TSCov(RTAQ)
TSCov()所属R语言包：RTAQ
Two time scale covariance estimation
两个时间尺度的协方差估计
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Function returns the two time scale covariance matrix proposed in Zhang et al (2005) and Zhang (2010). By the use of two time scales, this covariance estimate is robust to microstructure noise and non-synchronic trading.
函数返回两个时间尺度张等人（2005年），张（2010年）提出的协方差矩阵。通过使用两个时间尺度，该协方差的估计是鲁棒性的微观结构噪音和非同步交易。
用法----------Usage----------
TSCov(pdata, cor=FALSE, K = 300 , J = 1, K_cov = NULL , J_cov = NULL,
K_var = NULL , J_var = NULL, makePsd = FALSE);
参数----------Arguments----------
参数：pdata
a list. Each list-item i contains an xts object with the intraday price data of stock i for day t.
一个列表。每个目录项我包含一个XTS对象，盘中价格数据为t日股票i。
参数：cor
boolean, in case it is TRUE, the correlation is returned. FALSE by default.
布尔值，如果是TRUE，则返回相关。默认情况下，返回FALSE。
参数：K
positive integer, slow time scale returns are computed on prices that are K steps apart.
正整数，慢时间尺度的回报率计算K步除了价格上。
参数：J
positive integer, fast time scale returns are computed on prices that are J steps apart.
正整数，时间快的规模报酬是J步骤除了价格计算。
参数：K_cov
positive integer, for the extradiagonal covariance elements the slow time scale returns are computed on prices that are K steps apart.
正整数，为的extradiagonal的协方差元素缓慢的时间尺度回报率计算K步除了价格上。
参数：J_cov
positive integer, for the extradiagonal covariance elements the fast time scale returns are computed on prices that are J steps apart.
正整数，为的extradiagonal的协方差元素的快速规模报酬是J步骤除了价格计算。
参数：K_var
vector of positive integers, for the diagonal variance elements the slow time scale returns are computed on prices that are K steps apart.
向量的正整数，缓慢的时间尺度回报率计算K步除了价格上的斜方差元素。
参数：J_var
vector of positive integers, for the diagonal variance elements the fast time scale returns are computed on prices that are J steps apart.
正整数向量，对角方差元素的快速规模报酬是J步骤除了价格计算。
参数：makePsd
boolean, in case it is TRUE, the positive definite version of RTSCov is returned. FALSE by default.
布尔值，如果是，则返回TRUE，正定的RTSCov版本。默认情况下，返回FALSE。
Details
详细信息----------Details----------
The TSCov requires the tick-by-tick transaction prices. (Co)variances are then computed using log-returns calculated on a rolling basis on stock prices that are K (slow time scale) and J (fast time scale) steps apart.
TSCov需要刻度线刻度线交易价格。 （公司）的差异，然后采用对数收益计算的股票价格K（慢时间尺度）和J（快时间尺度）的步骤除了上滚动的基础上计算。
The diagonal elements of the TSCov matrix are the variances, computed for log-price series X with n price observations at times τ_1,τ_2,…,τ_n as follows:
的TSCov矩阵对角线元素的差异，计算价格log系列Xn的价格观察有时 τ_1,τ_2,…,τ_n如下：
where \overline{n}_K=(n-K+1)/K, \overline{n}_J=(n-J+1)/J and
\overline{n}_K=(n-K+1)/K，\overline{n}_J=(n-J+1)/J
The extradiagonal elements of the TSCov are the covariances. For their calculation, the data is first synchronized by the refresh time method proposed by Harris et al (1995). It uses the function refreshTime to collect first the so-called refresh times at which all assets have traded at least once since the last refresh time point. Suppose we have two log-price series: X and Y. Let Γ =\{ τ_1,τ_2,…,τ_{N^{\mbox{\tiny X}}_{\mbox{\tiny T}}}\} and Θ=\{θ_1,θ_2,…,θ_{N^{\mbox{\tiny Y}}_{\mbox{\tiny T}}}\} be the set of transaction times of these assets. The first refresh time corresponds to the first time at which both stocks have traded, i.e. φ_1=\max(τ_1,θ_1). The subsequent refresh time is defined as the first time when both stocks have again traded, i.e. φ_{j+1}=\max(τ_{N^{\mbox{\tiny{X}}}_{φ_j}+1},θ_{N^{\mbox{\tiny{Y}}}_{φ_j}+1}). The complete refresh time sample grid is Φ=\{φ_1,φ_2,...,φ_{M_N+1}\}, where M_N is the total number of paired returns. The sampling points of asset X and Y are defined to be t_i=\max\{τ\inΓ:τ≤q φ_i\} and s_i=\max\{θ\inΘ:θ≤q φ_i\}.
的extradiagonal的TSCov元素的协方差。他们的计算，数据是同步的刷新时间Harris等人（1995）提出的方法。它使用功能refreshTime收集第一个所谓的所有资产交易至少一次自上次刷新时间点的刷新时间。假设我们有两个系列：log价格X和Y。让我们 Γ =\{ τ_1,τ_2,…,τ_{N^{\mbox{\tiny X}}_{\mbox{\tiny T}}}\}和Θ=\{θ_1,θ_2,…,θ_{N^{\mbox{\tiny Y}}_{\mbox{\tiny T}}}\}是集这些资产的交易时间。第一次刷新时间对应于第一时间在这两只股票进行买卖，即φ_1=\max(τ_1,θ_1)。随后的刷新时间被定义为第一次当两股再次交易，即φ_{j+1}=\max(τ_{N^{\mbox{\tiny{X}}}_{φ_j}+1},θ_{N^{\mbox{\tiny{Y}}}_{φ_j}+1})。完整的刷新时间采样网格是Φ=\{φ_1,φ_2,...,φ_{M_N+1}\}，M_N的总人数已配对的回报。资产的采样点X和Y被定义为t_i=\max\{τ\inΓ:τ≤q φ_i\}和s_i=\max\{θ\inΘ:θ≤q φ_i\}。
Given these refresh times, the covariance is computed as follows:
鉴于这些刷新倍，协方差的计算方法如下：
where
哪里
Unfortunately, the TSCov is not always positive semidefinite. By setting the argument makePsd = TRUE, the function makePsd is used to return a positive semidefinite matrix. This function replaces the negative eigenvalues with zeroes.
不幸的是，TSCov并不总是半正定的。通过设置参数makePsd = TRUE，函数makePsd用于返回一个半正定矩阵。此函数替换用零负本征值。
值----------Value----------
an N x N matrix
N x N矩阵
（作者）----------Author(s)----------
Jonathan Cornelissen and Kris Boudt
参考文献----------References----------
correction, and price discovery on infomationally linked security markets. Journal of Financial and Quantitative Analysis 30, 563-581.
Determining integrated volatility with noisy high-frequency data. Journal of the American Statistical Association 100, 1394-1411.
of Econometrics 160, 33-47.
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注：
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发表于 2012-9-28 22:39:19
