Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-fit in Multivariate Regressions with Application to Asset Pricing Models

We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross-equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared to simulation-based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal, Student t; normal mixtures and stable error models. In the Gaussian case, finite-sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi-stage Monte Carlo test methods. For non-Gaussian distribution families involving nuisance parameters, confidence sets are derived for the the nuisance parameters and the error distribution. The procedures considered are evaluated in a small simulation experi-ment. Finally, the tests are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995.

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.

Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions

In this paper, we propose exact inference procedures for asset pricing models that can be formulated in the framework of a multivariate linear regression (CAPM), allowing for stable error distributions. The normality assumption on the distribution of stock returns is usually rejected in empirical studies, due to excess kurtosis and asymmetry. To model such data, we propose a comprehensive statistical approach which allows for alternative - possibly asymmetric - heavy tailed distributions without the use of large-sample approximations. The methods suggested are based on Monte Carlo test techniques. Goodness-of-fit tests are formally incorporated to ensure that the error distributions considered are empirically sustainable, from which exact confidence sets for the unknown tail area and asymmetry parameters of the stable error distribution are derived. Tests for the efficiency of the market portfolio (zero intercepts) which explicitly allow for the presence of (unknown) nuisance parameter in the stable error distribution are derived. The methods proposed are applied to monthly returns on 12 portfolios of the New York Stock Exchange over the period 1926-1995 (5 year subperiods). We find that stable possibly skewed distributions provide statistically significant improvement in goodness-of-fit and lead to fewer rejections of the efficiency hypothesis.

A Semi-Parametric Factor Model for Interest Rates.

Understanding the dynamics of interest rates and the term structure has important implications for issues as diverse as real economic activity, monetary policy, pricing of interest rate derivative securities and public debt financing. Our paper follows a longstanding tradition of using factor models of interest rates but proposes a semi-parametric procedure to model interest rates.

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.

Identifying and quantifying nonconservative energy production/destruction terms in hydrostatic Boussinesq primitive equation models

This paper seeks to illustrate the point that physical inconsistencies between thermodynamics and dynamics usually introduce nonconservative production/destruction terms in the local total energy balance equation in numerical ocean general circulation models (OGCMs). Such terms potentially give rise to undesirable forces and/or diabatic terms in the momentum and thermodynamic equations, respectively, which could explain some of the observed errors in simulated ocean currents and water masses. In this paper, a theoretical framework is developed to provide a practical method to determine such nonconservative terms, which is illustrated in the context of a relatively simple form of the hydrostatic Boussinesq primitive equation used in early versions of OGCMs, for which at least four main potential sources of energy nonconservation are identified; they arise from: (1) the “hanging” kinetic energy dissipation term; (2) assuming potential or conservative temperature to be a conservative quantity; (3) the interaction of the Boussinesq approximation with the parameterizations of turbulent mixing of temperature and salinity; (4) some adiabatic compressibility effects due to the Boussinesq approximation. In practice, OGCMs also possess spurious numerical energy sources and sinks, but they are not explicitly addressed here. Apart from (1), the identified nonconservative energy sources/sinks are not sign definite, allowing for possible widespread cancellation when integrated globally. Locally, however, these terms may be of the same order of magnitude as actual energy conversion terms thought to occur in the oceans. Although the actual impact of these nonconservative energy terms on the overall accuracy and physical realism of the oceans is difficult to ascertain, an important issue is whether they could impact on transient simulations, and on the transition toward different circulation regimes associated with a significant reorganization of the different energy reservoirs. Some possible solutions for improvement are examined. It is thus found that the term (2) can be substantially reduced by at least one order of magnitude by using conservative temperature instead of potential temperature. Using the anelastic approximation, however, which was initially thought as a possible way to greatly improve the accuracy of the energy budget, would only marginally reduce the term (4) with no impact on the terms (1), (2) and (3).

Bayesian model averaging and identification of structural breaks in time series

Bayesian Model Averaging (BMA) is used for testing for multiple break points in univariate series using conjugate normal-gamma priors. This approach can test for the number of structural breaks and produce posterior probabilities for a break at each point in time. Results are averaged over specifications including: stationary; stationary around trend and unit root models, each containing different types and number of breaks and different lag lengths. The procedures are used to test for structural breaks on 14 annual macroeconomic series and 11 natural resource price series. The results indicate that there are structural breaks in all of the natural resource series and most of the macroeconomic series. Many of the series had multiple breaks. Our findings regarding the existence of unit roots, having allowed for structural breaks in the data, are largely consistent with previous work.

Multiple-trait random regression models for the estimation of genetic parameters for milk, fat, and protein yield in buffaloes

In this study, genetic parameters for test-day milk, fat, and protein yield were estimated for the first lactation. The data analyzed consisted of 1,433 first lactations of Murrah buffaloes, daughters of 113 sires from 12 herds in the state of São Paulo, Brazil, with calvings from 1985 to 2007. Ten-month classes of lactation days were considered for the test-day yields. The (co)variance components for the 3 traits were estimated using the regression analyses by Bayesian inference applying an animal model by Gibbs sampling. The contemporary groups were defined as herd-year-month of the test day. In the model, the random effects were additive genetic, permanent environment, and residual. The fixed effects were contemporary group and number of milkings (1 or 2), the linear and quadratic effects of the covariable age of the buffalo at calving, as well as the mean lactation curve of the population, which was modeled by orthogonal Legendre polynomials of fourth order. The random effects for the traits studied were modeled by Legendre polynomials of third and fourth order for additive genetic and permanent environment, respectively, the residual variances were modeled considering 4 residual classes. The heritability estimates for the traits were moderate (from 0.21-0.38), with higher estimates in the intermediate lactation phase. The genetic correlation estimates within and among the traits varied from 0.05 to 0.99. The results indicate that the selection for any trait test day will result in an indirect genetic gain for milk, fat, and protein yield in all periods of the lactation curve. The accuracy associated with estimated breeding values obtained using multi-trait random regression was slightly higher (around 8%) compared with single-trait random regression. This difference may be because to the greater amount of information available per animal. © 2013 American Dairy Science Association.

A time series sequestration and storage model of atmospheric carbon dioxide

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Method for Visualizing Multivariate Time Series Data

Visualization and exploratory analysis is an important part of any data analysis and is made more challenging when the data are voluminous and high-dimensional. One such example is environmental monitoring data, which are often collected over time and at multiple locations, resulting in a geographically indexed multivariate time series. Financial data, although not necessarily containing a geographic component, present another source of high-volume multivariate time series data. We present the mvtsplot function which provides a method for visualizing multivariate time series data. We outline the basic design concepts and provide some examples of its usage by applying it to a database of ambient air pollution measurements in the United States and to a hypothetical portfolio of stocks.

On Time Series Analysis of Public Health and Biomedical Data

A time series is a sequence of observations made over time. Examples in public health include daily ozone concentrations, weekly admissions to an emergency department or annual expenditures on health care in the United States. Time series models are used to describe the dependence of the response at each time on predictor variables including covariates and possibly previous values in the series. Time series methods are necessary to account for the correlation among repeated responses over time. This paper gives an overview of time series ideas and methods used in public health research.

Time-Series Panel Analysis (TSPA): Multivariate Modeling of Temporal Associations in Psychotherapy Process.

Objective: Processes occurring in the course of psychotherapy are characterized by the simple fact that they unfold in time and that the multiple factors engaged in change processes vary highly between individuals (idiographic phenomena). Previous research, however, has neglected the temporal perspective by its traditional focus on static phenomena, which were mainly assessed at the group level (nomothetic phenomena). To support a temporal approach, the authors introduce time-series panel analysis (TSPA), a statistical methodology explicitly focusing on the quantification of temporal, session-to-session aspects of change in psychotherapy. TSPA-models are initially built at the level of individuals and are subsequently aggregated at the group level, thus allowing the exploration of prototypical models. Method: TSPA is based on vector auto-regression (VAR), an extension of univariate auto-regression models to multivariate time-series data. The application of TSPA is demonstrated in a sample of 87 outpatient psychotherapy patients who were monitored by postsession questionnaires. Prototypical mechanisms of change were derived from the aggregation of individual multivariate models of psychotherapy process. In a 2nd step, the associations between mechanisms of change (TSPA) and pre- to postsymptom change were explored. Results: TSPA allowed a prototypical process pattern to be identified, where patient's alliance and self-efficacy were linked by a temporal feedback-loop. Furthermore, therapist's stability over time in both mastery and clarification interventions was positively associated with better outcomes. Conclusions: TSPA is a statistical tool that sheds new light on temporal mechanisms of change. Through this approach, clinicians may gain insight into prototypical patterns of change in psychotherapy.

Thrombosis during pregnancy: Risks, prevention, and treatment for mother and fetus--harvesting the power of omic technology, biomarkers and in vitro or in vivo models to facilitate the treatment of thrombosis

Maternal thromboembolism and a spectrum of placenta-mediated complications including the pre-eclampsia syndromes, fetal growth restriction, fetal loss, and abruption manifest a shared etiopathogenesis and predisposing risk factors. Furthermore, these maternal and fetal complications are often linked to subsequent maternal health consequences that comprise the metabolic syndrome, namely, thromboembolism, chronic hypertension, and type II diabetes. Traditionally, several lines of evidence have linked vasoconstriction, excessive thrombosis and inflammation, and impaired trophoblast invasion at the uteroplacental interface as hallmark features of the placental complications. "Omic" technologies and biomarker development have been largely based upon advances in vascular biology, improved understanding of the molecular basis and biochemical pathways responsible for the clinically relevant diseases, and increasingly robust large cohort and/or registry based studies. Advances in understanding of innate and adaptive immunity appear to play an important role in several pregnancy complications. Strategies aimed at improving prediction of these pregnancy complications are often incorporating hemodynamic blood flow data using non-invasive imaging technologies of the utero-placental and maternal circulations early in pregnancy. Some evidence suggests that a multiple marker approach will yield the best performing prediction tools, which may then in turn offer the possibility of early intervention to prevent or ameliorate these pregnancy complications. Prediction of maternal cardiovascular and non-cardiovascular consequences following pregnancy represents an important area of future research, which may have significant public health consequences not only for cardiovascular disease, but also for a variety of other disorders, such as autoimmune and neurodegenerative diseases.

Absorption coefficients of particulate matter and chlorophyll a concentrations at time series station OLIPAC

Spectral absorption coefficients of total particulate matter ap (lambda) were determined using the in vitro filter technique. The present analysis deals with a set of 1166 spectra, determined in various oceanic (case 1) waters, with field chl a concentrations ([chl]) spanning 3 orders of magnitude (0.02-25 mg/m**3). As previously shown [Bricaud et al., 1995, doi:10.1029/95JC00463] for the absorption coefficients of living phytoplankton a phi (lamda), the ap (labda) coefficients also increase nonlinearly with [chl]. The relationships (power laws) that link ap (lambda) and a phi (lambda) to [chl] show striking similarities. Despite large fluctuations, the relative contribution of nonalgal particles to total absorption oscillates around an average value of 25-30% throughout the [chl] range. The spectral dependence of absorption by these nonalgal particles follows an exponential increase toward short wavelengths, with a weakly variable slope (0.011 ± 0.0025/nm). The empirical relationships linking ap (lambda) to ([chl]) can be used in bio-optical models. This parameterization based on in vitro measurements leads to a good agreement with a former modeling of the diffuse attenuation coefficient based on in situ measurements. This agreement is worth noting as independent methods and data sets are compared. It is stressed that for a given ([chl]), the ap (lambda) coefficients show large residual variability around the regression lines (for instance, by a factor of 3 at 440 nm). The consequences of such a variability, when predicting or interpreting the diffuse reflectance of the ocean, are examined, according to whether or not these variations in ap are associated with concomitant variations in particle scattering. In most situations the deviations in ap actually are not compensated by those in particle scattering, so that the amplitude of reflectance is affected by these variations.

Environmental variables modeling based on remote sensing data using time series analysis: forestry and agricultural applications

En la actualidad, el seguimiento de la dinámica de los procesos medio ambientales está considerado como un punto de gran interés en el campo medioambiental. La cobertura espacio temporal de los datos de teledetección proporciona información continua con una alta frecuencia temporal, permitiendo el análisis de la evolución de los ecosistemas desde diferentes escalas espacio-temporales. Aunque el valor de la teledetección ha sido ampliamente probado, en la actualidad solo existe un número reducido de metodologías que permiten su análisis de una forma cuantitativa. En la presente tesis se propone un esquema de trabajo para explotar las series temporales de datos de teledetección, basado en la combinación del análisis estadístico de series de tiempo y la fenometría. El objetivo principal es demostrar el uso de las series temporales de datos de teledetección para analizar la dinámica de variables medio ambientales de una forma cuantitativa. Los objetivos específicos son: (1) evaluar dichas variables medio ambientales y (2) desarrollar modelos empíricos para predecir su comportamiento futuro. Estos objetivos se materializan en cuatro aplicaciones cuyos objetivos específicos son: (1) evaluar y cartografiar estados fenológicos del cultivo del algodón mediante análisis espectral y fenometría, (2) evaluar y modelizar la estacionalidad de incendios forestales en dos regiones bioclimáticas mediante modelos dinámicos, (3) predecir el riesgo de incendios forestales a nivel pixel utilizando modelos dinámicos y (4) evaluar el funcionamiento de la vegetación en base a la autocorrelación temporal y la fenometría. Los resultados de esta tesis muestran la utilidad del ajuste de funciones para modelizar los índices espectrales AS1 y AS2. Los parámetros fenológicos derivados del ajuste de funciones permiten la identificación de distintos estados fenológicos del cultivo del algodón. El análisis espectral ha demostrado, de una forma cuantitativa, la presencia de un ciclo en el índice AS2 y de dos ciclos en el AS1 así como el comportamiento unimodal y bimodal de la estacionalidad de incendios en las regiones mediterránea y templada respectivamente. Modelos autorregresivos han sido utilizados para caracterizar la dinámica de la estacionalidad de incendios y para predecir de una forma muy precisa el riesgo de incendios forestales a nivel pixel. Ha sido demostrada la utilidad de la autocorrelación temporal para definir y caracterizar el funcionamiento de la vegetación a nivel pixel. Finalmente el concepto “Optical Functional Type” ha sido definido, donde se propone que los pixeles deberían ser considerados como unidades temporales y analizados en función de su dinámica temporal. ix SUMMARY A good understanding of land surface processes is considered as a key subject in environmental sciences. The spatial-temporal coverage of remote sensing data provides continuous observations with a high temporal frequency allowing the assessment of ecosystem evolution at different temporal and spatial scales. Although the value of remote sensing time series has been firmly proved, only few time series methods have been developed for analyzing this data in a quantitative and continuous manner. In the present dissertation a working framework to exploit Remote Sensing time series is proposed based on the combination of Time Series Analysis and phenometric approach. The main goal is to demonstrate the use of remote sensing time series to analyze quantitatively environmental variable dynamics. The specific objectives are (1) to assess environmental variables based on remote sensing time series and (2) to develop empirical models to forecast environmental variables. These objectives have been achieved in four applications which specific objectives are (1) assessing and mapping cotton crop phenological stages using spectral and phenometric analyses, (2) assessing and modeling fire seasonality in two different ecoregions by dynamic models, (3) forecasting forest fire risk on a pixel basis by dynamic models, and (4) assessing vegetation functioning based on temporal autocorrelation and phenometric analysis. The results of this dissertation show the usefulness of function fitting procedures to model AS1 and AS2. Phenometrics derived from function fitting procedure makes it possible to identify cotton crop phenological stages. Spectral analysis has demonstrated quantitatively the presence of one cycle in AS2 and two in AS1 and the unimodal and bimodal behaviour of fire seasonality in the Mediterranean and temperate ecoregions respectively. Autoregressive models has been used to characterize the dynamics of fire seasonality in two ecoregions and to forecasts accurately fire risk on a pixel basis. The usefulness of temporal autocorrelation to define and characterized land surface functioning has been demonstrated. And finally the “Optical Functional Types” concept has been proposed, in this approach pixels could be as temporal unities based on its temporal dynamics or functioning.