晁说之年谱简编

晁说之(1059～1129)是北宋一位不容忽视的经学家。他博通五经,尤精于《易》学,同时又是一位富有创作实绩的作家、画家,与苏轼、黄庭坚等苏门文人、江西诗派作家有着广泛的师友关系。由于元符上书入党籍,其仕途极其坎坷,长期沉沦下僚。他的一生经历了仁宗、神宗、哲宗、徽宗、钦宗、高宗六朝,是难得的一位身入南宋的"元名士"。     

An Investigation of two Sequence-Comparison Statistics

This paper describes an investigation of two statistics which compare two ordered sequences of objects by providing a measure of the discordance when the sequences are slotted together. Configurations having zero discordance are described. Plausible null models for data are postulated, and an account is given of a simulation study which investigated the distribution of the statistics when these models were used in the analysis of physical logging data from two wells.     

A STOCHASTIC LOGISTIC MODEL WITH TIME DELAY

The stochastic version of the logistic model for population growth is generalized to take account of continuously distributed time delay with an exponentially decaying kernel. The theory of diffusion processes is used to analyse the probability density function of the population size. The explicit expression for the stationary distribution is worked out and the effect of time delay on various statistics is discussed.     

Convergence of Discount Time Series Dynamic Linear Models

This article studies the limiting behavior of multiple discount time series dynamic linear models (TSDLMs). It is shown that, under mild conditions, all discount TSDLMs converge to the constant (time-invariant) TSDLM. In particular, the limiting posterior precision matrix of the superposition of multiple discount TSDLMs is explored. For non seasonal models, the elements of the limiting posterior precision of the states are given in a recurrence relationship, while for seasonal models the solution of a linear system provides the elements of the respective limiting precision matrix. The proposed methodology uses canonical Jordan forms and it is illustrated with a detailed example of simulated data featuring both trend and seasonal time series.     

Smoothing Time Series with Local Polynomial Regression on Time

Time series smoothers estimate the level of a time series at time t as its conditional expectation given present, past and future observations, with the smoothed value depending on the estimated time series model. Alternatively, local polynomial regressions on time can be used to estimate the level, with the implied smoothed value depending on the weight function and the bandwidth in the local linear least squares fit. In this article we compare the two smoothing approaches and describe their similarities. Through simulations, we assess the increase in the mean square error that results when approximating the estimated optimal time series smoother with the local regression estimate of the level.     

Nonparametric Trend Estimation for Periodic Autoregressive Time Series

A periodically stationary time series has seasonal variances. A local linear trend estimation is proposed to accommodate unequal variances. A comparison of this proposed estimator with the estimator commonly used for a stationary time series is provided. The optimal bandwidth selection for this new trend estimator is discussed.     

Unit Roots: Bayesian Significance Test

The unit root problem plays a central role in empirical applications in the time series econometric literature. However, significance tests developed under the frequentist tradition present various conceptual problems that jeopardize the power of these tests, especially for small samples. Bayesian alternatives, although having interesting interpretations and being precisely defined, experience problems due to the fact that that the hypothesis of interest in this case is sharp or precise. The Bayesian significance test used in this article, for the unit root hypothesis, is based solely on the posterior density function, without the need of imposing positive probabilities to sets of zero Lebesgue measure. Furthermore, it is conducted under strict observance of the likelihood principle. It was designed mainly for testing sharp null hypotheses and it is called FBST for Full Bayesian Significance Test.     

The Scale Invariant Wigner Spectrum Estimation of Gaussian Locally Self-Similar Processes

We study locally self-similar processes (LSSPs) in Silverman’s sense. By deriving the minimum mean-square optimal kernel within Cohen’s class counterpart of time–frequency representations, we obtain an optimal estimation for the scale invariant Wigner spectrum (SIWS) of Gaussian LSSPs. The class of estimators is completely characterized in terms of kernels, so the optimal kernel minimizes the mean-square error of the estimation. We obtain the SIWS estimation for two cases: global and local, where in the local case, the kernel is allowed to vary with time and frequency. We also introduce two generalizations of LSSPs: the locally self-similar chirp process and the multicomponent LSSP, and obtain their optimal kernels. Finally, the performance and accuracy of the estimation is studied via simulation.     

Multi-factor prediction of water flooding efficiency based on a time-varying system

ABSTRACT

The neural network prediction method gets good historical matching between prediction indices and influence factor indices, while the differential simulation prediction method can reflect the changing trend of prediction indices; considering these new traits, a new multi-factor prediction method is proposed to organically combine these two prediction methods. At first, the input–output relation between water flooding efficiency in ultra-high water cut stage and their influence factors is viewed as a time varying system, then the BP neural network is introduced in parameter identification of differential simulation to obtain a new multi-factor prediction method of functional simulation based on the time varying system. This new prediction model has got good self-adaptability since its parameters change by time. Moreover, it has better results in the mid-long-term water flooding efficiency prediction because the non convergence problem appeared in the coupling process can be overcome in the training process of the neural network by variable learning rates. In the end, practical output prediction cases in two different oilfield blocks in China are given. The computational results show that the prediction results obtained using the new multi-factor prediction method are in good agreement with the reality, even much better than the results obtained by other prediction methods.     

Bhattacharyya distance based linear discriminant function for stationary time series

The problem of classifying a covariance stationary normal time series is considered. Under certain regularity conditions, a compact form of the linear discriminant function in the sense of maximizing the Bhattacharyya distance is obtained.