Delay estimation for multivariate time series

Most traditional methods for extracting the relationships between two time series are based on cross-correlation. In a non-linear non-stationary environment, these techniques are not sufficient. We show in this paper how to use hidden Markov models (HMMs) to identify the lag (or delay) between different variables for such data. We first present a method using maximum likelihood estimation and propose a simple algorithm which is capable of identifying associations between variables. We also adopt an information-theoretic approach and develop a novel procedure for training HMMs to maximise the mutual information between delayed time series. Both methods are successfully applied to real data. We model the oil drilling process with HMMs and estimate a crucial parameter, namely the lag for return.

Time delay estimation with hidden Markov models

Most traditional methods for extracting the relationships between two time series are based on cross-correlation. In a non-linear non-stationary environment, these techniques are not sufficient. We show in this paper how to use hidden Markov models to identify the lag (or delay) between different variables for such data. Adopting an information-theoretic approach, we develop a procedure for training HMMs to maximise the mutual information (MMI) between delayed time series. The method is used to model the oil drilling process. We show that cross-correlation gives no information and that the MMI approach outperforms maximum likelihood.

Model specification and forecasting foreign exchange rates with vector autoregressions

This study examines the forecasting accuracy of alternative vector autoregressive models each in a seven-variable system that comprises in turn of daily, weekly and monthly foreign exchange (FX) spot rates. The vector autoregressions (VARs) are in non-stationary, stationary and error-correction forms and are estimated using OLS. The imposition of Bayesian priors in the OLS estimations also allowed us to obtain another set of results. We find that there is some tendency for the Bayesian estimation method to generate superior forecast measures relatively to the OLS method. This result holds whether or not the data sets contain outliers. Also, the best forecasts under the non-stationary specification outperformed those of the stationary and error-correction specifications, particularly at long forecast horizons, while the best forecasts under the stationary and error-correction specifications are generally similar. The findings for the OLS forecasts are consistent with recent simulation results. The predictive ability of the VARs is very weak.

Techniques to improve forecasting models: applications to energy demand and price

This thesis is a study of three techniques to improve performance of some standard fore-casting models, application to the energy demand and prices. We focus on forecasting demand and price one-day ahead. First, the wavelet transform was used as a pre-processing procedure with two approaches: multicomponent-forecasts and direct-forecasts. We have empirically compared these approaches and found that the former consistently outperformed the latter. Second, adaptive models were introduced to continuously update model parameters in the testing period by combining ?lters with standard forecasting methods. Among these adaptive models, the adaptive LR-GARCH model was proposed for the fi?rst time in the thesis. Third, with regard to noise distributions of the dependent variables in the forecasting models, we used either Gaussian or Student-t distributions. This thesis proposed a novel algorithm to infer parameters of Student-t noise models. The method is an extension of earlier work for models that are linear in parameters to the non-linear multilayer perceptron. Therefore, the proposed method broadens the range of models that can use a Student-t noise distribution. Because these techniques cannot stand alone, they must be combined with prediction models to improve their performance. We combined these techniques with some standard forecasting models: multilayer perceptron, radial basis functions, linear regression, and linear regression with GARCH. These techniques and forecasting models were applied to two datasets from the UK energy markets: daily electricity demand (which is stationary) and gas forward prices (non-stationary). The results showed that these techniques provided good improvement to prediction performance.

Non-invasive phakometric measurement of corneal and crystalline lens alignment in human eyes

We describe a non-invasive phakometric method for determining corneal axis rotation relative to the visual axis (β) together with crystalline lens axis tilt (α) and decentration (d) relative to the corneal axis. This does not require corneal contact A-scan ultrasonography for the measurement of intraocular surface separations. Theoretical inherent errors of the method, evaluated by ray tracing through schematic eyes incorporating the full range of human ocular component variations, were found to be larger than the measurement errors (β < 0.67°, α < 0.72° and d < 0.08 mm) observed in nine human eyes with known ocular component dimensions. Intersubject variations (mean ± S.D.: β = 6.2 ± 3.4° temporal, α = 0.2 ± 1.8° temporal and d = 0.1 ± 0.1 mm temporal) and repeatability (1.96 × S.D. of difference between repeat readings: β ± 2.0°, α ± 1.8° and d ± 0.2 mm) were studied by measuring the left eyes of 45 subjects (aged 18-42 years, 29 females and 16 males, 15 Caucasians, 29 Indian Asians, one African, refractive error range -7.25 to +1.25 D mean spherical equivalent) on two occasions. © 2005 The College of Optometrists.

The slope of the psychometric function and non-stationarity of thresholds in spatiotemporal contrast vision

The slope of the two-interval, forced-choice psychometric function (e.g. the Weibull parameter, ß) provides valuable information about the relationship between contrast sensitivity and signal strength. However, little is known about how or whether ß varies with stimulus parameters such as spatiotemporal frequency and stimulus size and shape. A second unresolved issue concerns the best way to estimate the slope of the psychometric function. For example, if an observer is non-stationary (e.g. their threshold drifts between experimental sessions), ß will be underestimated if curve fitting is performed after collapsing the data across experimental sessions. We measured psychometric functions for 2 experienced observers for 14 different spatiotemporal configurations of pulsed or flickering grating patches and bars on each of 8 days. We found ß ˜ 3 to be fairly constant across almost all conditions, consistent with a fixed nonlinear contrast transducer and/or a constant level of intrinsic stimulus uncertainty (e.g. a square law transducer and a low level of intrinsic uncertainty). Our analysis showed that estimating a single ß from results averaged over several experimental sessions was slightly more accurate than averaging multiple estimates from several experimental sessions. However, the small levels of non-stationarity (SD ˜ 0.8 dB) meant that the difference between the estimates was, in practice, negligible.

An alternating boundary integral based method for a Cauchy problem for the Laplace equation in a quadrant

We study the Cauchy problem for the Laplace equation in a quadrant (quarter-plane) containing a bounded inclusion. Given the values of the solution and its derivative on the edges of the quadrant the solution is reconstructed on the boundary of the inclusion. This is achieved using an alternating iterative method where at each iteration step mixed boundary value problems are being solved. A numerical method is also proposed and investigated for the direct mixed problems reducing these to integral equations over the inclusion. Numerical examples verify the efficiency of the proposed scheme.

An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions

We consider a Cauchy problem for the Laplace equation in a two-dimensional semi-infinite region with a bounded inclusion, i.e. the region is the intersection between a half-plane and the exterior of a bounded closed curve contained in the half-plane. The Cauchy data are given on the unbounded part of the boundary of the region and the aim is to construct the solution on the boundary of the inclusion. In 1989, Kozlov and Maz'ya [10] proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems in bounded domains. We extend their approach to our setting and in each iteration step mixed boundary value problems for the Laplace equation in the semi-infinite region are solved. Well-posedness of these mixed problems are investigated and convergence of the alternating procedure is examined. For the numerical implementation an efficient boundary integral equation method is proposed, based on the indirect variant of the boundary integral equation approach. The mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing the feasibility of the proposed method.

An iterative procedure for solving a Cauchy problem for second order elliptic equations

An iterative method for reconstruction of solutions to second order elliptic equations by Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the elliptic operator and its adjoint. The convergence proof of this method in a weighted L2 space is included. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

On the Busy Period in One Finite Queue of M/G/1 Type with Inactive Orbit

The paper deals with a single server finite queuing system where the customers, who failed to get service, are temporarily blocked in the orbit of inactive customers. This model and its variants have many applications, especially for optimization of the corresponding models with retrials. We analyze the system in non-stationary regime and, using the discrete transformations method study, the busy period length and the number of successful calls made during it. ACM Computing Classification System (1998): G.3, J.7.

Limit Theorems for Non-Critical Branching Processes with Continuous State Space

2000 Mathematics Subject Classification: Primary 60J80, Secondary 60G99.

Method for computing the optimal signal distribution and channel capacity

An iterative method for computing the channel capacity of both discrete and continuous input, continuous output channels is proposed. The efficiency of new method is demonstrated in comparison with the classical Blahut - Arimoto algorithm for several known channels. Moreover, we also present a hybrid method combining advantages of both the Blahut - Arimoto algorithm and our iterative approach. The new method is especially efficient for the channels with a priory unknown discrete input alphabet.

Essays on Job Search and Labor Market Dynamics

This dissertation consists of three separate essays on job search and labor market dynamics. In the first essay, “The Impact of Labor Market Conditions on Job Creation: Evidence from Firm Level Data”, I study how much changes in labor market conditions reduce employment fluctuations over the business cycle. Changes in labor market conditions make hiring more expensive during expansions and cheaper during recessions, creating counter-cyclical incentives for job creation. I estimate firm level elasticities of labor demand with respect to changes in labor market conditions, considering two margins: changes in labor market tightness and changes in wages. Using employer-employee matched data from Brazil, I find that all firms are more sensitive to changes in wages rather than labor market tightness, and there is substantial heterogeneity in labor demand elasticity across regions. Based on these results, I demonstrate that changes in labor market conditions reduce the variance of employment growth over the business cycle by 20% in a median region, and this effect is equally driven by changes along each margin. Moreover, I show that the magnitude of the effect of labor market conditions on employment growth can be significantly affected by economic policy. In particular, I document that the rapid growth of the national minimum wages in Brazil in 1997-2010 amplified the impact of the change in labor market conditions during local expansions and diminished this impact during local recessions.

In the second essay, “A Framework for Estimating Persistence of Local Labor

Demand Shocks”, I propose a decomposition which allows me to study the persistence of local labor demand shocks. Persistence of labor demand shocks varies across industries, and the incidence of shocks in a region depends on the regional industrial composition. As a result, less diverse regions are more likely to experience deeper shocks, but not necessarily more long lasting shocks. Building on this idea, I propose a decomposition of local labor demand shocks into idiosyncratic location shocks and nationwide industry shocks and estimate the variance and the persistence of these shocks using the Quarterly Census of Employment and Wages (QCEW) in 1990-2013.

In the third essay, “Conditional Choice Probability Estimation of Continuous- Time Job Search Models”, co-authored with Peter Arcidiacono and Arnaud Maurel, we propose a novel, computationally feasible method of estimating non-stationary job search models. Non-stationary job search models arise in many applications, where policy change can be anticipated by the workers. The most prominent example of such policy is the expiration of unemployment benefits. However, estimating these models still poses a considerable computational challenge, because of the need to solve a differential equation numerically at each step of the optimization routine. We overcome this challenge by adopting conditional choice probability methods, widely used in dynamic discrete choice literature, to job search models and show how the hazard rate out of unemployment and the distribution of the accepted wages, which can be estimated in many datasets, can be used to infer the value of unemployment. We demonstrate how to apply our method by analyzing the effect of the unemployment benefit expiration on duration of unemployment using the data from the Survey of Income and Program Participation (SIPP) in 1996-2007.

Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems

We present a detailed analysis of the application of a multi-scale Hierarchical Reconstruction method for solving a family of ill-posed linear inverse problems. When the observations on the unknown quantity of interest and the observation operators are known, these inverse problems are concerned with the recovery of the unknown from its observations. Although the observation operators we consider are linear, they are inevitably ill-posed in various ways. We recall in this context the classical Tikhonov regularization method with a stabilizing function which targets the specific ill-posedness from the observation operators and preserves desired features of the unknown. Having studied the mechanism of the Tikhonov regularization, we propose a multi-scale generalization to the Tikhonov regularization method, so-called the Hierarchical Reconstruction (HR) method. First introduction of the HR method can be traced back to the Hierarchical Decomposition method in Image Processing. The HR method successively extracts information from the previous hierarchical residual to the current hierarchical term at a finer hierarchical scale. As the sum of all the hierarchical terms, the hierarchical sum from the HR method provides an reasonable approximate solution to the unknown, when the observation matrix satisfies certain conditions with specific stabilizing functions. When compared to the Tikhonov regularization method on solving the same inverse problems, the HR method is shown to be able to decrease the total number of iterations, reduce the approximation error, and offer self control of the approximation distance between the hierarchical sum and the unknown, thanks to using a ladder of finitely many hierarchical scales. We report numerical experiments supporting our claims on these advantages the HR method has over the Tikhonov regularization method.

Salivary and serum cortisol levels, salivary alpha-amylase and unstimulated whole saliva flow rate in pregnant and non-pregnant

OBJETIVO: Comparar os níveis de cortisol sérico e salivar, alfa-amilase salivar (sAA) e fluxo de saliva não estimulada (UWS) em gestantes e não gestantes. MÉTODOS: Trata-se de um estudo longitudinal realizado no centro de promoção da saúde de um hospital universitário. Nove gestantes e 12 não gestantes participaram do estudo. Foram coletados e analisados soro e UWS nos três trimestres gestacionais e duas vezes por mês durante o ciclo menstrual. A análise do cortisol salivar e sérico foi realizada com o uso de quimiluminescência e a atividade da sAA foi determinada por meio de analisador automático para bioquímica. RESULTADOS: Foi verificado que a mediana (intervalo interquartil) dos níveis de cortisol sérico no grupo de gestantes foi maior que 23,8 µL/dL (19,4-29,4) quando comparado ao grupo de não gestantes, que teve média de 12,3 (9,6-16,8; p<0,001). Os níveis de sAA seguiram o mesmo padrão, com médias de 56,7 U/L (30,9-82,2) e 31,8 (18,1-53,2; p<0,001), respectivamente. Foram observadas diferenças dos níveis de cortisol sérico e salivar (µL/dL) e de sAA entre a fase folicular versus a fase lútea (p<0,001). As medianas dos fluxos salivares (UWS) foram semelhantes em gestantes (0,26 [0,15-0,30] mL/min) e não gestantes (0,23 [0,20-0,32] mL/min). Foram encontradas correlações significativas entre o cortisol salivar e o sérico (p=0,02) e entre o cortisol salivar e a sAA (p=0,01). CONCLUSÕES: Os níveis de cortisol sérico de sAA durante a gestação elevam-se. Na fase lútea do ciclo ovariano, os níveis de cortisol salivar aumentam ao passo que os níveis de cortisol sérico e sAA diminuem. _______________________________________________________________________________________ ABSTRACT