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矩阵分位数因子模型AI 解读

This paper introduces a matrix quantile factor model for matrix-valued data with low-rank structure. We estimate the row and column factor spaces via minimizing the empirical check loss function with orthogonal rotation constraints. We show that the estimates converge at rate (min{p1p2,p2T,p1T})−1/2 in the average Frobenius norm, where p1, p2 and T are the row dimensionality, column dimensionality and length of the matrix sequence, respectively. This rate is faster than that…

高频价格停滞因子与波动率估计AI 解读

In this article, we propose a price staleness factor model that accounts for pervasive market friction across assets and incorporates relevant covariates. Using large-panel high-frequency data, we derive the maximum likelihood estimators of the regression coefficients, the nonstationary factors, and their loading parameters. These estimators recover the time-varying price staleness probabilities. We develop asymptotic theory in which both the dimension d and the sampling…

高维广义矩阵因子模型的估计与推断AI 解读

This article introduces a nonlinear generalized matrix factor model, moving beyond the linear-Gaussian framework to accommodate a broader class of response models typically handled via logit, probit, Poisson, or Tobit structures. We introduce a novel Lagrange multiplier method carefully tailored to ensure that the penalized likelihood function is locally concave around the true factor and loading parameters. This leads to central limit theorems of the estimated factors and…

矩阵因子增强回归AI 解读

As matrix-variate observations are increasingly available, to incorporate the interplay between the multi-cross-sections, we introduce a matrix-factor-augmented regression model (M-FARM) that proposes to predict ahead of time with factors of matrix predictors augmented in the regression. We show that the estimation error in the factor matrices, estimated by the projection procedure in the first step, enters into the estimation error of the regression parameters and the…

潜在双向因子结构矩阵时间序列的在线变点检测AI 解读

This paper proposes a novel methodology for the online detection of changepoints in the factor structure of large matrix time series. Our approach is based on the well-known fact that, in the presence of a changepoint, the number of spiked eigenvalues in the second moment matrix of the data increases (e.g., in the presence of a change in the loadings, or if a new factor emerges). Based on this, we propose two families of procedures—one based on the fluctuations of partial…

矩阵因子分析：从最小二乘到迭代投影AI 解读

In this article, we study large-dimensional matrix factor models and estimate the factor loading matrices and factor score matrix by minimizing square loss function. Interestingly, the resultant estimators coincide with the Projected Estimators (PE) in Yu et al. which was proposed from the perspective of simultaneous reduction of the dimensionality and the magnitudes of the idiosyncratic error matrix. In other word, we provide a least-square interpretation of the PE for the…

矩阵序列应采用单向还是双向因子模型？AI 解读

This paper investigates the issue of determining the dimensions of row and column factor spaces in matrix-valued data. Exploiting the eigen-gap in the spectrum of sample second moment matrices of the data, we propose a family of randomised tests to check whether a one-way or two-way factor structure exists or not. Our tests do not require any arbitrary thresholding on the eigenvalues, and can be applied with (virtually) no restrictions on the relative rate of divergence of…

高维矩阵因子模型的投影估计AI 解读

In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor analysis for matrix series to that of a lower-dimensional tensor. This method also reduces the magnitudes of the idiosyncratic error components, thereby increasing the signal-to-noise ratio, because the projection matrix linearly filters the…

无矩约束的高维因子分析AI 解读

Large-dimensional factor model has drawn much attention in the big-data era, to reduce the dimensionality and extract underlying features using a few latent common factors. Conventional methods for estimating the factor model typically requires finite fourth moment of the data, which ignores the effect of heavy-tailedness and thus may result in unrobust or even inconsistent estimation of the factor space and common components. In this article, we propose to recover the…

基于随机扰动的因子个数秩估计AI 解读

Summary We introduce a random-perturbation-based rank estimator of the number of factors of a large-dimensional approximate factor model. An expansion of the rank estimator demonstrates that the random perturbation reduces the biases due to the persistence of the factor series and the dependence between the factor and error series. A central limit theorem for the rank estimator with convergence rate higher than root $n$ gives a new hypothesis-testing procedure for both…

因子成分与特异成分的经验过程AI 解读

The distributions of the common and idiosyncratic components for an individual variable are important in forecasting and applications. However, they are not identified with low-dimensional observations. Using the recently developed theory for large dimensional approximate factor model for large panel data, the common and idiosyncratic components can be estimated consistently. Based on the estimated common and idiosyncratic components, we construct the empirical processes for…

长期依赖下含近单位根解释变量的非参数回归AI 解读

We study the nonparametric estimation of a regression function with nonstationary (integrated or nearly integrated) covariates and the error series of the regressor process following a fractional integrated autoregressive moving average model. A local linear estimation method is developed to estimate the unknown regression function. The asymptotic results of the resulting estimator at both interior points and boundaries are obtained. The asymptotic distribution is mixed…