Mixing Conditions, Central Limit Theorems, and Invariance Principles: A Survey of the Literature with Some New Results on Heteroscedastic Sequences
This article is a survey of the main results on the central limit theorem (CLT) and its invariance principle (IP) for mixing sequences that have been obtained in the probabilistic literature in the last fifty years or so with a view towards econometric applications. Each of these theorems specifies a set of moment, dependence, and heterogeneity conditions on the underlying sequence that ensures the validity of CLT and IP. Special emphasis is paid to the case in which the underlying sequence has just barely infinite variance, since this case is relevant to econometrics applications that involve high-frequency financial data. Moreover, two new results on IPs that apply to heteroscedastic sequences are obtained. The first IP applies to sequences whose variances evolve over time in a polynomial-like fashion, whereas the second IP concerns sequences that experience a single variance break at some point within the sample.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 30 (2011)
Issue (Month): 1 ()
|Contact details of provider:|| Web page: http://www.tandfonline.com/LECR20|
|Order Information:||Web: http://www.tandfonline.com/pricing/journal/LECR20|
When requesting a correction, please mention this item's handle: RePEc:taf:emetrv:v:30:y:2011:i:1:p:88-108. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
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.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.