Maximum Likelihood and Restricted Likelihood Solutions in Multiple-Method Studies

A formulation of the problem of combining data from several sources is discussed in terms of random effects models. The unknown measurement precision is assumed not to be the same for all methods. We investigate maximum likelihood solutions in this model. By representing the likelihood equations as simultaneous polynomial equations, the exact form of the Groebner basis for their stationary points is derived when there are two methods. A parametrization of these solutions which allows their comparison is suggested. A numerical method for solving likelihood equations is outlined, and an alternative to the maximum likelihood method, the restricted maximum likelihood, is studied. In the situation when methods variances are considered to be known an upper bound on the between-method variance is obtained. The relationship between likelihood equations and moment-type equations is also discussed.     

基于太阳散射光测量系统反演痕量气体方法研究

为了克服利用太阳散射光作光源的被动差分吸收光谱(DOAS)系统中异方差对反演结果的影响,对DOAS反演算法进行了研究。鉴于局部多项式回归良好的统计性质,且当采用非参回归时不必人为设定异方差的结构,能适应几乎所有回归估计,提出利用非参稳健局部多项式回归方法估计DOAS系统测量谱中的慢变吸收部分,并据此反演痕量气体斜柱浓度。把该方法应用于外场实验获得光谱信息处理中,结果表明,本文方法比最小二乘多项式回归估计反演效果更好,降低了被动DOAS系统测量误差。     

Robust Automatic Bandwidth for Long Memory

The choice of bandwidth, or number of harmonic frequencies, is crucial to semiparametric estimation of long memory in a covariance stationary time series as it determines the rate of convergence of the estimate, and a suitable choice can insure robustness to some non-standard error specifications, such as (possibly long-memory) conditional heteroscedasticity. This paper considers mean squared error minimizing bandwidths proposed in the literature for the local Whittle, the averaged periodogram and the log periodogram estimates of long memory. Robustness of these optimal bandwidth formulae to conditional heteroscedasticity of general form in the errors is considered. Feasible approximations to the optimal bandwidths are assessed in an extensive Monte Carlo study that provides a good basis for comparison of the above-mentioned estimates with automatic bandwidth selection.     

基于小波变换的短期风速预测综合模型

针对风速序列具有非平稳性、非线性、异方差性的特点,首先利用db3小波对原始风速序列进行多分辨率分析,并对其系数进行单支重构,得到表征风速序列内在特性不同频段上的概貌风速与细节风速;其次对不同频段上的风速序列建立时间序列主模型,采用LM检验法分析所建模型的残差序列,提出用ARCH模型和GARCH模型进行改进,更贴近实际地反应了风速变化的规律;最后通过实例验证该文方法能够有效提高预测精度。     

小波分析和考虑外生变量的广义自回归条件异方差模型在电价预测中的应用

电力市场中的电价序列存在很大的随机波动和价格尖峰。文章提出根据电价序列的变化特点,通过小波变换将其分解为概貌序列和细节序列,从而在不同尺度上反映电价的变化规律。通过概貌分量找出电价的主要波动规律,并由此对电价进行预测,剔除细节分量所反映的电价的随机波动影响。建立考虑异方差的广义自回归条件异方差模型(generalized autoregressive conditional heteroscedasticity,GARCH)对概貌序列建模,并在GARCH模型中加入外生变量形成GARCHX模型,以弥补传统时间序列模型忽略外界影响的缺陷。对美国PJM电力市场的实例研究表明,所建立的W-GARCHX模型比传统时间序列模型的预测精度有明显提高。     

ARMA MODELS WITH ARCH ERRORS

Abstract. This paper considers the class of ARMA models with ARCH errors. Maximum Likelihood and Least Squares estimates of the parameters of the model and their covariance matrices are noted and incorporated into techniques for model building based upon the application of the usual Box-Jenkins methodology of identification, estimation and diagnostic checking to the ARMA equation, the ARCH equation, and the full model. The techniques are applied to 16 U.S. macroeconomic time series and it is seen that in many of the series, models from this class can be constructed.     

A METHOD TO IDENTIFY DISPERSION EFFECTS FROM UNREPLICATED MULTILEVEL EXPERIMENTS

The use of experimental design to identify dispersion effects is an effective tool for improving quality. In this article the problem of identifying such effects from unreplicated experiments is studied. We focus on a method developed for two-level 2^k-p experiments and discuss how the method can be generalized to a wider range of experimental designs. In particular, we show how dispersion effects can be identified from non-geometric Plackett–Burman designs and from experiments with more than two factor levels. In contrast to related methods our approach provides a test statistic with a well-known reference distribution. Three actual experiments are used to illustrate the method and to make comparisons to related methods. © 1997 John Wiley & Sons, Ltd.     

Tests for conditional heteroscedasticity of functional data

Functional data objects derived from high-frequency financial data often exhibit volatility clustering. Versions of functional generalized autoregressive conditionally heteroscedastic (FGARCH) models have recently been proposed to describe such data, however so far basic diagnostic tests for these models are not available. We propose two portmanteau type tests to measure conditional heteroscedasticity in the squares of asset return curves. A complete asymptotic theory is provided for each test. We also show how such tests can be adapted and applied to model residuals to evaluate adequacy, and inform order selection, of FGARCH models. Simulation results show that both tests have good size and power to detect conditional heteroscedasticity and model mis-specification in finite samples. In an application, the tests show that intra-day asset return curves exhibit conditional heteroscedasticity. This conditional heteroscedasticity cannot be explained by the magnitude of inter-daily returns alone, but it can be adequately modeled by an FGARCH(1,1) model.     

Properties of the Autocorrelation Function of Squared Observations for Second-order Garch Processes Under Two Sets of Parameter Constraints

Non-negativity constraints on the parameters of the GARCH( p , q ) process may be relaxed without giving up the requirement that the conditional variance remains non-negative with probability 1. In this paper we look into the consequences of adopting these less severe constraints in the GARCH(2, 2) case and its two second-order special cases, GARCH(2, 1) and GARCH(1, 2). This is done by comparing the autocorrelation function of squared observations under these two sets of constraints. The less severe constraints allow more flexibility in the shape of the autocorrelation function than the constraints restricting the parameters to be non-negative.