Large-dimensional factor modeling based on high-frequency observations

Pelger, Markus

doi:10.1016/j.jeconom.2018.09.004

Cited by 101 publications

(47 citation statements)

References 42 publications

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“…Despite the presence of multiple change-points, allowed both in the variance and autocorrelations of f t , the rate of convergence for χ it is almost as fast as the one derived for the stationary case, e.g., Theorem 3 of Bai (2003), and Theorem 1 of Pelger (2015) and Theorem 5 of Aït-Sahalia and Xiu (2017) in the context of factor modelling high-frequency data. We highlight that Theorem 1 derives a uniform bound on the estimation error over i = 1, .…”

Section: Estimation Of the Common And Idiosyncratic Componentsmentioning

confidence: 95%

Simultaneous multiple change-point and factor analysis for high-dimensional time series

Barigozzi

Cho

Fryźlewicz

2018

Journal of Econometrics

100

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We propose the first comprehensive treatment of high-dimensional time series factor models with multiple change-points in their second-order structure. We operate under the most flexible definition of piecewise stationarity, and estimate the number and locations of change-points consistently as well as identifying whether they originate in the common or idiosyncratic components. Through the use of wavelets, we transform the problem of change-point detection in the second-order structure of a high-dimensional time series, into the (relatively easier) problem of change-point detection in the means of high-dimensional panel data. Also, our methodology circumvents the difficult issue of the accurate estimation of the true number of factors in the presence of multiple change-points by adopting a screening procedure. We further show that consistent factor analysis is achieved over each segment defined by the change-points estimated by the proposed methodology. In extensive simulation studies, we observe that factor analysis prior to change-point detection improves the detectability of change-points, and identify and describe an interesting 'spillover' effect in which substantial breaks in the idiosyncratic components get, naturally enough, identified as change-points in the common components, which prompts us to regard the corresponding change-points as also acting as a form of 'factors'. Our methodology is implemented in the R package factorcpt, available from CRAN.

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Section: Estimation Of the Common And Idiosyncratic Componentsmentioning

confidence: 95%

Simultaneous multiple change-point and factor analysis for high-dimensional time series

Barigozzi

Cho

Fryźlewicz

2018

Journal of Econometrics

100

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“…Third, Pelger (, ) developed methods for determining the number of systematic jump factors and further proposes inference procedures for recovering the latent systematic jump factors from a large cross‐section of high‐frequency return data. The inference in Pelger (, ) is based on the quadratic variation of the jumps of the assets over the observation interval. The latter includes the contribution of the idiosyncratic jump risks, and hence, it cannot be used to separate between the null in () and alternatives that satisfy ().…”

Section: Introductionmentioning

confidence: 99%

Jump factor models in large cross‐sections

Todorov

Tauchen

2019

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We develop tests for deciding whether a large cross-section of asset prices obey an exact factor structure at the times of factor jumps. Such jump dependence is implied by standard linear factor models. Our inference is based on a panel of asset returns with asymptotically increasing cross-sectional dimension and sampling frequency, and essentially no restriction on the relative magnitude of these two dimensions of the panel. The test is formed from the high-frequency returns at the times when the risk factors are detected to have a jump. The test statistic is a cross-sectional average of a measure of discrepancy in the estimated jump factor loadings of the assets at consecutive jump times. Under the null hypothesis, the discrepancy in the factor loadings is due to a measurement error, which shrinks with the increase of the sampling frequency, while under an alternative of a noisy jump factor model this discrepancy contains also nonvanishing firmspecific shocks. The limit behavior of the test under the null hypothesis is nonstandard and reflects the strong-dependence in the cross-section of returns as well as their heteroskedasticity which is left unspecified. We further develop estimators for assessing the magnitude of firm-specific risk in asset prices at the factor jump events. Empirical application to S&P 100 stocks provides evidence for exact one-factor structure at times of big market-wide jump events. t∈[0 T ] Y t Y t includes also the quadratic variation due to the jumps in the idiosyncratic component Y (which happen outside the set T of factor jump times) which is a diagonal matrix.3 Note that b is a N × 1 vector that contains the slope coefficients (i.e., betas) for the N assets. There is no restriction on the relationship among individual assets' betas. 4 When the factors in the vector F do not have orthogonal jump components, then for τ ∈ T , we will have in general an exact multifactor model. The analysis of the paper can be extended to cover this more general setup but at the cost of significantly more involved derivations and notation. Given the empirical evidence presented in Section 6, however, such an extension seems to be of little practical relevance.

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“…Differently from their methodology, and also differently from the solution proposed by Amengual and Watson (), we can directly test the rank—say

q \leq r

—of the residual covariance (or correlation matrix) of a VAR model estimated on the factors themselves. Furthermore, our methods can be used to develop a new test for the question posed by Pelger () as to whether the factor spaces of statistical and economic factors are equal.…”

Section: Discussionmentioning

confidence: 99%

Inference in Group Factor Models With an Application to Mixed‐Frequency Data

Andreou,

Gagliardini,

Ghysels

et al. 2019

ECTA

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We derive asymptotic properties of estimators and test statistics to determine—in a grouped data setting—common versus group‐specific factors. Despite the fact that our test statistic for the number of common factors, under the null, involves a parameter at the boundary (related to unit canonical correlations), we derive a parameter‐free asymptotic Gaussian distribution. We show how the group factor setting applies to mixed‐frequency data. As an empirical illustration, we address the question whether Industrial Production (IP) is still the dominant factor driving the U.S. economy using a mixed‐frequency data panel of IP and non‐IP sectors. We find that a single common factor explains 89% of IP output growth and 61% of total GDP growth despite the diminishing role of manufacturing.

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Large-dimensional factor modeling based on high-frequency observations

Cited by 101 publications

References 42 publications

Simultaneous multiple change-point and factor analysis for high-dimensional time series

Simultaneous multiple change-point and factor analysis for high-dimensional time series

Jump factor models in large cross‐sections

Inference in Group Factor Models With an Application to Mixed‐Frequency Data

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