity Of Time Series Research Articles

European Option Pricing Under Fractional Brownian Motion with an Application to Realized Volatility

This study investigates European option pricing under fractional Brownian motion (fBm) and applies it to realized volatility (RV). The RV measure is selected because it uniquely exhibits simultaneous stationarity and long-range dependency properties in financial time series, as shown in our empirical study. Meanwhile, the Black-Scholes differential equation is not well defined when the underlying assets follow fBm with the Hurst exponent H not equal to 1/2 because fBm is not a semimartingale. Thus, we compute the European option prices using a previously proposed fractional Black-Scholes formula. Our empirical study is conducted on Tokyo Stock Price Index data from January 06, 1997 to December 30, 2013 with a sample size of 4177.

Perspective of the Relationship between Stock Returns and Macroeconomic Indicators: Case of Tunisia

First, we will be interested in the statistical properties of the data collected and especially stationarity. The test was used to identify the properties of the previously studied series is the test Adjusted Dickey Fuller (1981). Indeed, the first step is to study the stationarity of individual time series. In addition, they must be non-stationary as a necessary condition to implement causality tests. In a second step; we will choose the Johanson cointegration test to analyze the long-run equilibrium relationship between stock returns and different macroeconomic variables .In fact the cointegration relationships assume that all variables are integrated of the same order: the level integration will be achieved through the implementation of the ADF test .The third step is to test in a uni-frame varied the type of the relationship between the stock index (TUNINDEX) and the two-monetary and economic variables two and the direction and the sign of a possible causal relationship (if it exists). This type of tests are designed to test whether the economic and monetary activity predict stock returns or not. Finally; and in a final stage; we will try to decompose the variance of the forecast error in order to highlight the proportion related to each shock.

A Study of Co-variation and Convergence of Alternative Measures of Sustainability on the Basis of Panel Data

The study highlights the need for creating alternative indicators of sustainability for considering a well guarded view about sustainable development of a country. The aim of the study is (1) to focus on different alternative measures of sustainability, (2) to assess whether these alternative measures move in the same direction which indicates peoples’ wellbeing as well as maintenance of environmental health and (3) to ascertain whether there has been some tendency towards convergence among the considered countries based on the alternative sustainability measures. Four alternative sustainability indicators like Green Net National Product, Ecological Footprint, Sustainable Human Development Index and Pollution Sensitive Human Development Index, for 22 developing countries have been constructed. Correlation matrix has been considered to focus on the extent of consistency between alternative indices. Unit root test has been done to ensure the stationarity of time series of such indices. The issue of convergence of different sustainability indices has been analysed by use of beta and sigma convergence employing pooled OLS and fixed effect model. It has been found that the different indices are more or less mutually consistent and stationary and over time they have converged across the considered countries. The results indicate that despite convergence coherent with Environmental Kuznets Curve hypothesis, the level of environmental degradation when linked to GDP per capita gives rise to an N-shaped pattern. The study suggests the need for diverse economic pollution control instruments to avoid degradation of the environment.

STATIONARITY OF ANNUAL MAXIMUM DAILY STREAMFLOW TIME SERIES IN SOUTH-EAST BRAZILIAN RIVERS

DOI: 10.12957/cadest.2014.18302 The paper presents a statistical analysis of annual maxima daily streamflow between 1931 and 2013 in South-East Brazil focused in detecting and modelling non-stationarity aspects. Flood protection for the large valleys in South-East Brazil is provided by multiple purpose reservoir systems built during 20th century, which design and operation plans has been done assuming stationarity of historical flood time series. Land cover changes and rapidly-increasing level of atmosphere greenhouse gases of the last century may be affecting flood regimes in these valleys so that it can be that nonstationary modelling should be applied to re-asses dam safety and flood control operation rules at the existent reservoir system. Six annual maximum daily streamflow time series are analysed. The time series were plotted together with fitted smooth loess functions and non-parametric statistical tests are performed to check the significance of apparent trends shown by the plots. Non-stationarity is modelled by fitting univariate extreme value distribution functions which location varies linearly with time. Stationarity and non-stationarity modelling are compared with the likelihood ratio statistic. In four of the six analyzed time series non-stationarity modelling outperformed stationarity modelling. Keywords : Stationarity; Extreme Value Distributions; Flood Frequency Analysis; Maximum Likelihood Method.

Behavioral relevance of the dynamics of the functional brain connectome.

While many previous studies assumed the functional connectivity (FC) between brain regions to be stationary, recent studies have demonstrated that FC dynamically varies across time. However, two challenges have limited the interpretability of dynamic FC information. First, a principled framework for selecting the temporal extent of the window used to examine the dynamics is lacking and this has resulted in ad-hoc selections of window lengths and subsequent divergent results. Second, it is unclear whether there is any behavioral relevance to the dynamics of the functional connectome in addition to that obtained from conventional static FC (SFC). In this work, we address these challenges by first proposing a principled framework for selecting the extent of the temporal windows in a dynamic and data-driven fashion based on statistical tests of the stationarity of time series. Further, we propose a method involving three levels of clustering-across space, time, and subjects-which allow for group-level inferences of the dynamics. Next, using a large resting-state functional magnetic resonance imaging and behavioral dataset from the Human Connectome Project, we demonstrate that metrics derived from dynamic FC can explain more than twice the variance in 75 behaviors across different domains (alertness, cognition, emotion, and personality traits) as compared with SFC in healthy individuals. Further, we found that individuals with brain networks exhibiting greater dynamics performed more favorably in behavioral tasks. This indicates that the ease with which brain regions engage or disengage may provide potential biomarkers for disorders involving altered neural circuitry.

Extreme storm surges: a comparative study of frequency analysis approaches

Abstract. In France, nuclear facilities were designed around very low probabilities of failure. Nevertheless, some extreme climatic events have given rise to exceptional observed surges (outliers) much larger than other observations, and have clearly illustrated the potential to underestimate the extreme water levels calculated with the current statistical methods. The objective of the present work is to conduct a comparative study of three approaches to extreme value analysis, including the annual maxima (AM), the peaks-over-threshold (POT) and the r-largest order statistics (r-LOS). These methods are illustrated in a real analysis case study. All data sets were screened for outliers. Non-parametric tests for randomness, homogeneity and stationarity of time series were used. The shape and scale parameter stability plots, the mean excess residual life plot and the stability of the standard errors of return levels were used to select optimal thresholds and r values for the POT and r-LOS method, respectively. The comparison of methods was based on (i) the uncertainty degrees, (ii) the adequacy criteria and tests, and (iii) the visual inspection. It was found that the r-LOS and POT methods have reduced the uncertainty on the distribution parameters and return level estimates and have systematically shown values of the 100 and 500-year return levels smaller than those estimated with the AM method. Results have also shown that none of the compared methods has allowed a good fit at the right tail of the distribution in the presence of outliers. As a perspective, the use of historical information was proposed in order to increase the representativeness of outliers in data sets. Findings are of practical relevance, not only to nuclear energy operators in France, for applications in storm surge hazard analysis and flood management, but also for the optimal planning and design of facilities to withstand extreme environmental conditions, with an appropriate level of risk.

Empirical Fokker-Planck-based test of stationarity for time series.

We propose a test of stationarity based on the drift coefficients of the Langevin type and the associated Fokker-Planck equations. The test relies on the estimation of the drift coefficients of the underlying probability densities and posits that a time series is nonstationary if the estimated drift term is a nonlinear function of the random variable of the observed time series and the Markov property holds. We provide ample empirical evidence that demonstrates that well- known stationary systems give rise to linear estimates of the drift coefficients, whereas nonstationary time series exhibit nonlinear estimates of the drift term. This does not, indeed, imply that a nonlinear drift term in the Fokker-Planck equation of a dynamic stochastic process causes nonstationarity.

Combined stationarity index for the estimation of turbulent fluxes of scalars and particles in the atmospheric surface layer

In this work the performances of three different tests widely used in scientific community for assessing turbulent flow stationarity have been tested and compared. The stationarity tests have been applied to turbulent fluxes of different scalars (temperature, carbon dioxide and water vapour concentration, ultrafine particle number concentration), collected over a wide range of surface roughness conditions, from almost smooth surfaces to surfaces with different degrees of complexity: suburban, urban and forested canopies. The application of the selected tests to the scalar and particle turbulent fluxes measured above the different experimental sites has frequently shown an ambiguous identification of non-stationarity in turbulent flux records, regardless of the surface conditions and of the transported quantity. The potential impact of surface characteristics, transported scalar, atmospheric stratification and micrometeorological conditions on test performances has been investigated. Finally a new operative stationarity index obtained by the combination of two tests has been proposed to assess the second-order stationarity of turbulence time series.

An investigation of fMRI time series stationarity during motor sequence learning foot tapping tasks

Understanding complex brain networks using functional magnetic resonance imaging (fMRI) is of great interest to clinical and scientific communities. To utilize advanced analysis methods such as graph theory for these investigations, the stationarity of fMRI time series needs to be understood as it has important implications on the choice of appropriate approaches for the analysis of complex brain networks. In this paper, we investigated the stationarity of fMRI time series acquired from twelve healthy participants while they performed a motor (foot tapping sequence) learning task. Since prior studies have documented that learning is associated with systematic changes in brain activation, a sequence learning task is an optimal paradigm to assess the degree of non-stationarity in fMRI time-series in clinically relevant brain areas. We predicted that brain regions involved in a "learning network" would demonstrate non-stationarity and may violate assumptions associated with some advanced analysis approaches. Six blocks of learning, and six control blocks of a foot tapping sequence were performed in a fixed order. The reverse arrangement test was utilized to investigate the time series stationarity. Our analysis showed some non-stationary signals with a time varying first moment as a major source of non-stationarity. We also demonstrated a decreased number of non-stationarities in the third block as a result of priming and repetition. Most of the current literature does not examine stationarity prior to processing. The implication of our findings is that future investigations analyzing complex brain networks should utilize approaches robust to non-stationarities, as graph-theoretical approaches can be sensitive to non-stationarities present in data.

Snowfall time-series reconstruction in Italy over the last 300 years

Snow events are not a rare episode in Mediterranean area, especially in northern and hilly areas of Italy. However, snowfall occurring quasi-simultaneously in the whole peninsula is extraordinary. This study collects, reconstructs, and analyzes the extraordinary snowfall episodes that occurred simultaneously in the whole Italian peninsula since 1709. This is the longest snowfall time series in the central Mediterranean area. The data, obtained by several documentary sources (from ancient archival to online databases), have been analyzed using different statistical tests, in order to explore normality, homogeneity, and stationarity. The results are characterized by a time-series stationarity with a quasi 60- and 100-year-dominant oscillation. No clear trend in the snowfall episode records is found. The 60-year cycle roughly matches with global-scale oscillations linked to natural forces, such as the Atlantic Multidecadal Oscillation and the winter North Atlantic Oscillation. Particular attention was directed to analyze the impact of snowfall on pre-industrial society, underlining the differences among northern and central regions, where snow was a more usual phenomenon, and its impact was mainly on transports of supplies or exceptionally on buildings, and southern regions, where it had a stronger impact also on orchards and cattle.

Data normalisation for Lamb wave–based damage detection using cointegration: A case study with single- and multiple-temperature trends

This article presents an application of the cointegration technique for temperature effect removal (i.e. data normalisation) in Lamb wave–based damage detection. The method is based on the concept of stationarity of time series. Analysis of cointegrating residuals and stationary statistical characteristics – before and after the cointegration process – are used for damage detection. The method is validated using Lamb wave data from undamaged and damaged aluminium plates instrumented with low-profile, surface-bonded piezoceramic transducers. Two temperature variation cases (single- and multiple-temperature trends) are investigated. The experimental results show that the cointegration process can remove undesired temperature effects and accurately detect damage.

Testing stationarity of functional time series

Economic and financial data often take the form of a collection of curves observed consecutively over time. Examples include, intraday price curves, yield and term structure curves, and intraday volatility curves. Such curves can be viewed as a time series of functions. A fundamental issue that must be addressed, before an attempt is made to statistically model such data, is whether these curves, perhaps suitably transformed, form a stationary functional time series. This paper formalizes the assumption of stationarity in the context of functional time series and proposes several procedures to test the null hypothesis of stationarity. The tests are nontrivial extensions of the broadly used tests in the KPSS family. The properties of the tests under several alternatives, including change-point and I(1), are studied, and new insights, present only in the functional setting are uncovered. The theory is illustrated by a small simulation study and an application to intraday price curves.

A multiresolution approach to cointegration for enhanced SHM of structures under varying conditions – An exploratory study

Cointegration has now been established as a powerful means of projecting out long-term trends from time-series data in the context of econometrics. Recent work has further established that cointegration can be applied profitably in the context of structural health monitoring (SHM), where it is desirable to project out the effects of environmental and operational variations from data in order that they do not generate false positives in diagnostic tests. These variations typically impose a time-varying nature on SHM data on a much longer time scale than those at which the dynamics of the structures of interest usually manifest themselves. This situation means that cointegration can be used to remove long-term time variations and thus projects out the operational and environmental effects. The concept of cointegration is partly built on a clear understanding of the ideas of stationarity and nonstationarity for time-series. The current paper will discuss the distinction between different types of nonstationarity in the context of SHM data and will extend the discussion by the introduction of multiresolution (discrete wavelet) analysis as a means of characterising the time scales on which nonstationarity manifests itself. One of the major results of the current study is to demonstrate how a multiresolution approach to cointegration can lead to enhanced sensitivity for damage detection. The discussion will be based on synthetic data and also on experimental data for the guided-wave SHM of a composite plate.

A Kind of Statistics Data Processing with Indicators in an Autocorrelation Network

Efforts to develop data processing or some variable evaluation of the components autocorrelation network or interpersonal relationship network have been hampered by many obstacles. One important reason is the lag of autocorrelation network model (ANM) development. Autocorrelation network models are used to deal with the data with autocorrelation network data. However, some data are correlated with its lag station, so its necessary to introduce the time series in the ANM. The network autocorrelation model with lag and auto-correlated indicators or variables is put forward based on the expansion of the existing social network effect model. The estimation method of the network autocorrelation model is illustrated; the time series stationarity, the consistency and effectiveness of the estimation method are discussed. Also the application of the model is discussed, especially the practical significance on the forecasting and controlling.

Oil prices: Breaks and trends

This paper contributes to the literature of the stationarity of financial time series and the literature on oil and macroeconomics in several ways. First, it uses Kejriwal and Perron (2010) sequential procedure to endogenously determine multiple structural changes in real oil prices without facing the circular testing problem between structural changes and stationary assumptions of previous tests. Second, it performs a diagnostic check to detect the significance and magnitude of the potential breaks. Third, it uses the above information to test for the existence of stochastic trends in real oil prices, and fourth, it speculates about possible explanations for the break dates found in order to encourage further work and discussions. The exercise uses monthly data from January 1861 to August 2011.

Costationarity of Locally Stationary Time Series Usingcostat

This article describes the R package costat. This package enables a user to (i) perform a test for time series stationarity; (ii) compute and plot time-localized autocovariances, and (iii) to determine and explore any costationary relationship between two locally stationary time series. Two locally stationary time series are said to be costationary if there exists two time-varying combination functions such that the linear combination of the two series with the functions produces another time series which is stationary. Costationarity existing between two time series indicates a relationship between the series that might be usefully exploited in a number of ways. Sometimes the relationship itself is of interest, sometimes the derived stationary series is of interest and useful as a substitute for either of the original stationary series in some applications.

On Certain Stationarity Tests for Hydrologic Series

AbstractThe main aim of the article was application of some statistical tests for investigation of weak stationarity of hydrologic time series. The tests were applied to mean monthly flow and maximum annual flow on three rivers: two Polish and one American river. Firstly, the modified Mann–Kendall test for autocorrelated data was used to detect trend. After detrending we used “unit root tests” based on the DF test and “stationarity tests” based on the KPSS test. The tests were investigated and compared in some aspects: analysis of residuals, application to seasonal series, AIC and Schwarz values.

How Do You Make A Time Series Sing Like a Choir? Extracting Embedded Frequencies from Economic and Financial Time Series using Empirical Mode Decomposition

Empirical Mode Decomposition (EMD) was developed late last century, but has still to be introduced to the vast majority of economists. EMD was originally one of the components of Hilbert Huang Transform (HHT) which was a process of extracting the frequency mode features of cycles embedded in any time series using an adaptive data method which can be applied without making any assumption about stationarity or linear data-generating properties of time series. This paper introduces economists to the two constituent parts of the HHT transform, namely EMD and the Hilbert Spectrum, and also a new variant of this methodology, Ensemble EMD (EEMD). Several illustrative applications using the methodology are also included.

The Baltic countries sectoral share price indexes VAR model

According to the same modern Baltic countries economical and political integration, united OMXBaltic security market created.The main purpose of this article is to forecast her sectoral share price indexes according to their interdependent relationship during 2000-2010 year.Time series models, linear regression models and a vector autoregression model (VAR) can be used to model and forecast indexes processes.Therefore, the vector autoregression model is proposed for modelling.Theoretical aspects of model estimation are reviewed: time series stationarity, model identification, parameterestimation, model usage and forecasts.

Application of modern tests for stationarity to single-trial MEG data

Stationarity is a crucial yet rarely questioned assumption in the analysis of time series of magneto- (MEG) or electroencephalography (EEG). One key drawback of the commonly used tests for stationarity of encephalographic time series is the fact that conclusions on stationarity are only indirectly inferred either from the Gaussianity (e.g. the Shapiro-Wilk test or Kolmogorov-Smirnov test) or the randomness of the time series and the absence of trend using very simple time-series models (e.g. the sign and trend tests by Bendat and Piersol). We present a novel approach to the analysis of the stationarity of MEG and EEG time series by applying modern statistical methods which were specifically developed in econometrics to verify the hypothesis that a time series is stationary. We report our findings of the application of three different tests of stationarity--the Kwiatkowski-Phillips-Schmidt-Schin (KPSS) test for trend or mean stationarity, the Phillips-Perron (PP) test for the presence of a unit root and the White test for homoscedasticity--on an illustrative set of MEG data. For five stimulation sessions, we found already for short epochs of duration of 250 and 500 ms that, although the majority of the studied epochs of single MEG trials were usually mean-stationary (KPSS test and PP test), they were classified as nonstationary due to their heteroscedasticity (White test). We also observed that the presence of external auditory stimulation did not significantly affect the findings regarding the stationarity of the data. We conclude that the combination of these tests allows a refined analysis of the stationarity of MEG and EEG time series.