Consistently determining the number of factors in multivariate volatility modelling

Xia, Qiang; Xu, Wangli; Zhu, Lixing

doi:10.5705/ss.2013.252

Cited by 41 publications

(39 citation statements)

References 15 publications

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“…RRE . This estimate is in spirit similar to the one proposed by Xia et al (), but with a different ridge value. It is quite simple and easy to implement.…”

Section: Test Statistic Construction and Relevant Propertiessupporting

confidence: 79%

Enhancements of Non‐parametric Generalized Likelihood Ratio Test: Bias Correction and Dimension Reduction

Niu¹,

Guo²,

Zhu

2017

Scandinavian J Statistics

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Nonparametric generalized likelihood ratio test is popularly used for model checking for regressions. However, there are two issues that may be the barriers for its powerfulness. First, the bias term in its liming null distribution causes the test not to well control type I error and thus Monte Carlo approximation for critical value determination is required. Second, it severely suffers from the curse of dimensionality due to the use of multivariate nonparametric function estimation.The purpose of this paper is thus two-fold: a bias-correction is suggested to this test and a dimension reduction-based model-adaptive enhancement is recommended to promote the power performance. The proposed test still possesses the Wilks phenomenon, and the test statistic can converge to its limit at a much faster rate and is much more sensitive to alternative models than the original nonparametric generalized likelihood ratio test as if the dimension of covariates were one. Simulation studies are conducted to evaluate the finite sample performance and to compare with other popularly used tests. A real data analysis is conducted for illustration.

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“…RRE . This estimate is in spirit similar to the one proposed by Xia et al (), but with a different ridge value. It is quite simple and easy to implement.…”

Section: Test Statistic Construction and Relevant Propertiessupporting

confidence: 79%

Enhancements of Non‐parametric Generalized Likelihood Ratio Test: Bias Correction and Dimension Reduction

Niu¹,

Guo²,

Zhu

2017

Scandinavian J Statistics

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“…The discussion so far assumes that r is known, but that is not so in practice. To obtain a consistent estimator of r , we adopt the ridge‐type ratio estimator (Chang et al ., ; Xia et al ., ). In particular, an estimator of r can be obtained through an optimization problem, i.e.

\overset{false^}{r} = arg min_{j = 1, \dots, p - 1} \frac{{\overset{λ}{true}}_{j + 1} + C_{n}}{{\overset{λ}{true}}_{j} + C_{n}},

where C n is a positive constant.…”

Section: Latent Factors Recoverymentioning

confidence: 99%

“…Xia et al . () suggested C n =(10 n ) −1 log ( n ) for selecting the number of factors when modelling the volatility of multivariate time series. As will be seen later, we use a simulation study to assess the performance of C n = n −1 log ( n ) and C n = n −1 log { log ( n )} in finite sample.…”

Section: Latent Factors Recoverymentioning

confidence: 99%

Modelling Non-Stationary Multivariate Time Series of Counts via Common Factors

Wang

2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary We develop a new parameter‐driven model for multivariate time series of counts. The time series is not necessarily stationary. We model the mean process as the product of modulating factors and unobserved stationary processes. The former characterizes the long‐run movement in the data, whereas the latter is responsible for rapid fluctuations and other unknown or unavailable covariates. The unobserved stationary processes evolve independently of the past observed counts and might interact with each other. We express the multivariate unobserved stationary processes as a linear combination of possibly low dimensional factors that govern the contemporaneous and serial correlation within and across the observed counts. Regression coefficients in the modulating factors are estimated via pseudo‐maximum‐likelihood estimation, and identification of common factor(s) is carried out through eigenanalysis on a positive definite matrix that pertains to the autocovariance of the observed counts at non‐zero lags. Theoretical validity of the two‐step estimation procedure is documented. In particular, we establish consistency and asymptotic normality of the pseudo‐maximum‐likelihood estimator in the first step and the convergence rate of the second‐step estimator. We also present an exhaustive simulation study to examine the finite sample performance of the estimators, and numerical results corroborate our theoretical findings. Finally, we illustrate the use of the proposed model through an application to the numbers of National Science Foundation fundings awarded to seven research universities from January 2001 to December 2012.

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“…Xia et al () propose a ridge‐type ratio estimate (RRE), which modified Lam and Yao ()'s method by adding a positive value c to the eigenvalues λ i ,

\overset{r}{true} = \underset{1 \leq i \leq p}{arg min} \frac{{\overset{λ}{true}}_{i + 1} + c}{{\overset{λ}{true}}_{i} + c} .

When i ≥ r and c is chosen to be larger than

{\overset{λ}{true}}_{i + 1}

, the minimum over i = 1,..., p is equivalent to the minimum over i = 1,..., r 0 . They propose c = log n /(10 n ) for practitioners.…”

Section: Simulation Studiesmentioning

confidence: 99%

“…In Lam and Yao (2012), r 0 D p=2 is suggested. Xia et al (2015) propose a ridge-type ratio estimate (RRE), which modified Lam and Yao (2012)'s method by adding a positive value c to the eigenvalues i ,…”

Section: Information Criterionmentioning

confidence: 99%

Factor Modelling for High‐Dimensional Time Series: Inference and Model Selection

Chan

Yau

2016

Journal Time Series Analysis

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Analysis of high‐dimensional time series data is of increasing interest among different fields. This article studies high‐dimensional time series from a dimension reduction perspective using factor modelling. Statistical inference is conducted using eigen‐analysis of a certain non‐negative definite matrix related to autocovariance matrices of the time series, which is applicable to fixed or increasing dimension. When the dimension goes to infinity, the rate of convergence and limiting distributions of estimated factors are established. Using the limiting distributions of estimated factors, a high‐dimensional final prediction error criterion is proposed to select the number of factors. Asymptotic properties of the criterion are illustrated by simulation studies and real applications.

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Consistently determining the number of factors in multivariate volatility modelling

Cited by 41 publications

References 15 publications

Enhancements of Non‐parametric Generalized Likelihood Ratio Test: Bias Correction and Dimension Reduction

Enhancements of Non‐parametric Generalized Likelihood Ratio Test: Bias Correction and Dimension Reduction

Modelling Non-Stationary Multivariate Time Series of Counts via Common Factors

Factor Modelling for High‐Dimensional Time Series: Inference and Model Selection

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