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误设模型惩罚似然估计中正则化参数选择的效率AI 解读

It has been shown that Akaike information criterion (AIC)-type criteria are asymptotically efficient selectors of the tuning parameter in nonconcave penalized regression methods under the assumption that the population variance is known or that a consistent estimator is available. We relax this assumption to prove that AIC itself is asymptotically efficient and we study its performance in finite samples. In classical regression, it is known that AIC tends to select overly…

产生协整关系的交易层面纯跳跃价格模型AI 解读

We propose a new transaction-level bivariate log-price model that yields fractional or standard cointegration. The model provides a link between market microstructure and lower-frequency observations. The two ingredients of our model are a long-memory stochastic duration process for the waiting times, {τk}, between trades and a pair of stationary noise processes, ({ek} and {ηk}), which determine the jump sizes in the pure-jump log-price process. Our model includes feedback…

持续期记忆参数向计数与已实现波动率传递的条件AI 解读

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter $d \in [0,{\textstyle{1 \over 2}})$ to ensure that the corresponding counting process N ( t ) satisfies Var N ( t ) ~ Ct 2 d +1 ( C > 0) as t → ∞, with the same memory parameter $d \in [0,{\textstyle{1 \over 2}})$ that was assumed for the durations. Thus, these conditions ensure that the memory parameter in durations propagates to the same memory parameter in the…

持续期驱动长程依赖过程的渐近理论AI 解读

We consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration-driven long range dependence (DDLRD), as opposed to the more widely studied linear long range dependence based on fractional differencing of an iid process. We consider in detail two specific processes having DDLRD, originally presented in Taqqu and Levy (1986), and Parke (1999). For these processes, we obtain the limiting distribution…

分数协整子空间的半参数估计AI 解读

We consider a common-components model for multivariate fractional cointegration, in which the $s\geq1$ components have different memory parameters. The cointegrating rank may exceed 1. We decompose the true cointegrating vectors into orthogonal fractional cointegrating subspaces such that vectors from distinct subspaces yield cointegrating errors with distinct memory parameters. We estimate each cointegrating subspace separately, using appropriate sets of eigenvectors of an…

波动率长记忆的估计AI 解读

We consider semiparametric estimation of the memory parameter in a model that includes as special cases both long-memory stochastic volatility and fractionally integrated exponential GARCH (FIEGARCH) models. Under our general model the logarithms of the squared returns can be decomposed into the sum of a long-memory signal and a white noise. We consider periodogram-based estimators using a local Whittle criterion function. We allow the optional inclusion of an additional…

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波动率长记忆检验AI 解读

We consider the asymptotic behavior of log-periodogram regression estimators of the memory parameter in long-memory stochastic volatility models, under the null hypothesis of short memory in volatility. We show that in this situation, if the periodogram is computed from the log squared returns, then the estimator is asymptotically normal, with the same asymptotic mean and variance that would hold if the series were Gaussian. In particular, for the widely used GPH estimator…

长记忆随机波动率模型中记忆参数的对数周期图回归估计AI 解读

We consider semiparametric estimation of the memory parameter in a long memory stochastic volatility model. We study the estimator based on a log periodogram regression as originally proposed by Geweke and Porter-Hudak (1983, Journal of Time Series Analysis 4, 221–238). Expressions for the asymptotic bias and variance of the estimator are obtained, and the asymptotic distribution is shown to be the same as that obtained in recent literature for a Gaussian long memory series.…

利用改进的 Akaike 信息准则选择非参数回归的平滑参数AI 解读

Summary Many different methods have been proposed to construct nonparametric estimates of a smooth regression function, including local polynomial, (convolution) kernel and smoothing spline estimators. Each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set. In this paper an improved version of a criterion based on the Akaike information criterion (AIC), termed AICC, is derived and examined as a way to choose the…

线性回归中有效模型选择准则的相对收敛速度AI 解读

Two approaches to estimating a smooth regression function not specified by a finite number of parameters are (i) to fit a parametric model to the data, with the number of parameters selected by the Akaike information criterion, AIC, and (ii) to use nonparametric smoothing techniques, with the smoothing parameter selected by cross-validation or some other automatic method. We consider the relative rate of convergence of the mean integrated squared error of the selected…

线性回归中有效模型选择准则的相对收敛速度AI 解读

Two approaches to estimating a smooth regression function not specified by a finite number of parameters are (i) to fit a parametric model to the data, with the number of parameters selected by the Akaike information criterion, AIC, and (ii) to use nonparametric smoothing techniques, with the smoothing parameter selected by cross-validation or some other automatic method. We consider the relative rate of convergence of the mean integrated squared error of the selected…

时间序列分析的高崩溃点方法AI 解读

SUMMARY A robust form of the discrete Fourier transform is developed that can handle large amounts of contamination and patchy outliers. We use robust regression to fit a sine and cosine coefficient at each Fourier frequency, and these coefficients are then inverse Fourier transformed to give a filtered version of the data. The filtered series can then be analysed with conventional methods. The limiting breakdown bound of the filter is 50%. Other properties of the filter are…

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欠拟合回归与时间序列模型中修正 AIC 的偏差AI 解读

The Akaike Information Criterion, AIC (Akaike, 1973), and a bias-corrected version, AICC(Sugiura, 1978; Hurvich & Tsai, 1989) are two methods for selection of regression and autoregressive models. Both criteria may be viewed as estimators of the expected Kullback-Leibler information. The bias of AIC and AICC is studied in the underfitting case, where none of the candidate models includes the true model (Shibata, 1980, 1981; Parzen, 1978). Both normal linear regression and…

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小样本自回归模型选择中 Kullback–Leibler 信息的改进估计AI 解读

A new estimator, AICl, of the Kuliback-Leibler information is proposed for Gaussian autoregressive time series model selection. The expected information is decomposed into two terms, the first being estimated without bias. The second term is a penalty function which depends only weakly on the model parameters, and hence can be tabulated by simulation from a white noise process. The estimated information, AICl, is very nearly unbiased when the model is either correct or…

小样本中的回归与时间序列模型选择AI 解读

A bias correction to the Akaike information criterion, AIC, is derived for regression and autoregressive time series models. The correction is of particular use when the sample size is small, or when the number of fitted parameters is a moderate to large fraction of the sample size. The corrected method, called AICC, is asymptotically efficient if the true model is infinite dimensional. Furthermore, when the true model is of finite dimension, AICC is found to provide better…

时间序列数据窗的均方误差准则AI 解读

A periodogram mean integrated squared error criterion is proposed for assessing the performance of time series data windows, or tapers. The criterion is evaluated numerically for several known autoregressive processes to determine the optimal amount of tapering in Tukey's cosine window. It is found that tapering can be extremely beneficial if the spectrum contains sharp peaks. Also, in all cases studied, the optimal number of points tapered converges to a constant as the…

时间序列数据窗的均方误差准则AI 解读

A periodogram mean integrated squared error criterion is proposed for assessing the performance of time series data windows, or tapers. The criterion is evaluated numerically for several known autoregressive processes to determine the optimal amount of tapering in Tukey's cosine window. It is found that tapering can be extremely beneficial if the spectrum contains sharp peaks. Also, in all cases studied, the optimal number of points tapered converges to a constant as the…

频域中位数时间序列AI 解读

This article discusses the median of a batch of time series. We focus on the frequency-domain median (FDM) series (Zeger 1985), which is calculated from the “mediancenters” (Gower 1974) of the discrete Fourier transforms. Like the univariate median, it has a breakdown value of 50%. Like the mean, the FDM time series of independent realizations from a stationary Gaussian process has a spectrum proportional to that of the component series. Analogs of the univariate median have…

频域中位数时间序列AI 解读

This article discusses the median of a batch of time series. We focus on the frequency-domain median (FDM) series (Zeger 1985), which is calculated from the “mediancenters” (Gower 1974) of the discrete Fourier transforms. Like the univariate median, it has a breakdown value of 50%. Like the mean, the FDM time series of independent realizations from a stationary Gaussian process has a spectrum proportional to that of the component series. Analogs of the univariate median have…

谱估计的数据驱动选择：拓展交叉验证方法的适用范围AI 解读

I develop methods of objectively choosing a spectrum estimate from a general class C of available estimates. C can, for example, simultaneously include Blackman—Tukey and autoregressive estimates, so the statistician no longer needs to choose one type or the other arbitrarily. The methods work by extending the applicability of existing cross-validatory techniques through the introduction of generalized leave-out-one spectrum estimates. As special cases, I obtain new…