Short run and long run causality in time series: Inference

We propose methods for testing hypotheses of non-causality at various horizons, as defined in Dufour and Renault (1998, Econometrica). We study in detail the case of VAR models and we propose linear methods based on running vector autoregressions at different horizons. While the hypotheses considered are nonlinear, the proposed methods only require linear regression techniques as well as standard Gaussian asymptotic distributional theory. Bootstrap procedures are also considered. For the case of integrated processes, we propose extended regression methods that avoid nonstandard asymptotics. The methods are applied to a VAR model of the U.S. economy.

Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form

In this paper, we study the asymptotic distribution of a simple two-stage (Hannan-Rissanen-type) linear estimator for stationary invertible vector autoregressive moving average (VARMA) models in the echelon form representation. General conditions for consistency and asymptotic normality are given. A consistent estimator of the asymptotic covariance matrix of the estimator is also provided, so that tests and confidence intervals can easily be constructed.

Modelling and Analysis of Some Time Series

The thesis deals with some of the non-linear Gaussian and non-Gaussian time models and mainly concentrated in studying the properties and application of a first order autoregressive process with Cauchy marginal distribution. In this thesis some of the non-linear Gaussian and non-Gaussian time series models and mainly concentrated in studying the properties and application of a order autoregressive process with Cauchy marginal distribution. Time series relating to prices, consumptions, money in circulation, bank deposits and bank clearing, sales and profit in a departmental store, national income and foreign exchange reserves, prices and dividend of shares in a stock exchange etc. are examples of economic and business time series. The thesis discuses the application of a threshold autoregressive(TAR) model, try to fit this model to a time series data. Another important non-linear model is the ARCH model, and the third model is the TARCH model. The main objective here is to identify an appropriate model to a given set of data. The data considered are the daily coconut oil prices for a period of three years. Since it is a price data the consecutive prices may not be independent and hence a time series based model is more appropriate. In this study the properties like ergodicity, mixing property and time reversibility and also various estimation procedures used to estimate the unknown parameters of the process.

Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

ARMA modeling of time series based on rational approximation of spectral density function

This study is concerned with Autoregressive Moving Average (ARMA) models of time series. ARMA models form a subclass of the class of general linear models which represents stationary time series, a phenomenon encountered most often in practice by engineers, scientists and economists. It is always desirable to employ models which use parameters parsimoniously. Parsimony will be achieved by ARMA models because it has only finite number of parameters. Even though the discussion is primarily concerned with stationary time series, later we will take up the case of homogeneous non stationary time series which can be transformed to stationary time series. Time series models, obtained with the help of the present and past data is used for forecasting future values. Physical science as well as social science take benefits of forecasting models. The role of forecasting cuts across all fields of management-—finance, marketing, production, business economics, as also in signal process, communication engineering, chemical processes, electronics etc. This high applicability of time series is the motivation to this study.

Handlungsinduktionen durch die visuelle Wahrnehmung von Linear- und Drehbewegungen im Sport

Die vorliegende Arbeit beschäftigt sich mit den Einflüssen visuell wahrgenommener Bewegungsmerkmale auf die Handlungssteuerung eines Beobachters. Im speziellen geht es darum, wie die Bewegungsrichtung und die Bewegungsgeschwindigkeit als aufgabenirrelevante Reize die Ausführung von motorischen Reaktionen auf Farbreize beeinflussen und dabei schnellere bzw. verzögerte Reaktionszeiten bewirken. Bisherige Studien dazu waren auf lineare Bewegungen (von rechts nach links und umgekehrt) und sehr einfache Reizumgebungen (Bewegungen einfacher geometrischer Symbole, Punktwolken, Lichtpunktläufer etc.) begrenzt (z.B. Ehrenstein, 1994; Bosbach, 2004, Wittfoth, Buck, Fahle & Herrmann, 2006). In der vorliegenden Dissertation wurde die Gültigkeit dieser Befunde für Dreh- und Tiefenbewegungen sowie komplexe Bewegungsformen (menschliche Bewegungsabläufe im Sport) erweitert, theoretisch aufgearbeitet sowie in einer Serie von sechs Reaktionszeitexperimenten mittels Simon-Paradigma empirisch überprüft. Allen Experimenten war gemeinsam, dass Versuchspersonen an einem Computermonitor auf einen Farbwechsel innerhalb des dynamischen visuellen Reizes durch einen Tastendruck (links, rechts, proximal oder distal positionierte Taste) reagieren sollten, wobei die Geschwindigkeit und die Richtung der Bewegungen für die Reaktionen irrelevant waren. Zum Einfluss von Drehbewegungen bei geometrischen Symbolen (Exp. 1 und 1a) sowie bei menschlichen Drehbewegungen (Exp. 2) zeigen die Ergebnisse, dass Probanden signifikant schneller reagieren, wenn die Richtungsinformationen einer Drehbewegung kompatibel zu den räumlichen Merkmalen der geforderten Tastenreaktion sind. Der Komplexitätsgrad des visuellen Ereignisses spielt dabei keine Rolle. Für die kognitive Verarbeitung des Bewegungsreizes stellt nicht der Drehsinn, sondern die relative Bewegungsrichtung oberhalb und unterhalb der Drehachse das entscheidende räumliche Kriterium dar. Zum Einfluss räumlicher Tiefenbewegungen einer Kugel (Exp. 3) und einer gehenden Person (Exp. 4) belegen unsere Befunde, dass Probanden signifikant schneller reagieren, wenn sich der Reiz auf den Beobachter zu bewegt und ein proximaler gegenüber einem distalen Tastendruck gefordert ist sowie umgekehrt. Auch hier spielt der Komplexitätsgrad des visuellen Ereignisses keine Rolle. In beiden Experimenten führt die Wahrnehmung der Bewegungsrichtung zu einer Handlungsinduktion, die im kompatiblen Fall eine schnelle und im inkompatiblen Fall eine verzögerte Handlungsausführung bewirkt. In den Experimenten 5 und 6 wurden die Einflüsse von wahrgenommenen menschlichen Laufbewegungen (freies Laufen vs. Laufbandlaufen) untersucht, die mit und ohne eine Positionsveränderung erfolgten. Dabei zeigte sich, dass unabhängig von der Positionsveränderung die Laufgeschwindigkeit zu keiner Modulation des richtungsbasierten Simon Effekts führt. Zusammenfassend lassen sich die Studienergebnisse gut in effektbasierte Konzepte zur Handlungssteuerung (z.B. die Theorie der Ereigniskodierung von Hommel et al., 2001) einordnen. Weitere Untersuchungen sind nötig, um diese Ergebnisse auf großmotorische Reaktionen und Displays, die stärker an visuell wahrnehmbaren Ereignissen des Sports angelehnt sind, zu übertragen.

On-the-Fly Maintenance of Series-Parallel Relationships in Fork-Join Multithreaded Programs

A key capability of data-race detectors is to determine whether one thread executes logically in parallel with another or whether the threads must operate in series. This paper provides two algorithms, one serial and one parallel, to maintain series-parallel (SP) relationships "on the fly" for fork-join multithreaded programs. The serial SP-order algorithm runs in O(1) amortized time per operation. In contrast, the previously best algorithm requires a time per operation that is proportional to Tarjan’s functional inverse of Ackermann’s function. SP-order employs an order-maintenance data structure that allows us to implement a more efficient "English-Hebrew" labeling scheme than was used in earlier race detectors, which immediately yields an improved determinacy-race detector. In particular, any fork-join program running in T₁ time on a single processor can be checked on the fly for determinacy races in O(T₁) time. Corresponding improved bounds can also be obtained for more sophisticated data-race detectors, for example, those that use locks. By combining SP-order with Feng and Leiserson’s serial SP-bags algorithm, we obtain a parallel SP-maintenance algorithm, called SP-hybrid. Suppose that a fork-join program has n threads, T₁ work, and a critical-path length of T[subscript ∞]. When executed on P processors, we prove that SP-hybrid runs in O((T₁/P + PT[subscript ∞]) lg n) expected time. To understand this bound, consider that the original program obtains linear speed-up over a 1-processor execution when P = O(T₁/T[subscript ∞]). In contrast, SP-hybrid obtains linear speed-up when P = O(√T₁/T[subscript ∞]), but the work is increased by a factor of O(lg n).

Time-series regression models to study the short-term effects of environmental factors on health

Time series regression models are especially suitable in epidemiology for evaluating short-term effects of time-varying exposures on health. The problem is that potential for confounding in time series regression is very high. Thus, it is important that trend and seasonality are properly accounted for. Our paper reviews the statistical models commonly used in time-series regression methods, specially allowing for serial correlation, make them potentially useful for selected epidemiological purposes. In particular, we discuss the use of time-series regression for counts using a wide range Generalised Linear Models as well as Generalised Additive Models. In addition, recently critical points in using statistical software for GAM were stressed, and reanalyses of time series data on air pollution and health were performed in order to update already published. Applications are offered through an example on the relationship between asthma emergency admissions and photochemical air pollutants

Comparing meta-analysis and ecological-longitudinal analysis in time-series studies: a case study of the effects of air pollution on mortality in three Spanish cities

The objective of this paper is to introduce a diVerent approach, called the ecological-longitudinal, to carrying out pooled analysis in time series ecological studies. Because it gives a larger number of data points and, hence, increases the statistical power of the analysis, this approach, unlike conventional ones, allows the complementation of aspects such as accommodation of random effect models, of lags, of interaction between pollutants and between pollutants and meteorological variables, that are hardly implemented in conventional approaches. Design—The approach is illustrated by providing quantitative estimates of the short-termeVects of air pollution on mortality in three Spanish cities, Barcelona,Valencia and Vigo, for the period 1992–1994. Because the dependent variable was a count, a Poisson generalised linear model was first specified. Several modelling issues are worth mentioning. Firstly, because the relations between mortality and explanatory variables were nonlinear, cubic splines were used for covariate control, leading to a generalised additive model, GAM. Secondly, the effects of the predictors on the response were allowed to occur with some lag. Thirdly, the residual autocorrelation, because of imperfect control, was controlled for by means of an autoregressive Poisson GAM. Finally, the longitudinal design demanded the consideration of the existence of individual heterogeneity, requiring the consideration of mixed models. Main results—The estimates of the relative risks obtained from the individual analyses varied across cities, particularly those associated with sulphur dioxide. The highest relative risks corresponded to black smoke in Valencia. These estimates were higher than those obtained from the ecological-longitudinal analysis. Relative risks estimated from this latter analysis were practically identical across cities, 1.00638 (95% confidence intervals 1.0002, 1.0011) for a black smoke increase of 10 μg/m3 and 1.00415 (95% CI 1.0001, 1.0007) for a increase of 10 μg/m3 of sulphur dioxide. Because the statistical power is higher than in the individual analysis more interactions were statistically significant,especially those among air pollutants and meteorological variables. Conclusions—Air pollutant levels were related to mortality in the three cities of the study, Barcelona, Valencia and Vigo. These results were consistent with similar studies in other cities, with other multicentric studies and coherent with both, previous individual, for each city, and multicentric studies for all three cities

Linear amplification of marginally neutral baroclinic waves

Baroclinic wave development is investigated for unstable parallel shear flows in the limit of vanishing normal-mode growth rate. This development is described in terms of the propagation and interaction mechanisms of two coherent structures, called counter-propagating Rossby waves (CRWs). It is shown that, in this limit of vanishing normal-mode growth rate, arbitrary initial conditions produce sustained linear amplification of the marginally neutral normal mode (mNM). This linear excitation of the mNM is subsequently interpreted in terms of a resonance phenomenon. Moreover, while the mathematical character of the normal-mode problem changes abruptly as the bifurcation point in the dispersion diagram is encountered and crossed, it is shown that from an initial-value viewpoint, this transition is smooth. Consequently, the resonance interpretation remains relevant (albeit for a finite time) for wavenumbers slightly different from the ones defining cut-off points. The results are further applied to a two-layer version of the classic Eady model in which the upper rigid lid has been replaced by a simple stratosphere.

U-series isochron dating of immature and mature calcretes as a basis for constructing Quaternary landform chronologies for the Sorbas basin, southeast Spain

Immature and mature calcretes from an alluvial terrace sequence in the Sorbas basin, southeast Spain, were dated by the U-series isochron technique. The immature horizons consistently produced statistically reliable ages of high precision. The mature horizons typically produced statistically unreliable ages but, because of linear trends in the dataset and low errors associated with each data point, it was still possible to place a best-fit isochron through the dataset to produce an age with low associated uncertainties. It is, however, only possible to prove that these statistically unreliable ages have geochronological significance if multiple isochron ages are produced for a single site, and if these multiple ages are stratigraphically consistent. The geochronological significance of such ages can be further proven if at least one of the multiple ages is statistically reliable. By using this technique to date calcretes that have formed during terrace aggradation and at the terrace surface after terrace abandonment it is possible not only to date the timing of terrace aggradation but also to constrain the age at which the river switched from aggradation to incision. This approach, therefore, constrains the timing of changes in fluvial processes more reliably than any currently used geochronological procedure and is appropriate for dating terrace sequences in dryland regions worldwide, wherever calcrete horizons are present. (c) 2005 University of Washington. All rights reserved.

Robust identification for linear-in-the-parameters models

In this paper new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness, including three algorithms using combined A- or D-optimality or PRESS statistic (Predicted REsidual Sum of Squares) with regularised orthogonal least squares algorithm respectively. A common characteristic of these algorithms is that the inherent computation efficiency associated with the orthogonalisation scheme in orthogonal least squares or regularised orthogonal least squares has been extended such that the new algorithms are computationally efficient. A numerical example is included to demonstrate effectiveness of the algorithms. Copyright (C) 2003 IFAC.

Empirical mode decomposition: a novel technique for the study of tremor time series

Tremor is a clinical feature characterized by oscillations of a part of the body. The detection and study of tremor is an important step in investigations seeking to explain underlying control strategies of the central nervous system under natural (or physiological) and pathological conditions. It is well established that tremorous activity is composed of deterministic and stochastic components. For this reason, the use of digital signal processing techniques (DSP) which take into account the nonlinearity and nonstationarity of such signals may bring new information into the signal analysis which is often obscured by traditional linear techniques (e.g. Fourier analysis). In this context, this paper introduces the application of the empirical mode decomposition (EMD) and Hilbert spectrum (HS), which are relatively new DSP techniques for the analysis of nonlinear and nonstationary time-series, for the study of tremor. Our results, obtained from the analysis of experimental signals collected from 31 patients with different neurological conditions, showed that the EMD could automatically decompose acquired signals into basic components, called intrinsic mode functions (IMFs), representing tremorous and voluntary activity. The identification of a physical meaning for IMFs in the context of tremor analysis suggests an alternative and new way of detecting tremorous activity. These results may be relevant for those applications requiring automatic detection of tremor. Furthermore, the energy of IMFs was visualized as a function of time and frequency by means of the HS. This analysis showed that the variation of energy of tremorous and voluntary activity could be distinguished and characterized on the HS. Such results may be relevant for those applications aiming to identify neurological disorders. In general, both the HS and EMD demonstrated to be very useful to perform objective analysis of any kind of tremor and can therefore be potentially used to perform functional assessment.

Optimal piecewise locally linear modeling

Associative memory networks such as Radial Basis Functions, Neurofuzzy and Fuzzy Logic used for modelling nonlinear processes suffer from the curse of dimensionality (COD), in that as the input dimension increases the parameterization, computation cost, training data requirements, etc. increase exponentially. Here a new algorithm is introduced for the construction of a Delaunay input space partitioned optimal piecewise locally linear models to overcome the COD as well as generate locally linear models directly amenable to linear control and estimation algorithms. The training of the model is configured as a new mixture of experts network with a new fast decision rule derived using convex set theory. A very fast simulated reannealing (VFSR) algorithm is utilized to search a global optimal solution of the Delaunay input space partition. A benchmark non-linear time series is used to demonstrate the new approach.

Cumulant-based deconvolution and identification: several new families of linear equations

This paper presents several new families of cumulant-based linear equations with respect to the inverse filter coefficients for deconvolution (equalisation) and identification of nonminimum phase systems. Based on noncausal autoregressive (AR) modeling of the output signals and three theorems, these equations are derived for the cases of 2nd-, 3rd and 4th-order cumulants, respectively, and can be expressed as identical or similar forms. The algorithms constructed from these equations are simpler in form, but can offer more accurate results than the existing methods. Since the inverse filter coefficients are simply the solution of a set of linear equations, their uniqueness can normally be guaranteed. Simulations are presented for the cases of skewed series, unskewed continuous series and unskewed discrete series. The results of these simulations confirm the feasibility and efficiency of the algorithms.