Strategies for sequential prediction of stationary time series

We present simple procedures for the prediction of a real valued sequence. The algorithms are based on a combinationof several simple predictors. We show that if the sequence is a realization of a bounded stationary and ergodic random process then the average of squared errors converges, almost surely, to that of the optimum, given by the Bayes predictor. We offer an analog result for the prediction of stationary gaussian processes.

Fusion of data sets in multivariate linear regression with errors-in-variables

We consider the application of normal theory methods to the estimation and testing of a general type of multivariate regressionmodels with errors--in--variables, in the case where various data setsare merged into a single analysis and the observable variables deviatepossibly from normality. The various samples to be merged can differ on the set of observable variables available. We show that there is a convenient way to parameterize the model so that, despite the possiblenon--normality of the data, normal--theory methods yield correct inferencesfor the parameters of interest and for the goodness--of--fit test. Thetheory described encompasses both the functional and structural modelcases, and can be implemented using standard software for structuralequations models, such as LISREL, EQS, LISCOMP, among others. An illustration with Monte Carlo data is presented.

On a series of Goldbach and Euler

Theorem 1 of Euler s paper of 1737 'Variae Observationes Circa Series Infinitas', states the astonishing result that the series of all unit fractions whose denominators are perfect powers of integers minus unity has sum one. Euler attributes the Theorem to Goldbach. The proof is one of those examples of misuse of divergent series to obtain correct results so frequent during the seventeenth and eighteenth centuries. We examine this proof closelyand, with the help of some insight provided by a modern (and completely dierent) proof of the Goldbach-Euler Theorem, we present a rational reconstruction in terms which could be considered rigorous by modern Weierstrassian standards. At the same time, with a few ideas borrowed from nonstandard analysis we see how the same reconstruction can be also be considered rigorous by modern Robinsonian standards. This last approach, though, is completely in tune with Goldbach and Euler s proof. We hope to convince the reader then how, a few simple ideas from nonstandard analysis, vindicate Euler's work.

Improved nonparametric confidence intervals in time series regressions

Condence intervals in econometric time series regressions suffer fromnotorious coverage problems. This is especially true when the dependencein the data is noticeable and sample sizes are small to moderate, as isoften the case in empirical studies. This paper suggests using thestudentized block bootstrap and discusses practical issues, such as thechoice of the block size. A particular data-dependent method is proposedto automate the method. As a side note, it is pointed out that symmetricconfidence intervals are preferred over equal-tailed ones, since theyexhibit improved coverage accuracy. The improvements in small sampleperformance are supported by a simulation study.

Subsampling the mean of heavy-tailed dependent observations

We establish the validity of subsampling confidence intervals for themean of a dependent series with heavy-tailed marginal distributions.Using point process theory, we study both linear and nonlinear GARCH-liketime series models. We propose a data-dependent method for the optimalblock size selection and investigate its performance by means of asimulation study.

Equivalence of piecewise-linear approximation and Lagrangian relaxation for network revenue management

The network revenue management (RM) problem arises in airline, hotel, media,and other industries where the sale products use multiple resources. It can be formulatedas a stochastic dynamic program but the dynamic program is computationallyintractable because of an exponentially large state space, and a number of heuristicshave been proposed to approximate it. Notable amongst these -both for their revenueperformance, as well as their theoretically sound basis- are approximate dynamic programmingmethods that approximate the value function by basis functions (both affinefunctions as well as piecewise-linear functions have been proposed for network RM)and decomposition methods that relax the constraints of the dynamic program to solvesimpler dynamic programs (such as the Lagrangian relaxation methods). In this paperwe show that these two seemingly distinct approaches coincide for the network RMdynamic program, i.e., the piecewise-linear approximation method and the Lagrangianrelaxation method are one and the same.

Human large granular lymphocytes contain an esterase activity usually considered as specific for the myeloid series.

A cytochemical marker such as alpha-naphthyl acetate esterase (ANAE) has been found useful for the morphological identification of the subset of T lymphocytes having receptors for Fcμ (TM cells). ANAE reaction on TM cells gives a typical pattern of one to four positive spots, whereas this pattern is not found on T cells with receptors for Fcγ (TG cells). ANAE is abundant in monocytes but not detectable in granulocytes. Herein another type of esterase activity, naphthol-AS-D chloroacetate esterase (NCAE), is described; it is known to be abundant in granulocytes and was found to give a specific pattern of reactivity with the subpopulation of large granular lymphocytes (LGL). This pattern of fine granular staining was observed not only on LGL present in the TG cell subpopulation but also in LGL present in the non-T, non-B cells. Fractions of peripheral blood mononuclear cells which were ènriched up to 80% in LGL by Percoll discontinuous density gradient gave a similar percentage of specific NCAE pattern. In addition, among the different fractions from Percoll gradient, there was a good correlation (r = 0.94) between the number of NCAE-positive cells and the natural killer activity against the natural killer susceptible K562 target cells. It will be important to determine whether or not this enzymatic activity plays a role in the cytotoxic activities of LGL.

A new compact linear programming formulation for choice network revenue management

The choice network revenue management model incorporates customer purchase behavioras a function of the offered products, and is the appropriate model for airline and hotel networkrevenue management, dynamic sales of bundles, and dynamic assortment optimization.The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalencerelaxation of the dynamic program, called the choice deterministic linear program(CDLP) is usually used to generate dyamic controls. Recently, a compact linear programmingformulation of this linear program was given for the multi-segment multinomial-logit (MNL)model of customer choice with non-overlapping consideration sets. Our objective is to obtaina tighter bound than this formulation while retaining the appealing properties of a compactlinear programming representation. To this end, it is natural to consider the affine relaxationof the dynamic program. We first show that the affine relaxation is NP-complete even for asingle-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a newcompact linear program that approximates the dynamic programming value function betterthan CDLP, provably between the CDLP value and the affine relaxation, and often comingclose to the latter in our numerical experiments. When the segment consideration sets overlap,we show that some strong equalities called product cuts developed for the CDLP remain validfor our new formulation. Finally we perform extensive numerical comparisons on the variousbounds to evaluate their performance.

Asymptotic robustness in multi-sample analysis of multivariate linear relations

Standard methods for the analysis of linear latent variable models oftenrely on the assumption that the vector of observed variables is normallydistributed. This normality assumption (NA) plays a crucial role inassessingoptimality of estimates, in computing standard errors, and in designinganasymptotic chi-square goodness-of-fit test. The asymptotic validity of NAinferences when the data deviates from normality has been calledasymptoticrobustness. In the present paper we extend previous work on asymptoticrobustnessto a general context of multi-sample analysis of linear latent variablemodels,with a latent component of the model allowed to be fixed across(hypothetical)sample replications, and with the asymptotic covariance matrix of thesamplemoments not necessarily finite. We will show that, under certainconditions,the matrix $\Gamma$ of asymptotic variances of the analyzed samplemomentscan be substituted by a matrix $\Omega$ that is a function only of thecross-product moments of the observed variables. The main advantage of thisis thatinferences based on $\Omega$ are readily available in standard softwareforcovariance structure analysis, and do not require to compute samplefourth-order moments. An illustration with simulated data in the context ofregressionwith errors in variables will be presented.

Finite sample nonparametric tests for linear regressions

We introduce several exact nonparametric tests for finite sample multivariatelinear regressions, and compare their powers. This fills an important gap inthe literature where the only known nonparametric tests are either asymptotic,or assume one covariate only.

Solving non-linear stochastic models by parameterizing expectations: An application to asset pricing with production

A new algorithm called the parameterized expectations approach(PEA) for solving dynamic stochastic models under rational expectationsis developed and its advantages and disadvantages are discussed. Thisalgorithm can, in principle, approximate the true equilibrium arbitrarilywell. Also, this algorithm works from the Euler equations, so that theequilibrium does not have to be cast in the form of a planner's problem.Monte--Carlo integration and the absence of grids on the state variables,cause the computation costs not to go up exponentially when the numberof state variables or the exogenous shocks in the economy increase. \\As an application we analyze an asset pricing model with endogenousproduction. We analyze its implications for time dependence of volatilityof stock returns and the term structure of interest rates. We argue thatthis model can generate hump--shaped term structures.

Fate of linear and supercoiled multinucleosomic templates during transcription.

Electron microscopy was used to monitor the fate of reconstituted nucleosome cores during in vitro transcription of long linear and supercoiled multinucleosomic templates by the prokaryotic T7 RNA polymerase and the eukaryotic RNA polymerase II. Transcription by T7 RNA polymerase disrupted the nucleosomal configuration in the transcribed region, while nucleosomes were preserved upstream of the transcription initiation site and in front of the polymerase. Nucleosome disruption was independent of the topology of the template, linear or supercoiled, and of the presence or absence of nucleosome positioning sequences in the transcribed region. In contrast, the nucleosomal configuration was preserved during transcription from the vitellogenin B1 promoter with RNA polymerase II in a rat liver total nuclear extract. However, the persistence of nucleosomes on the template was not RNA polymerase II-specific, but was dependent on another activity present in the nuclear extract. This was demonstrated by addition of the extract to the T7 RNA polymerase transcription reaction, which resulted in retention of the nucleosomal configuration. This nuclear activity, also found in HeLa cell nuclei, is heat sensitive and could not be substituted by nucleoplasmin, chromatin assembly factor (CAF-I) or a combination thereof. Altogether, these results identify a novel nuclear activity, called herein transcription-dependent chromatin stabilizing activity I or TCSA-I, which may be involved in a nucleosome transfer mechanism during transcription.

Geometric and long run aspects of Granger causality

This paper extends multivariate Granger causality to take into account the subspacesalong which Granger causality occurs as well as long run Granger causality. The propertiesof these new notions of Granger causality, along with the requisite restrictions, are derivedand extensively studied for a wide variety of time series processes including linear invertibleprocess and VARMA. Using the proposed extensions, the paper demonstrates that: (i) meanreversion in L2 is an instance of long run Granger non-causality, (ii) cointegration is a specialcase of long run Granger non-causality along a subspace, (iii) controllability is a special caseof Granger causality, and finally (iv) linear rational expectations entail (possibly testable)Granger causality restriction along subspaces.