基于矩陣值因子模型的高維已實(shí)現(xiàn)協(xié)方差矩陣建模
發(fā)布時(shí)間：2019-08-03 17:16
【摘要】：隨著大數(shù)據(jù)時(shí)代的來臨,待分析數(shù)據(jù)維度越來越高,高維協(xié)方差矩陣的估計(jì)與建模已經(jīng)成為統(tǒng)計(jì)學(xué)領(lǐng)域的一個(gè)基本問題。本文提出基于Cholesky分解的可預(yù)測(cè)矩陣值因子模型,對(duì)高維已實(shí)現(xiàn)協(xié)方差矩陣進(jìn)行了建模及預(yù)測(cè)。模型有效地降低了矩陣維度,顯著減少了待估參數(shù)數(shù)目,有效地避免了估計(jì)誤差的累積,且因子分析降維使得協(xié)方差矩陣元素之間的相依關(guān)系更加清晰。實(shí)際建模結(jié)果表明,模型與VAR-LASSO方法預(yù)測(cè)誤差較為接近,但是降維效果更加明顯,待估參數(shù)數(shù)目大大減少,更加具備應(yīng)用價(jià)值。基于矩陣值因子模型構(gòu)建的投資組合收益更加貼近真實(shí)投資組合收益,而且比VAR-LASSO方法更加穩(wěn)健。
[Abstract]:With the advent of big data's era, the dimension of data to be analyzed is getting higher and higher. The estimation and modeling of high-dimensional covariance matrix has become a basic problem in the field of statistics. In this paper, a predictable matrix value factor model based on Cholesky decomposition is proposed, and the high dimensional realized covariance matrix is modeled and predicted. The model effectively reduces the matrix dimension, significantly reduces the number of parameters to be estimated, and effectively avoids the accumulation of estimation errors, and the factor analysis reduces the dimension to make the dependent relationship between the elements of the covariance matrix clearer. The actual modeling results show that the prediction error of the model is close to that of the VAR-LASSO method, but the dimensionality reduction effect is more obvious, the number of parameters to be estimated is greatly reduced, and it has more application value. The portfolio return based on matrix value factor model is closer to the real portfolio return and more robust than the VAR-LASSO method.
【作者單位】： 中央財(cái)經(jīng)大學(xué)統(tǒng)計(jì)與數(shù)學(xué)學(xué)院;中國(guó)現(xiàn)場(chǎng)統(tǒng)計(jì)研究會(huì);中國(guó)現(xiàn)場(chǎng)統(tǒng)計(jì)研究會(huì)統(tǒng)計(jì)綜合評(píng)價(jià)研究分會(huì);
【基金】：國(guó)家自然科學(xué)基金面上項(xiàng)目“穩(wěn)健投資組合選擇的并行最優(yōu)化算法研究與實(shí)現(xiàn)”(61272193) 中央財(cái)經(jīng)大學(xué)研究生科研創(chuàng)新基金項(xiàng)目“高維協(xié)方差陣建模及投資組合應(yīng)用”(201607)資助
【分類號(hào)】：O212.1
[Abstract]:With the advent of big data's era, the dimension of data to be analyzed is getting higher and higher. The estimation and modeling of high-dimensional covariance matrix has become a basic problem in the field of statistics. In this paper, a predictable matrix value factor model based on Cholesky decomposition is proposed, and the high dimensional realized covariance matrix is modeled and predicted. The model effectively reduces the matrix dimension, significantly reduces the number of parameters to be estimated, and effectively avoids the accumulation of estimation errors, and the factor analysis reduces the dimension to make the dependent relationship between the elements of the covariance matrix clearer. The actual modeling results show that the prediction error of the model is close to that of the VAR-LASSO method, but the dimensionality reduction effect is more obvious, the number of parameters to be estimated is greatly reduced, and it has more application value. The portfolio return based on matrix value factor model is closer to the real portfolio return and more robust than the VAR-LASSO method.
【作者單位】： 中央財(cái)經(jīng)大學(xué)統(tǒng)計(jì)與數(shù)學(xué)學(xué)院;中國(guó)現(xiàn)場(chǎng)統(tǒng)計(jì)研究會(huì);中國(guó)現(xiàn)場(chǎng)統(tǒng)計(jì)研究會(huì)統(tǒng)計(jì)綜合評(píng)價(jià)研究分會(huì);
【基金】：國(guó)家自然科學(xué)基金面上項(xiàng)目“穩(wěn)健投資組合選擇的并行最優(yōu)化算法研究與實(shí)現(xiàn)”(61272193) 中央財(cái)經(jīng)大學(xué)研究生科研創(chuàng)新基金項(xiàng)目“高維協(xié)方差陣建模及投資組合應(yīng)用”(201607)資助
【分類號(hào)】：O212.1
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