统计代写|风险建模代写Financial risk modeling代考|The statistical significance of the economic gains

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  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等楖率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
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统计代写|风险建模代写Financial risk modeling代考|The statistical significance of the economic gains

统计代写|风险建模代写Financial risk modeling代考|The statistical significance of the economic gains

One way to assess the statistical significance of the economic gains resulting from Tables $1.7-1.9$ is to perform the following joint statistical test. For any target $\mu_{p}$ and any estimator, one can define alternative covariance forecasts $\hat{C}{t}$ and portfolio returns $R{t+1}^{p(C)}$. Define
a_{t+1}^{\hat{C}}=\left(R_{t+1}^{p(\text { Fourier })}-\bar{R}^{p(\text { Fourier })}\right)^{2}-\left(R_{t+1}^{p(\mathcal{C})}-\bar{R}^{p(\hat{C})}\right)^{2} .
Assessing the statistical significance of the economic gains of the Fourier estimate over alternative forecasts can be conducted by testing whether the mean of $a_{t+1}^{\hat{C}}$ is larger than (or equal to) zero against the alternative that the mean is smaller than zero. Following Bandi et al.

(2006), for any target return $d=0.09,0.12,0.15$, we define the vector
A_{t+1}^{d}=\left(a_{t+1}^{\hat{C}{1}}, a{t+1}^{\hat{C}{2}}, \ldots, a{t+1}^{\hat{C}{r}}\right)^{\prime}, $$ where the $r$-uple of estimators $\left(\hat{C}{1}, \hat{C}{2}, \ldots, \hat{C}{r}\right)$ is given by $\left(R C^{1 \min }, R C^{5 \mathrm{~min}}\right.$, $\left.R C^{10 m i n}\right),\left(R C L L^{1 m i n}, R C L L^{5 m i n}, R C L L^{10 m i n}\right)$ and (RCopt $\left., A O, K, A O_{s u b}\right)$ or any other combination of methods we want to test. We also stack all the methods simultaneously and check the overall ability of the Fourier method to yield a significant economic gain over the others. We write the regression model
A_{t+1}^{d}=\delta^{d} \mathbf{1}{r}+\varepsilon{t+1},
where $\delta^{d}$ is a scalar parameter. Series $a_{t+1}^{\hat{C}}$ associated to losses (i.e. negative values in Tables $1.7-1.9$ ) are multiplied by $-1$ before regression. We perform the one-sided test $H_{0}: \delta^{d} \geq 0$, against $H_{A}: \delta^{d}<0$. The parameter $\delta^{d}$ is estimated by GMM using a Bartlett HAC covariance matrix. A similar approach is used by Engle and Colacito (2006). The $t$-statistics of all the tests imply rejection of the null hypothesis, and hence statistical significance of the economic gains/losses at the 5 percent level. In particular, we remark that when testing the different methods altogether $(r=10)$ we get rejection of the null hypothesis even if we do not change the sign of the series $a_{t+1}^{\hat{C}}$ associated to losses. Indeed, in this case the corresponding $t$-statistics are $-5.69,-4.44$ and $-7.30$, respectively, revealing that on average the Fourier methodology yields a statistically significant economic gain at the 1 percent level.

统计代写|风险建模代写Financial risk modeling代考|Conclusion

We have analyzed the gains offered by the Fourier estimator from the perspective of an asset-allocation decision problem. The comparison is extended to realized covariance-type estimators, to lead-lag bias corrections, to the all-overlapping estimator, to its subsampled version and to the realized kernel estimator.

We show that the Fourier estimator carefully extracts information from noisy high-frequency asset-price data and allows for nonnegligible utility gains in portfolio management. Specifically, our simulations show that the gains yielded by the Fourier methodology are statistically significant and can be economically large, while only the subsampled alloverlapping estimator and, for low levels of market microstructure noise, the realized covariance with one lead-lag bias correction and suitable sampling frequency can be competitive. Analyzing the in-sample and out-of-sample properties of different covariance measures, we find that for increasing values of microstructure noise the Fourier estimator continues to provide precise variance/ covariance estimates which translate into more precise forecasts with respect to the other estimators under consideration, $A O_{s u b}$ being the only competitive method.

统计代写|风险建模代写Financial risk modeling代考|References

Aitt-Sahalia, Y. and Mancini, L. (2008) “Out of Sample Forecasts of Quadratic Variations, “Joumal of Econometrics, 147 (1): 17-33.
Ait-t-Sahalia, Y., Mykland, P. and Zhang. L. (2005) “How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise,” Review of Financial Studies, 18 (2): 351-416.
Andersen, T. and Bollerslev, T. (1998) “Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts, ” International Economic Review, 39 (4): 885-905.
Bandi, F.M. and Russell, J.R. (2006) “Separating Market Microstructure Noise from Volatility, ” Joumal of Financial Economics, 79 (3): $655-692$.
Bandi, F.M. and Russell, J.R. (2008) “Microstructure Noise, Realized Variance and Optimal Sampling,” Review of Economic Studies, 75 (2): 339-369.
Bandi, F.M., Russel, J.R. and Zhu, Y. (2008) “Using High-frequency Data in Dynamic Portfolio Choice,” Econometric Reviews, 27 (1-3): 163-198.
Barndorff-Nielsen, O.E., Hansen, P.R., Lunde, A. and Shephard, N. (2008a) “Multivariate Realised Kernels: Consistent Positive Semi-Definite Estimators of the Covariation of Equity Prices with Noise and Non-synchronous Trading, ” Economics Series Working Paper No 397, University of Oxford, Oxford, United Kingdom.
Barndorff-Nielsen, O.E., Hansen, P.R., Lunde, A. and Shephard, N. (2008b) “Designing Realized Kernels to Measure the Ex-Post Variation of Equity Prices in the Presence of Noise,” Econometrica, 76 (6): 1481-1536.
Barucci, E., Magno, D. and Mancino, M.E. (2008) “Forecasting Volatility with High Frequency Data in the Presence of Microstructure Noise,” Working paper, University of Firenze, Firenze, Italy.
De Pooter, M., Martens, M. and van Dijk, D. (2008) “Predicting the Daily Covariance Matrix for S\&P100 Stocks Using Intraday Data: But Which Frequency to Use?” Econometric Reviews, 27 (1): 199-229.
Engle, R. and Colacito, R. (2006) “Testing and Valuing Dynamic Correlations for Asset Allocation,” Journal of Business \& Economic Statistics, 24 (2): 238-253.

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统计代写|风险建模代写Financial risk modeling代考|The statistical significance of the economic gains


统计代写|风险建模代写Financial risk modeling代考|The statistical significance of the economic gains

一种评估表格产生的经济收益的统计显着性的方法1.7−1.9是进行以下联合统计检验。对于任何目标μp和任何估计器,可以定义替代协方差预测C^吨和投资组合回报R吨+1p(C). 定义
一种吨+1C^=(R吨+1p( 傅立叶 )−R¯p( 傅立叶 ))2−(R吨+1p(C)−R¯p(C^))2.

一种吨+1d=(一种吨+1C^1,一种吨+1C^2,…,一种吨+1C^r)′,在哪里r- 多个估计器(C^1,C^2,…,C^r)是(谁)给的(RC1分钟,RC5 米一世n, RC10米一世n),(RC大号大号1米一世n,RC大号大号5米一世n,RC大号大号10米一世n)和(RCopt,一种这,ķ,一种这s在b)或我们想要测试的任何其他方法组合。我们还同时堆叠所有方法,并检查傅立叶方法的整体能力,以产生比其他方法显着的经济收益。我们写回归模型
在哪里dd是一个标量参数。系列一种吨+1C^与损失相关(即表中的负值1.7−1.9) 乘以−1回归前。我们进行单边测试H0:dd≥0, 反对H一种:dd<0. 参数dd由 GMM 使用 Bartlett HAC 协方差矩阵估计。Engle 和 Colacito (2006) 使用了类似的方法。这吨- 所有检验的统计数据都意味着拒绝零假设,因此经济收益/损失在 5% 的水平上具有统计显着性。特别是,我们注意到,当完全测试不同的方法时(r=10)即使我们不改变序列的符号,我们也会拒绝原假设一种吨+1C^与损失有关。实际上,在这种情况下,相应的吨-统计数据是−5.69,−4.44和−7.30,分别表明傅里叶方法在 1% 的水平上产生了统计上显着的经济收益。

统计代写|风险建模代写Financial risk modeling代考|Conclusion



统计代写|风险建模代写Financial risk modeling代考|References

Aitt-Sahalia, Y. 和 Mancini, L. (2008)“二次变分的样本预测之外”,“计量经济学杂志”,147 (1): 17-33。
Ait-t-Sahalia, Y.、Mykland, P. 和张。L. (2005) “在存在市场微观结构噪声的情况下多久对连续时间过程进行采样”,金融研究评论,18 (2): 351-416。
Andersen, T. 和 Bollerslev, T. (1998) “回答怀疑论者:是的,标准波动率模型确实提供了准确的预测,” 国际经济评论,39 (4): 885-905。
Bandi, FM 和 Russell, JR (2006) “从波动性中分离市场微观结构噪声”,金融经济学杂志,79 (3):655−692.
Bandi, FM 和 Russell, JR (2008) “微观结构噪声、实现方差和最优抽样”,经济研究评论,75 (2): 339-369。
Bandi, FM, Russel, JR 和 Zhu, Y. (2008) “在动态投资组合选择中使用高频数据”,计量经济学评论,27 (1-3): 163-198。
Barndorff-Nielsen, OE, Hansen, PR, Lunde, A. 和 Shephard, N. (2008a) “Multivariate Realized Kernels: Consistent Positive Semi-Definite Estimators of the Covariation of the Covariation with Noise and Non-synchronous Trading”,经济学系列第 397 号工作文件,牛津大学,英国牛津。
Barndorff-Nielsen, OE, Hansen, PR, Lunde, A. 和 Shephard, N. (2008b) “设计已实现的内核以测量存在噪声时股票价格的事后变化”,计量经济学,76 (6): 1481-1536。
Barucci, E.、Magno, D. 和 Mancino, ME(2008 年)“Forecasting Volatility with High Frequency Data in the Presence of Microstructure Noise”,工作论文,意大利佛罗伦萨大学。
De Pooter, M.、Martens, M. 和 van Dijk, D.(2008 年)“使用盘中数据预测 S\&P100 股票的每日协方差矩阵:但使用哪个频率?” 计量经济学评论,27 (1): 199-229。
Engle, R. 和 Colacito, R. (2006) “Testing and Valuing Dynamic Correlations for Asset Allocation”,商业与经济统计杂志,24 (2): 238-253。

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术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


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