We consider the problem of using an autoregressive (AR) approximation to estimate the spectral density function and the
- Award ID(s):
- 1651995
- NSF-PAR ID:
- 10232139
- Date Published:
- Journal Name:
- Journal of Financial Econometrics
- ISSN:
- 1479-8409
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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n ×n autocovariance matrix based on stationary dataX 1, … ,X n . The consistency of the autoregressive spectral density estimator has been proven since the 1970s under a linearity assumption. We extend these ideas to the nonlinear setting, and give an application to estimating then ×n autocovariance matrix. Under mild assumptions on the underlying dependence structure and the orderp of the fittedAR (p ) model, we are able to show that the autoregressive spectral estimate and the associated AR‐based autocovariance matrix estimator are consistent. We are also able to establish an explicit bound on the rate of convergence of the proposed estimators. -
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This article is categorized under:
Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
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