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Conference Paper: Spectral distribution of the sample covariance of high-dimensional time series with unit roots
Title | Spectral distribution of the sample covariance of high-dimensional time series with unit roots |
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Authors | |
Issue Date | 2019 |
Citation | The 3rd International Conference on Econometrics and Statistics (EcoSta 2019), National Chung Hsing University (NCHU), Taichung, Taiwan, 25-27 June 2019 How to Cite? |
Abstract | The aim is to study the empirical spectral distributions of two sample-covariance-type matrices associated with high-dimensional time series with unit roots. The first matrix is $S = XX'/T$; where $X$ is an $n imes T$ data matrix with rows represented by $n$ i.i.d. copies of $T$ consecutive observations of a difference-stationary process. The second matrix is $W = nint_0^1 B_n (t)B_n (t)' dt$; where $B_n(t)$ is an $n$-dimensional vector with i.i.d. Brownian motion components. We show that, as $n$ and $T$ diverge to infinity proportionally, the two distributions weakly converge to non-random limits. The limit corresponding to $S$ has a density $f(x)$ that decays as $x^{-3/2}$ when $x oinfty$. The limit corresponding to $W$ is a Feller-Pareto distribution. |
Description | Session EO019: New developments in time series analysis - no. E0300 / A0300 This Conference is co-organized by the Working Group on Computational and Methodological Statistics (CMStatistics), the network of Computational and Financial Econometrics (CFENetwork), the Department of Applied Mathematics and the Institute of Statistics of the National Chung Hsing University. |
Persistent Identifier | http://hdl.handle.net/10722/296464 |
DC Field | Value | Language |
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dc.contributor.author | Wang, C | - |
dc.contributor.author | Onatski, A | - |
dc.date.accessioned | 2021-02-25T08:33:34Z | - |
dc.date.available | 2021-02-25T08:33:34Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | The 3rd International Conference on Econometrics and Statistics (EcoSta 2019), National Chung Hsing University (NCHU), Taichung, Taiwan, 25-27 June 2019 | - |
dc.identifier.uri | http://hdl.handle.net/10722/296464 | - |
dc.description | Session EO019: New developments in time series analysis - no. E0300 / A0300 | - |
dc.description | This Conference is co-organized by the Working Group on Computational and Methodological Statistics (CMStatistics), the network of Computational and Financial Econometrics (CFENetwork), the Department of Applied Mathematics and the Institute of Statistics of the National Chung Hsing University. | - |
dc.description.abstract | The aim is to study the empirical spectral distributions of two sample-covariance-type matrices associated with high-dimensional time series with unit roots. The first matrix is $S = XX'/T$; where $X$ is an $n imes T$ data matrix with rows represented by $n$ i.i.d. copies of $T$ consecutive observations of a difference-stationary process. The second matrix is $W = nint_0^1 B_n (t)B_n (t)' dt$; where $B_n(t)$ is an $n$-dimensional vector with i.i.d. Brownian motion components. We show that, as $n$ and $T$ diverge to infinity proportionally, the two distributions weakly converge to non-random limits. The limit corresponding to $S$ has a density $f(x)$ that decays as $x^{-3/2}$ when $x oinfty$. The limit corresponding to $W$ is a Feller-Pareto distribution. | - |
dc.language | eng | - |
dc.relation.ispartof | The 3rd International Conference on Econometrics and Statistics (EcoSta 2019) | - |
dc.title | Spectral distribution of the sample covariance of high-dimensional time series with unit roots | - |
dc.type | Conference_Paper | - |
dc.identifier.email | Wang, C: stacw@hku.hk | - |
dc.identifier.authority | Wang, C=rp02404 | - |
dc.identifier.hkuros | 299221 | - |