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高维协整的迹检验AI 解读

This paper studies Johansen’s (J. Econom. Dynam. Control 12 (1988) 231–254) trace test for cointegration in high-dimensional data. We show that when both cross-sectional and temporal dimension of the data go to infinity proportionally, the shifted and scaled modified trace statistic converges to a Gaussian random variable. We give explicit formulae for the shift and scale parameters as well as for the mean and variance of the Gaussian limit. Monte Carlo analysis shows…

具有局部单位根的数据中的伪因子AI 解读

This paper extends the spurious factor analysis of Onatski and Wang (2021, Spurious factor analysis. Econometrica , 89(2), 591–614.) to high-dimensional data with heterogeneous local-to-unit roots. We find a spurious factor phenomenon similar to that observed in the data with unit roots. Namely, the “factors” estimated by the principal components analysis converge to principal eigenfunctions of a weighted average of the covariance kernels of the demeaned Ornstein–Uhlenbeck…

伪因子分析AI 解读

This paper draws parallels between the principal components analysis of factorless high‐dimensional nonstationary data and the classical spurious regression. We show that a few of the principal components of such data absorb nearly all the data variation. The corresponding scree plot suggests that the data contain a few factors, which is corroborated by the standard panel information criteria. Furthermore, the Dickey–Fuller tests of the unit root hypothesis applied to the…

极端典型相关与高维协整分析AI 解读

We prove that the extreme squared sample canonical correlations between a random walk and its own innovations almost surely converge to the upper and lower boundaries of the support of the Wachter distribution when the sample size and the dimensionality go to infinity proportionally. This result is used to derive previously unknown analytic expressions for the Bartlett-type correction coefficients for Johansen’s trace and maximum eigenvalue tests in a high-dimensional…

大维VAR协整检验的替代渐近分析AI 解读

Johansen's (1988,1991) likelihood ratio test for cointegration rank of a vector autoregression (VAR) depends only on the squared sample canonical correlations between current changes and past levels of a simple transformation of the data. We study the asymptotic behavior of the empirical distribution of those squared canonical correlations when the number of observations and the dimensionality of the VAR diverge to infinity simultaneously and proportionally. We find that the…

因子数设定错误时估计平方误差的渐近分析AI 解读

In this paper, we obtain asymptotic approximations to the squared error of the least squares estimator of the common component in large approximate factor models with possibly misspecified number of factors. The approximations are derived under both strong and weak factors asymptotics assuming that the cross-sectional and temporal dimensions of the data are comparable. We develop consistent estimators of these approximations and propose to use them for model comparison and…

大型 DSGE 模型的因子分析AI 解读

SUMMARY We study the workings of the factor analysis of high‐dimensional data using artificial series generated from a large, multi‐sector dynamic stochastic general equilibrium (DSGE) model. The objective is to use the DSGE model as a laboratory that allows us to shed some light on the practical benefits and limitations of using factor analysis techniques on economic data. We explain in what sense the artificial data can be thought of having a factor structure, study the…

弱影响因子下大型因子模型主成分估计量的渐近理论AI 解读

This paper introduces a drifting-parameter asymptotic framework to derive accurate approximations to the finite sample distribution of the principal components (PC) estimator in situations when the factors’ explanatory power does not strongly dominate the explanatory power of the cross-sectionally and temporally correlated idiosyncratic terms. Under our asymptotics, the PC estimator is inconsistent. We find explicit formulae for the amount of the inconsistency, and propose…

白噪声中的单位根AI 解读

We show that the empirical distribution of the roots of the vector autoregression (VAR) of order p fitted to T observations of a general stationary or nonstationary process converges to the uniform distribution over the unit circle on the complex plane, when both T and p tend to infinity so that (ln T )/ p → 0 and p 3 / T → 0. In particular, even if the process is a white noise, nearly all roots of the estimated VAR will converge by absolute value to unity. For fixed p , we…

利用特征值经验分布确定因子数AI 解读

We develop a new estimator of the number of factors in the approximate factor models. The estimator works well even when the idiosyncratic terms are substantially correlated. It is based on the fact, established in the paper, that any finite number of the largest "idiosyncratic" eigenvalues of the sample covariance matrix cluster around a single point. In contrast, all the "systematic" eigenvalues, the number of which equals the number of factors, diverge to infinity. The…