One of the most frequently used methods to model the autocovariance function of a second-order stationary time series is to use the parametric framework of autoregressive and moving average models developed by Box and Jenkins. However, such parametric models, though very flexible, may not always be adequate to model autocovariance functions with sharp changes. Furthermore, if the data do not follow the parametric model and are censored at a certain value, the estimation results may not be reliable. We develop a Gaussian imputation method to estimate an autocovariance structure via nonparametric estimation of the autocovariance function in order to address both censoring and incorrect model specification. We demonstrate the effectiveness of the technique in terms of bias and efficiency with simulations under various rates of censoring and underlying models. We describe its application to a time series of silicon concentrations in the Arctic.
|Original language||English (US)|
|Number of pages||19|
|Journal||Journal of Nonparametric Statistics|
|State||Published - Feb 2009|
Bibliographical noteFunding Information:
The authors would like to thank the Editor, the Associate Editor, and two referees for comments that improved this manuscript. This research was partially supported by NSF grants DMS-0504896 and CMG ATM-0620624.
- Gibbs sampling
- Nonparametric estimation
- Truncated multivariate normal distribution
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty