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高维静态与动态因子模型的识别理论AI 解读

High dimensional factor models can involve thousands of parameters. The Jacobian matrix for identification is of a large dimension. It can be difficult and numerically inaccurate to evaluate the rank of such a Jacobian matrix. We reduce the identification problem to a small rank problem, which is easy to check. The identification conditions allow both linear and nonlinear restrictions. Under reasonable assumptions for high dimensional factor models, the small rank conditions…

静态因子的主成分估计与识别AI 解读

It is known that the principal component estimates of the factors and the loadings are rotations of the underlying latent factors and loadings. We study conditions under which the latent factors can be estimated asymptotically without rotation. We derive the limiting distributions for the estimated factors and factor loadings when N and T are large and make precise how identification of the factors affects inference based on factor augmented regressions. We also consider…

高维因子模型的统计分析AI 解读

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We establish not only consistency but also the rate of convergence and the limiting distributions. Five different sets of identification conditions are considered. We show that the distributions of the MLE estimators depend on the identification…

条件马尔可夫链及其在经济时间序列分析中的应用AI 解读

Motivated by the great moderation in major US macroeconomic time series, we formulate the regime switching problem through a conditional Markov chain. We model the long-run volatility change as a recurrent structure change, while short-run changes in the mean growth rate as regime switches. Both structure and regime are unobserved. The structure is assumed to be Markovian. Conditioning on the structure, the regime is also Markovian, whose transition matrix is…

数据丰富环境中的工具变量估计AI 解读

We consider estimation of parameters in a regression model with endogenous regressors. The endogenous regressors along with a large number of other endogenous variables are driven by a small number of unobservable exogenous common factors. We show that the estimated common factors can be used as instrumental variables and they are more efficient than the observed variables in our framework. Whereas standard optimal generalized method of moments estimator using a large number…

存在截面依赖的面板单位根检验：进一步研究AI 解读

An effective way to control for cross-section correlation when conducting a panel unit root test is to remove the common factors from the data. However, there remain many ways to use the defactored residuals to construct a test. In this paper, we use the panel analysis of nonstationarity in idiosyncratic and common components (PANIC) residuals to form two new tests. One estimates the pooled autoregressive coefficient, and one simply uses a sample moment. We establish their…

面板数据均值与方差的共同断点AI 解读

This paper establishes the consistency of the estimated common break point in panel data. Consistency is obtainable even when a regime contains a single observation, making it possible to quickly identify the onset of a new regime. We also propose a new framework for developing the limiting distribution for the estimated break point, and show how to construct confidence intervals. The least squares method is used for estimating breaks in means and the quasi-maximum…

扩散指数预测中的提升法AI 解读

Abstract In forecasting and regression analysis, it is often necessary to select predictors from a large feasible set. When the predictors have no natural ordering, an exhaustive evaluation of all possible combinations of the predictors can be computationally costly. This paper considers ‘boosting’ as a methodology of selecting the predictors in factor‐augmented autoregressions. As some of the predictors are being estimated, we propose a stopping rule for boosting to prevent…

含全球随机趋势的面板协整AI 解读

This paper studies estimation of panel cointegration models with cross-sectional dependence generated by unobserved global stochastic trends. The standard least squares estimator is, in general, inconsistent owing to the spuriousness induced by the unobservable I(1) trends. We propose two iterative procedures that jointly estimate the slope parameters and the stochastic trends. The resulting estimators are referred to respectively as CupBC (continuously-updated and…

使用定向预测变量预测经济时间序列AI 解读

This paper studies two refinements to the method of factor forecasting. First, we consider the method of quadratic principal components that allows the link function between the predictors and the factors to be non-linear. Second, the factors used in the forecasting equation are estimated in a way to take into account that the goal is to forecast a specific series. This is accomplished by applying the method of principal components to 'targeted predictors' selected using…

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因子模型中原始冲击数量的确定AI 解读

A widely held but untested assumption underlying macroeconomic analysis is that the number of shocks driving economic fluctuations, q, is small. In this article we associate q with the number of dynamic factors in a large panel of data. We propose a methodology to determineq without having to estimate the dynamic factors. We first estimate a VAR in r static factors, where the factors are obtained by applying the method of principal components to a large panel of data, then…

扩散指数预测的置信区间与因子增强回归推断AI 解读

We consider the situation when there is a large number of series, N, each with T observations, and each series has some predictive ability for some variable of interest. A methodology of growing interest is first to estimate common factors from the panel of data by the method of principal components and then to augment an otherwise standard regression with the estimated factors. In this paper, we show that the least squares estimates obtained from these factor-augmented…

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时间序列数据的偏度、峰度与正态性检验AI 解读

We present the sampling distributions for the coefficient of skewness, kurtosis, and a joint test of normality for time series observations. We show that when the data are serially correlated, consistent estimates of three-dimensional long-run covariance matrices are needed for testing symmetry or kurtosis. These tests can be used to make inference about any conjectured coefficients of skewness and kurtosis. In the special case of normality, a joint test for the skewness…

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This paper develops a new methodology that makes use of the factor structure of large dimensional panels to understand the nature of nonstationarity in the data. We refer to it as PANIC-Panel Analysis of Nonstationarity in Idiosyncratic and Common components. PANIC can detect whether the nonstationarity in a series is pervasive, or variable-specific, or both. It can determine the number of independent stochastic trends driving the common factors. PANIC also permits valid…

高维因子模型的推断理论AI 解读

This paper develops an inferential theory for factor models of large dimensions. The principal components estimator is considered because it is easy to compute and is asymptotically equivalent to the maximum likelihood estimator (if normality is assumed). We derive the rate of convergence and the limiting distributions of the estimated factors, factor loadings, and common components. The theory is developed within the framework of large cross sections ("N") and a large time…

多重结构变化模型的计算与分析AI 解读

Abstract In a recent paper, Bai and Perron ( 1998 ) considered theoretical issues related to the limiting distribution of estimators and test statistics in the linear model with multiple structural changes. In this companion paper, we consider practical issues for the empirical applications of the procedures. We first address the problem of estimation of the break dates and present an efficient algorithm to obtain global minimizers of the sum of squared residuals. This…

确定近似因子模型中的因子数AI 解读

In this paper we develop some econometric theory for factor models of large dimensions. The focus is the determination of the number of factors (r), which is an unresolved issue in the rapidly growing literature on multifactor models. We first establish the convergence rate for the factor estimates that will allow for consistent estimation of r. We then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria. The…

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伪结构断点现象札记AI 解读

When the disturbances of a regression model follow an I (1) process there is a tendency to estimate a break point in the middle of the sample, even though a break point does not actually exist. In this note, we provide a mathematical proof for this phenomenon.

含多重结构变化的线性模型：估计与检验AI 解读

This paper develops the statistical theory for testing and estimating multiple change points in regression models. The rate of convergence and limiting distribution for the estimated parameters are obtained. Several test statistics are proposed to determine the existence as well as the number of change points. A partial structural change model is considered. The authors study both fixed and shrinking magnitudes of shifts. In addition, the models allow for serially correlated…