基于Spatial AIC准则的空间自回归模型变量选择研究

变量选择直接决定着空间计量经济模型的有效程度与实证研究结果。为有效解决空间自回归模型(即SAR模型)的变量选择问题,本文利用Kullback-Laible信息量最大化,把AIC准则运用到SAR模型构建,推导出Spatial AIC统计量,提出Spatial AIC准则。然后利用统计理论证明Spatial AIC准则选择SAR模型变量的渐近最优性;利用蒙特卡洛模拟方法,比较Spatial AIC准则、经典AIC准则和Lasso方法用于SAR模型变量选择的有限大样本性质;利用空间相关的沪深300成分股股票收益率数据,采用Spatial AIC准则和Lasso方法,分别构建股票收益率财务因素的空间自相关模型,实证比较其相对有效性。三种结果均表明Spatial AIC准则能够更好地解决SAR模型变量选择问题。     

银行业如何影响房地产业?Copula分位数回归及预测方法

众所周知,房地产业与银行业是高度相关的,如何确定银行业股票收益率对房地产业股票收益率的影响以及如何根据银行业股票收益率预测房地产业股票收益率的波动是非常重要的问题。本文首先使用Copula分位数回归建立了银行业股票收益率对房地产业股票收益率的回归模型,并且给出了Copula分位数回归基础上的CopuIa选择新标准,即分位数损失函数距离意义下的Copula函数选择准则,依据该准则我们选取Clayton Copula分位数回归模型刻画了低迷时期银行业股票收益率如何影响房地产业股票收益率,并据此对房地产业股票收益率的波动进行了预测     

改进的函数系数自回归建模方法对上海股市实证分析

函数系数自回归模型(FAR)是一类更具有适应性的模型。本文利用函数系数自回归模型对上海股市日收益率进行建模及短期预测,改进现有建模对带宽、模型的依赖变量以及阶数确定方法。并与上海股市日收益率的自回归模型结果进行了比较,结果表明改进的函数系数模型具有很好的预测能力。     

分位数变系数模型基于核光滑的变量选择

分位数变系数模型是一种稳健的非参数建模方法.使用变系数模型分析数据时,一个自然的问题是如何同时选择重要变量和从重要变量中识别常数效应变量.本文基于分位数方法研究具有稳健和有效性的估计和变量选择程序.利用局部光滑和自适应组变量选择方法,并对分位数损失函数施加双惩罚,我们获得了惩罚估计.通过BIC准则合适地选择调节参数,提出的变量选择方法具有oracle理论性质,并通过模拟研究和脂肪实例数据分析来说明新方法的有用性.数值结果表明,在不需要知道关于变量和误差分布的任何信息前提下,本文提出的方法能够识别不重要变量同时能区分出常数效应变量.     

固定效应空间自回归分位数模型的变量选择

本文研究了固定效应空间自回归分位数模型的变量选择问题.通过惩罚压缩相关参数,达到了同时识别空间效应、估计未知参数和选择解释变量的目的.此外,给出了变量选择的实现算法并证明了惩罚估计量的大样本性质.数值模拟和实例分析均表明了所提方法的优良表现.     

改进的强相关数据的变量选择方法

针对高维强相关数据的变量选择问题,本文提出了改进的变量选择方法.该方法先利用自适应弹性网方法(Aenet)在原始的强相关数据上建立模型,选出对响应变量起重要作用的群组变量和独立变量;再通过偏最小二乘方法(PLS)对选出的变量作模型估计;最后,将两种方法得到的估计系数做线性组合,并以此系数来建立回归模型.新模型具有精度高、解释性好的优点,数值实验验证了该方法的有效性.     

单变量空间自回归测量误差模型的参数估计

本文在经典的空间自回归模型中引入测量误差,从只有一个自变量入手,构建单变量空间自回归测量误差模型,探讨自变量存在的测量误差对空间自回归模型的影响,建立单变量空间自回归测量误差模型的参数估计方法和算法,通过数值模拟验证估计方法的可行性和可靠性.     

基于区域房价的空间自回归模型平均

文章是基于模型平均的方法对我国重点省会城市月度房价数据的空间自回归模型的拓展研究.通过一定的宏观经济解释变量和房价数据,构建区域房价的空间自回归模型,并在基于MMA准则的模型平均框架下,将不同的候选模型组合进行房价预测.对比经典空间自回归模型的预测,基于模型平均的MMA, SAIC和SBIC的预测有更高的精确度和更好的稳定性.     

基于LPRE和LASSO方法的股指追踪研究

将最小化乘积相对误差(LPRE)和最小绝对压缩选择算子(LASSO)方法应用到乘积回归模型,结合BIC信息准则实现股票指数的追踪,成功选取了26支对上证50指数影响较大的成分股,并比较了所提方法与线性模型下LASSO方法的表现,验证了所提方法的有效性.     

超高维部分线性模型的PGFR变量筛选

本文考虑超高维部分线性模型,其中线性部分的维数p大于样本量n,且维数p随着样本量n呈指数阶增长.首先,利用半参数回归的profile方法,把超高维部分线性模型转化成超高维线性模型.其次,为了对高维线性分量进行有效的变量筛选,考虑到协变量之间的相关性,结合贪婪算法和向前回归变量筛选方法,针对部分线性模型,提出了profile贪婪向前回归(PGFR)变量筛选方法.在一定正则条件下,证明了所提PGFR方法具有筛选相合性.为了确定所选模型是否能够依概率趋于1包含真实模型,进一步提出了BIC准则.最后,通过模拟研究和实例分析验证了PGFR方法在有限样本下的完成情况.     

Sparse Vector Autoregressive Modeling

The vector autoregressive (VAR) model has been widely used for modeling temporal dependence in a multivariate time series. For large (and even moderate) dimensions, the number of the AR coefficients can be prohibitively large, resulting in noisy estimates, unstable predictions, and difficult-to-interpret temporal dependence. To overcome such drawbacks, we propose a two-stage approach for fitting sparse VAR (sVAR) models in which many of the AR coefficients are zero. The first stage selects nonzero AR coefficients based on an estimate of the partial spectral coherence (PSC) together with the use of BIC. The PSC is useful for quantifying the conditional relationship between marginal series in a multivariate process. A refinement second stage is then applied to further reduce the number of parameters. The performance of this two-stage approach is illustrated with simulation and real data examples. Supplementary materials for this article are available online.     

Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes

We consider anr-dimensional multivariate time series {y_t, tZ} which is generated by an infinite order vector autoregressive process. We show that a bootstrap procedure which works by generating time series replicates via an estimated finitek-order vector autoregressive process (k→∞ at an appropriate rate with the sample size) gives asymptotically valid approximations to the joint distribution of the growing set of estimated autoregressive coefficients and to the corresponding set of estimated moving average coefficients (impuls responses).     

EV自回归模型的一个相合估计

考虑带有测量误差的自回归模型,在不对替代变量和真实变量之间的关系做任何模型假设的情况下,借助核实数据,给出未知参数的一个基于核实与替代两方面信息的最小二乘估计量,并证得该估计量是相合估计.     

Autoregressive model fitting for control

Summary The use of a multidimensional extension of the minimum final prediction error (FPE) criterion which was originally developed for the decision of the order of one-dimensional autoregressive process [1] is discussed from the standpoint of controller design. It is shown by numerical examples that the criterion will also be useful for the decision of inclusion or exclusion of a variable into the model. Practical utility of the procedure was verified in the real controller design process of cement rotary kilns. The Institute of Statistical Mathematics     

Outlier Detections in Autoregressive Models

This article proposes a new technique for detecting outliers in autoregressive models and identifying the type as either innovation or additive. This technique can be used without knowledge of the true model order, outlier location, or outlier type. Specifically, we perturb an observation to obtain the perturbation size that minimizes the resulting residual sum of squares (SSE). The reduction in the SSE yields outlier detection and identification measures. In addition, the perturbation size can be used to gauge the magnitude of the outlier. Monte Carlo studies and empirical examples are presented to illustrate the performance of the proposed method as well as the impact of outliers on model selection and parameter estimation. We also obtain robust estimators and model selection criteria, which are shown in simulation studies to perform well when large outliers occur.     

Asymptotic Normality of Autoregressive Processes

In the present paper, the form of iterated limits of the moderate deviation principle for dependent variables is considered and as an application, the moderate deviation principle of m-dependent random variables is obtained.     

Multivariate Generalized Autoregressive Conditional Heteroscedastic Model

1 IlltroductionThe concept of ARCH, which stands for autoregressit,e conditional heteroscedasticity wasfrist introduced by EngelI1J to handIe time series with a changing conditional tariance.Bollersle.I2] extended the ARCH model into the sChcalled generalized autoregressive con-ditional heteroscedastic model(GARCH). This class of models has important applitalions,particularly in finance and economics(see, e.g., [3], [4]). Lingl5] found some simple sufficientconditions fOr the strict st…     

General Autoregressive Models with Long-Memory Noise

We give the limiting distribution of the least-squares estimator in the general autoregressive model driven by a long-memory process. We prove that with an appropriate normalization the estimation error converges, in distribution, to a random vector which contains: (1) a stochastic component, due to the presence of the unstable roots, which are multiple Wiener–Itô integrals and a non-linear functionals of stochastic integrals with respect to a Brownian motion; (2) a constant component due to the stable roots; (3) a stochastic component, due to the presence of the explosive roots, which is a mixture of normal distributions.