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因子数量的频带估计AI 解读

We introduce consistent estimators for the number of shocks driving large-dimensional dynamic factor models. Our estimator can be applied to single frequencies and specific frequency bands, making it suitable for disentangling shocks affecting dynamic models with a factor model representation. Noticeably, our estimator requires the time-series and cross-section size to diverge simultaneously without any constraint, and it is free of nuisance parameters, such as penalization…

广义动态因子模型的推断理论AI 解读

We provide the asymptotic distributional theory for the so-called General or Generalized Dynamic Factor Model (GDFM), laying the foundations for an inferential approach in the GDFM analysis of high-dimensional time series. By exploiting the duality between common shocks and dynamic loadings, we derive the asymptotic distribution and associated standard errors for a class of estimators for common shocks, dynamic loadings, common components, and impulse response functions. We…

具有因子结构的大型面板的稳健估计AI 解读

This article studies estimation of linear panel regression models with heterogeneous coefficients using a class of weighted least squares estimators, when both the regressors and the error possibly contain a common latent factor structure. Our theory is robust to the specification of such a factor structure because it does not require any information on the number of factors or estimation of the factor structure itself. Moreover, our theory is efficient, in certain…

一般多变量时间序列谱密度估计的渐近理论AI 解读

We derive uniform convergence results of lag-window spectral density estimates for a general class of multivariate stationary processes represented by an arbitrary measurable function of iid innovations. Optimal rates of convergence, that hold as both the time series and the cross section dimensions diverge, are obtained under mild and easily verifiable conditions. Our theory complements earlier results, most of which are univariate, which primarily concern in-probability,…

无限维因子空间动态因子模型的渐近分析AI 解读

Factor models, all particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forni et al., (2000), have become extremely popular in the theory and practice of large panels of time series data. The asymptotic properties (consistency and rates) of the corresponding estimators have been studied in Forni et al. (2004). Those estimators, however, rely on Brillinger’s concept of dynamic principal components, and thus involve two-sided filters, which leads to…

具有长记忆状态变量的仿射期限结构模型AI 解读

We develop a Gaussian discrete time essentially affine term structure model with long memory state variables. This feature reconciles the strong persistence observed in nominal yields and inflation with the theoretical implications of affine models, especially for long maturities. We characterize in closed-form the dynamic and cross-sectional implications of long memory for our model. We explain how long memory can naturally arise within the term structure of interest rates,…

无限维因子空间动态因子模型的单边表示AI 解读

Factor model methods recently have become extremely popular in the theory and practice of large panels of time series data. Those methods rely on various factor models which all are particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forniet al. (2000). That paper, however, rests on Brillinger’s dynamic principal components. The corresponding estimators are two-sided filters whose performance at the end of the observation period or for forecasting…

ARCH 无穷阶模型的伪极大似然估计AI 解读

Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH$(\infty)$ processes are established. The conditions are shown to hold in case of exponential and hyperbolic decay in the ARCH weights, though in the latter case a faster decay rate is required for the central limit theorem than for the law of large numbers. Particular parameterizations are discussed.

ARCH(∞) 模型的平稳性与记忆AI 解读

We establish the necessary and sufficient conditions for covariance stationarity of ARCH(∞), for both the levels and the squares. The result applies to any form of the conditional variance coefficients. This includes GARCH(p,q) and also specifications with hyperbolically decaying coefficients, such as the autoregressive coefficients of the autoregressive fractionally integrated moving average model. The covariance stationarity condition for the levels rules out long memory…