Least squares estimation of ARCH models with missing observations

A least squares estimator for ARCH models in the presence of missing data is proposed. Strong consistency and asymptotic normality are derived. Monte Carlo simulation results are analysed and an application to real data of a Chilean stock index is reported.     

GARCH模型的经验似然估计

以计量经济学中ARCH模型族为背景,对GARCH模型进行讨论和研究。讨论了基于GED分布的β-ARCH模型和GARCH模型的经验极大似然估计的求解方法,得到了相应的平稳模型的大样本性质定理。     

Timing of resources exploration in the behavior of firm – Innovative approach and empirical simulation

We have insight into the importance of resource exploration derived from the quest for sustaining competitive advantage as well as the growth of the firm, which are well-explicated in the resources point of view. However, we really do not know when the firm will seriously commit to this kind of activities. Therefore, this study proposes an innovative approach using quantum minimization (QM) to tune a composite model comprising adaptive neuron-fuzzy inference system (ANFIS) and nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) such that it constitutes the relationship among five indicators, the growth rate of long-term investment, the firm size, the return on total asset, the return on common equity, and the return on sales. In particularly, this proposed approach outperforms several typical methods such as auto-regressive moving-average regression (ARMAX), back-propagation neural network (BPNN), or adaptive support vector regression (ASVR) for this timing problem in term of comparing their achievement and the goodness-of-fit. Consequently, the preceding methods involved in this problem truly explain the timing of resources exploration in the behavior of firm. Meanwhile, the performance summary among methods is compared quantitatively.     

Diversity of quantum optimizations for training adaptive support vector regression and its prediction applications

Three kinds of quantum optimizations are introduced in this paper as follows: quantum minimization (QM), neuromorphic quantum-based optimization (NQO), and logarithmic search with quantum existence testing (LSQET). In order to compare their optimization ability for training adaptive support vector regression, the performance evaluation is accomplished in the basis of forecasting the complex time series through two real world experiments. The model used for this complex time series prediction comprises both BPNN-Weighted Grey-C3LSP (BWGC) and nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) that is tuned perfectly by quantum-optimized adaptive support vector regression. Finally, according to the predictive accuracy of time series forecast and the cost of the computational complexity, the concluding remark will be made to illustrate and discuss these quantum optimizations.     

A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables.

Uncorrectable skew and heteroscedasticity are among the "lemons" of psychological data, yet many important variables naturally exhibit these properties. For scales with a lower and upper bound, a suitable candidate for models is the beta distribution, which is very flexible and models skew quite well. The authors present maximum-likelihood regression models assuming that the dependent variable is conditionally beta distributed rather than Gaussian. The approach models both means (location) and variances (dispersion) with their own distinct sets of predictors (continuous and/or categorical), thereby modeling heteroscedasticity. The location submodel link function is the logit and thereby analogous to logistic regression, whereas the dispersion submodel is log linear. Real examples show that these models handle the independent observations case readily. The article discusses comparisons between beta regression and alternative techniques, model selection and interpretation, practical estimation, and software. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

中国城镇居民住房自有率影响因素的数量分析

目的研究中国社会、经济因素对城镇居民住房自有率的影响。为改善中国居民住房水平提供理论依据．方法采用中国各省份2003年的截面数据，建立计量经济模型，通过F-检验、t-检验、异方差检验和多重共线性检验，对各变量进行显著性分析．结果经计算我国城镇居民住房自有率有4个主要的影响因素，其中，城镇化率、家庭规模与之呈负相关关系，政府消费、人均实际可支配收入增长呈正相关关系．4个变量的解释能力达到53％．结论多元线性回归的计量分析方法，能有效地筛选、分析城镇居民住房自有率的各种影响变量，对住房政策的制定有重要的参考价值．     

A Note on Diagnosing Multivariate Conditional Heteroscedasticity Models

In this paper we consider several tests for model misspecification after a multivariate conditional heteroscedasticity model has been fitted. We examine the performance of the recent test due to Ling and Li ( J. Time Ser. Anal. 18 (1997), 447–64), the Box–Pierce test and the residual-based F test using Monte Carlo methods. We find that there are situations in which the Ling–Li test has very weak power. The residual-based diagnostics demonstrate significant under-rejection under the null. In contrast, the Box–Pierce test based on the cross-products of the standardized residuals often provides a useful diagnostic that has reliable empirical size as well as good power against the alternatives considered.     

Composite of adaptive support vector regression and nonlinear conditional heteroscedasticity tuned by quantum minimization for forecasts

Adaptive support vector regression (ASVR) applied to the forecast of complex time series is superior to the other traditional prediction methods. However, the effect of volatility clustering occurred in time-series actually deteriorates ASVR prediction accuracy. Therefore, incorporating nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) model into ASVR is employed for dealing with the problem of volatility clustering to best fit the forecast’s system. Interestingly, quantum-based minimization algorithm is proposed in this study to tune the resulting coefficients between ASVR and NGARCH, in such a way that the ASVR/NGARCH composite model can achieve the best accuracy of prediction. Quantum optimization here tackles so-called NP-completeness problem and outperforms the real-coded genetic algorithm on the same problem because it accomplishes better approach to the optimal or near-optimal coefficient-found. It follows that the proposed method definitely obtains the satisfactory results because of highly balancing generalization and localization for composite model and thus improving forecast accuracy. Bao Rong Chang is currently an Associate Professor in the Department of Computer Science and Information Engineering at National Taitung University in Taitung, Taiwan. He completed his BS degree from the Department of Electronic Engineering, Tam Kang University, Taiwan. In 1990, he earned his ME degree from the Department of Electrical Engineering, University of Missouri-Columbia, USA, and his Ph.D. in 1994 at the same University. His current research interests include Intelligent Computations, Applied Computer Network, and Financial Engineering. Hsiu-Fen Tsai is currently a Senior Lecturer in the Department of International Business at Shu Te University in Kaohsiung, Taiwan. She completed her BA degree from the Department of International Business, National Taiwan University, Taiwan. In 1995, she earned her MBA degree from the Department of Business Administration, National Taiwan University, Taiwan. At present, she is a Ph. D. Candidate in Department of International Business since 2004 at the same University. Her current research interests include Intelligent Analysis of Business Models and Applications of Strategy Management.     

A note on non‐parametric testing for Gaussian innovations in AR–ARCH models

In this paper, we consider autoregressive models with conditional autoregressive variance, including the case of homoscedastic AR models and the case of ARCH models. Our aim is to test the hypothesis of normality for the innovations in a completely non‐parametric way, that is, without imposing parametric assumptions on the conditional mean and volatility functions. To this end, the Cramér–von Mises test based on the empirical distribution function of non‐parametrically estimated residuals is shown to be asymptotically distribution‐free. We demonstrate its good performance for finite sample sizes in a small simulation study. AMS 2010 Classification: Primary 62 M10, Secondary 62 G10     

Genotype by environment interaction for production traits while accounting for heteroscedasticity

Grazing (G) provides an alternative management system for dairy production. Heteroscedasticity (HV) of the data may bias estimates of genetic correlations of yield traits between environments, an indicator of genotype-by-environment interaction (G×E). The objective of this study was to investigate the effect of HV on estimates of heritabilities and genetic correlations for mature-equivalent milk, protein, and fat yield, and lactation-average somatic cell scores of daughters, and to determine if HV affects the ability of sire's predicted transmitting ability (PTA) to predict daughter production in G and confinement (C) herds. Data consisted of 72,489 records from 35,674 cows in 366 G herds from 11 states, and 117,629 records from 50,963 cows in 373 C herds from the same 11 states plus 1 geographically contiguous state. Herds were divided into variance quartiles (Q_V1-Q_V4) based on milk yield. A transformation was used to reduce HV by standardizing the within-herd standard deviation to the average across-herd standard deviation of a base year for each parity, and was similar to the method used in current USDA-DHIA genetic evaluations. Regression of daughter yield on sire PTA showed that PTA overestimated production of all traits in Q_V1-Q_V3 and of milk in Q_V4 of G herds. For C herds, yields of milk in Q_V1 and Q_V2, and of protein and fat in Q_V1 were overestimated, and protein was underestimated in Q_V4. Reducing HV had little effect on G herds, but for C herds, regression did not differ from unity for milk and protein in Q_V1 and Q_V2. For milk, protein, and fat in G, heritabilities were approximately 0.17, 0.17, and 0.19, respectively. The heritabilities for milk, protein, and fat in C herds were approximately 0.16, 0.17, and 0.21, respectively. Genetic correlations between C and G did not suggest a G×E in 3 upper quartiles, but a possible G×E (correlation = 0.21, estimated standard error = 0.22) for the lowest quartile. Reducing HV did not affect estimates of heritabilities or genetic correlations. Results indicated that modest evidence for existence of G×E did not arise solely from HV.