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具有共同随机趋势的高维门限因子模型AI 解读

We study inference for threshold regression in the context of a large factor model with common stochastic trends. We develop a Least Squares estimator for the threshold level, deriving almost sure rates of convergence and proposing a novel way of constructing confidence intervals based on a randomized test. Our confidence intervals are constructed using the rates of convergence of the estimated threshold level, and no limiting distribution is required. We also develop a…

资产定价模型中 Alpha 的一般随机化检验AI 解读

We propose a methodology to test for the null hypothesis that the alphas of a panel of asset returns are jointly equal to zero in a linear factor pricing model with observable and tradable factors — that is, the null of “zero alpha”. The test is based on equation-by-equation estimation, using a randomized version of the estimated alphas, which only requires rates of convergence. The distinct features of the proposed methodology are that it does not require the estimation of…

动态状态空间 HAR 模型AI 解读

The Heterogeneous AutoRegressive model for the logs of Realised Volatility (HARL) has established itself as the benchmark specification for modelling and forecasting return volatility, owing to its parsimony and ability to capture the strong persistence typically observed in RV. To address potential concerns such as measurement errors, nonlinearities, and non-spherical residuals, numerous variants of the baseline HARL model have been developed in the literature. This paper…

随机系数自回归模型的实时变点监测AI 解读

We propose a family of weighted statistics based on the CUSUM process of the WLS residuals for the online detection of changepoints in a Random Coefficient Autoregressive model, using both the standard CUSUM and the Page-CUSUM process. We derive the asymptotics under the null of no changepoint for all possible weighing schemes, including the case of the standardized CUSUM, for which we derive a Darling–Erdös-type limit theorem; our results guarantee the procedure-wise size…

基于估计函数的弱条件位置时间序列模型断点推断AI 解读

Drawing on Godambe’s theory of estimating functions, we present a statistical approach for identifying breaks in time series dynamics under weak assumptions. We assume a parametric form for the conditional mean but make no specific assumptions about the data-generating process (DGP), nor about the other conditional moments. The cumulative sum (CUSUM) statistics and segmentation of minimal cost (SMC) statistics that we consider depend on a sequence of weights that influence…

基于重加权 CUSUM 与否决式决策规则的快速在线变点检测AI 解读

We study on-line changepoint detection in the context of a linear regression model, developing two novel contributions. Firstly, we propose a class of heavily weighted statistics based on the CUSUM process of the regression residuals, which are specifically designed to ensure timely detection of breaks occurring early on during the monitoring horizon. Secondly, we develop a class of composite statistics using different weighting schemes; the decision rule to mark a…

利用经验能量距离检测函数型数据变点AI 解读

We propose a novel family of test statistics to detect the presence of changepoints in a sequence of dependent, possibly multivariate, functional-valued observations. Our approach allows to test for a very general class of changepoints, including the “classical” case of changes in the mean, and even changes in the whole distribution. Our statistics are based on a generalisation of the empirical energy distance; we propose weighted functionals of the energy distance process,…

随机系数模型中的最大化似然比检验AI 解读

Summary In a recent contribution, we developed a family of cumulative sum-based change-point tests in the context of a random coefficient autoregressive model of order 1. In the current paper, we complement the results in that contribution by studying the (maximally selected) likelihood ratio statistic. We show that this has power versus breaks occurring even as close as periods from the beginning/end of sample; moreover, the use of quasi-maximum likelihood-based estimates…

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…

重尾非平稳多元时间序列中的推断AI 解读

We study inference on the common stochastic trends in a non-stationary, $N$-variate time series $y_{t}$, in the possible presence of heavy tails. We propose a novel methodology which does not require any knowledge or estimation of the tail index, or even knowledge as to whether certain moments (such as the variance) exist or not, and develop an estimator of the number of stochastic trends $m$ based on the eigenvalues of the sample second moment matrix of $y_{t}$. We study…

异方差随机系数自回归模型的变点检测AI 解读

We propose a family of CUSUM-based statistics to detect the presence of changepoints in the deterministic part of the autoregressive parameter in a Random Coefficient Autoregressive (RCA) sequence. Our tests can be applied irrespective of whether the sequence is stationary or not, and no prior knowledge of stationarity or lack thereof is required. Similarly, our tests can be applied even when the error term and the stochastic part of the autoregressive coefficient are non…

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…

大型非平稳数据集的共同趋势检验AI 解读

We propose a testing-based procedure to determine the number of common trends in a large nonstationary dataset. Our procedure is based on a factor representation, where we determine whether there are (and how many) common factors (i) with linear trends, and (ii) with stochastic trends. Cointegration among the factors is also permitted. Our analysis is based on the fact that those largest eigenvalues of a suitably scaled covariance matrix of the data corresponding to the…

大规模面板中异质性与协整的推断理论AI 解读

This paper provides an estimation and testing framework to assess the presence and the extent of slope heterogeneity and cointegration when the units are a mixture of spurious and/or cointegrating regressions. We propose two moment estimators for the degree of heterogeneity (measured by the dispersion of the slope coefficients around their average) and for the fraction of spurious regressions, which are found to be consistent in the whole parameter space. Based on these…

随机系数自回归模型中系数随机性的检验AI 解读

We propose a test to discern between an ordinary autoregressive model, and a random coefficient one. To this end, we develop a full-fledged estimation theory for the variances of the idiosyncratic innovation and of the random coefficient, based on a two-stage WLS approach. Our results hold irrespective of whether the series is stationary or nonstationary, and, as an immediate result, they afford the construction of a test for ”relevant” randomness. Further, building on these…

确定因子数量的随机化序贯程序AI 解读

This article proposes a procedure to estimate the number of common factors k in a static approximate factor model. The building block of the analysis is the fact that the first k eigenvalues of the covariance matrix of the data diverge, while the others stay bounded. On the grounds of this, we propose a test for the null that the ith eigenvalue diverges, using a randomized test statistic based directly on the estimated eigenvalue. The test only requires minimal assumptions…

随机系数面板模型中的统计推断AI 解读

This paper studies the asymptotics of the Weighted Least Squares (WLS) estimator of the autoregressive root in a panel Random Coefficient Autoregression (RCA). We show that, in an RCA context, there is no “unit root problem” : the WLS estimator is always asymptotically normal, irrespective of the average value of the autoregressive root, of whether the autoregressive coefficient is random or not, and of the presence and degree of cross dependence. Our simulations indicate…

检验随机变量的矩是否有限AI 解读

This paper proposes a test to verify whether the kth moment of a random variable is finite. We use the fact that, under general assumptions, sample moments either converge to a finite number or diverge to infinity according as the corresponding population moment is finite or not. Building on this, we propose a test for the null that the kth moment does not exist. Since, by construction, our test statistic diverges under the null and converges under the alternative, we…

异质面板中因子结构的推断AI 解读

This paper develops an estimation and testing framework for a stationary large panel model with observable regressors and unobservable common factors. We allow for slope heterogeneity and for correlation between the common factors and the regressors. We propose a two stage estimation procedure for the unobservable common factors and their loadings, based on Common Correlated Effects estimator and the Principal Component estimator. We also develop two tests for the null of no…

面板因子序列的自助法AI 解读

This paper studies the asymptotic validity of sieve bootstrap for nonstationary panel factor series. Two main results are shown. Firstly, a bootstrap Invariance Principle is derived pointwise in i, obtaining an upper bound for the order of truncation of the AR polynomial that depends on n and T. Consistent estimation of the long run variances is also studied for (n,T)→∞. Secondly, joint bootstrap asymptotics is also studied, investigating the conditions under which the…

异质性面板中的微观与宏观协整AI 解读

We consider the issue of cross-sectional aggregation in nonstationary and heterogeneous panels where each unit cointegrates. We derive asymptotic properties of the aggregate estimate, and necessary and sufficient conditions for cointegration to hold in the aggregate relationship. We then analyze the case when cointegration does not carry through the aggregation process, and we investigate whether the violation of the formal conditions for perfect aggregation can still lead…

异质面板中的共同随机趋势与聚合AI 解读

In nonstationary heterogeneous panels where the number of units is finite and where each unit cointegrates, a large number of conditions needs to be satisfied for cointegration to be preserved in the aggregate relationship. In reality, the conditions most likely will not hold. This paper takes a closer look at what happens when the conditions are violated. In this case, the question of whether an aggregate relationship is observationally equivalent to a cointegrating…