Author
Listed:
- Zhaoxing Gao
- Ruey S. Tsay
Abstract
This article proposes a new approach to modeling high-dimensional time series by treating a p-dimensional time series as a nonsingular linear transformation of certain common factors and idiosyncratic components. Unlike the approximate factor models, we assume that the factors capture all the nontrivial dynamics of the data, but the cross-sectional dependence may be explained by both the factors and the idiosyncratic components. Under the proposed model, (a) the factor process is dynamically dependent and the idiosyncratic component is a white noise process, and (b) the largest eigenvalues of the covariance matrix of the idiosyncratic components may diverge to infinity as the dimension p increases. We propose a white noise testing procedure for high-dimensional time series to determine the number of white noise components and, hence, the number of common factors, and introduce a projected principal component analysis (PCA) to eliminate the diverging effect of the idiosyncratic noises. Asymptotic properties of the proposed method are established for both fixed p and diverging p as the sample size n increases to infinity. We use both simulated data and real examples to assess the performance of the proposed method. We also compare our method with two commonly used methods in the literature concerning the forecastability of the extracted factors and find that the proposed approach not only provides interpretable results, but also performs well in out-of-sample forecasting. Supplementary materials for this article are available online.
Suggested Citation
Zhaoxing Gao & Ruey S. Tsay, 2022.
"Modeling High-Dimensional Time Series: A Factor Model With Dynamically Dependent Factors and Diverging Eigenvalues,"
Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1398-1414, September.
Handle:
RePEc:taf:jnlasa:v:117:y:2022:i:539:p:1398-1414
DOI: 10.1080/01621459.2020.1862668
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
Corrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:117:y:2022:i:539:p:1398-1414. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
We have no bibliographic references for this item. You can help adding them by using this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .
Please note that corrections may take a couple of weeks to filter through
the various RePEc services.