An exhaustive analysis of prime modulus multiplicative congruential random number generators with modulus smaller than 215

This paper presents the results of an exhaustive analysis of all of the prime modulus multiplicative congruential random number (RN) generators with moduli smaller than 2¹⁵. In an amount of around 20 million multipliers which are able to produce a full period of RNs, 239 multipliers have a good lattice structure. Among which 52 multipliers further pass a comprehensive battery of empirical tests. These 52 multipliers thus possess good local and global statistical properties. It is worthwhile to note that some empirically tested multipliers recommended in some previous studies are not on this list. The conclusion is that both theoretical and empirical tests are mandatory to sieve out good multipliers. To generate RNs of very long period, many existing techniques can be applied without further effort.     

Estimation in long memory time series models

A regression type estimator of the parameter d in fractionally differenced ARMA (p,q) processes is presented. The proposed estimator is shown to be mean square consistent. Its performance is compared with some of the existing estimators via a simulation study.     

Distribution of the coates-diggle test statistic in case of replicated observations

A closed form expression for the distribution of a test statistic for comparing the spectral densities of stationary processes is given. This test statistic was introduced by COATES and DIGGLE ( 1986 ) for the unreplicated case and has been extended to the case of replicated observations by POTSCHER and RESCHENHOFER ( 1988 ). A simple method for computing approximate critical values in case of large numbers of replications is also provided. As a by-product an explicit expression for the distribution function of the range of independent variates each distributed as the logarithm of an F-variate i.e up to a factor of 2 each followin Fishers z-distriution is obtained     

Testing Semiparametric Hypotheses in Locally Stationary Processes

In this paper, we investigate the problem of testing semiparametric hypotheses in locally stationary processes. The proposed method is based on an empirical version of the L₂‐distance between the true time varying spectral density and its best approximation under the null hypothesis. As this approach only requires estimation of integrals of the time varying spectral density and its square, we do not have to choose a smoothing bandwidth for the local estimation of the spectral density – in contrast to most other procedures discussed in the literature. Asymptotic normality of the test statistic is derived both under the null hypothesis and the alternative. We also propose a bootstrap procedure to obtain critical values in the case of small sample sizes. Additionally, we investigate the finite sample properties of the new method and compare it with the currently available procedures by means of a simulation study. Finally, we illustrate the performance of the new test in two data examples, one regarding log returns of the S&P 500 and the other a well‐known series of weekly egg prices.     

Use of satellite data in agricultural surveys

A major application of satellite remote sensing is the estimation of the acreage of agricultural crops. The potential for crop yield estimation using satellite remote sensing exists, but research in this area is still in its early stages. In this paper we survey the methodology for using remotely sensed data in agricultural surveys, based primarily on research conducted during the Large Area Crop Inventory Experiment (LACIE) and the follow-on program Agricultural Research and Inventory Surveys Through Aerospace Remote Sensing (AgRISTARS). The data obtained from multispectral scanner (MSS) and thematic mapper (TM) sensors onboard the Landsat series of satellites are described. Approaches for preprocessing, transferring, and modeling these data for understanding the relationship between their temporal behavior and crop growth cycles are discussed. Finally, techniques for crop identification and area and yield estimation are briefly described     

A note on maximum entropy spectrum estimation

This article studies the maximum entropy spectrum estimation. After a bnei discussion on iiow co select ciic appropriate constraints and tiie objec¬tive functions, we decide to choose the constraints containing only the first four sample moments and, consequently, to employ the second order spectral entropy as the objective function. The resulting (maximum entropy) spectral estimate is the power spectral density of an ARMA sequence. Examples for comparing our proposal with the traditional maximum entropy spectral estimate follow at the end.     

Band Spectral Regression with Trending Data

Band spectral regression with both deterministic and stochastic trends is considered. It is shown that trend removal by regression in the time domain prior to band spectral regression can lead to biased and inconsistent estimates in models with frequency dependent coefficients. Both semiparametric and nonparametric regression formulations are considered, the latter including general systems of two‐sided distributed lags such as those arising in lead and lag regressions. The bias problem arises through omitted variables and is avoided by careful specification of the regression equation. Trend removal in the frequency domain is shown to be a convenient option in practice. An asymptotic theory is developed and the two cases of stationary data and cointegrated nonstationary data are compared. In the latter case, a levels and differences regression formulation is shown to be useful in estimating the frequency response function at nonzero as well as zero frequencies.     

基于天然气客户的消费波动特征与顾客分类研究

如何有效满足连续型消费且消费量呈周期性波动的客户需要,是生产供应商急需解决的现实问题。本研究对连续型客户日消费量的时间序列数据,首次利用谱分析方法进行消费量的波动特征分析,再根据客户不同波动指标经过分层聚类分析以及判别分析,构建了判别函数方程。基于WE销售公司在江苏省的用气客户的日消费量数据进行了分析验证,研究发现,客户消费的波动特征可以通过谱分析得出的13项指标进行刻画反映,并根据这些波动指标对广大客户进行分类,以便供应商针对不同波动类别的客户采取不同的调峰手段,为供应商优化调峰方案提供分析基础,特别是根据新用户未来用气波动需求进行判别归类,有利于生产供应商提前主动地采取有效措施解决新用户的消费波动问题。     

Dynamic Identification of Dynamic Stochastic General Equilibrium Models

This paper studies dynamic identification of parameters of a dynamic stochastic general equilibrium model from the first and second moments of the data. Classical results for dynamic simultaneous equations do not apply because the state space solution of the model does not constitute a standard reduced form. Full rank of the Jacobian matrix of derivatives of the solution parameters with respect to the parameters of interest is necessary but not sufficient for identification. We use restrictions implied by observational equivalence to obtain two sets of rank and order conditions: one for stochastically singular models and another for nonsingular models. Measurement errors, mean, long‐run, and a priori restrictions can be accommodated. An example is considered to illustrate the results.     

一类M-矩阵阿达玛积最小特征根的下界

讨论一个 M- 矩阵与另一个 M- 矩阵的逆的阿达玛积的最小特征根,证明了对任一矩阵B,如果 B- 1 的主对角线元素的值相等,则q( A‘B- 1) > 1n ·q( A)q( B) .