The curve time series framework provides a convenient vehicle to accommodate
some nonstationary features into a stationary setup. We propose a new method to
identify the dimensionality of curve time series based on the dynamical
dependence across different curves. The practical implementation of our method
boils down to an eigenanalysis of a finite-dimensional matrix. Furthermore, the
determination of the dimensionality is equivalent to the identification of the
nonzero eigenvalues of the matrix, which we carry out in terms of some
bootstrap tests. Asymptotic properties of the proposed method are investigated.
In particular, our estimators for zero-eigenvalues enjoy the fast convergence
rate n while the estimators for nonzero eigenvalues converge at the standard
$\sqrt{n}$-rate. The proposed methodology is illustrated with both simulated
and real data sets.Comment: Published in at http://dx.doi.org/10.1214/10-AOS819 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Kernel smoothing techniques free the traditional parametric
estimators of volatility from the constraints related to their
specific models. In this paper the nonparametric local exponential
estimator is applied to estimate conditional volatility functions,
ensuring its nonnegativity. Its asymptotic properties are
established and compared with those for the local linear estimator.
It theoretically enables us to determine when the exponential
is expected to be superior to the linear estimator. A very strong
and novel result is achieved: the exponential estimator is
asymptotically fully adaptive to unknown conditional mean
functions. Also, our simulation study shows superior performance
of the exponential estimator.
This paper deals with the estimation of seasonal long-memory time series models in the presence of 'outliers'. It is long known that the presence of outliers can lead to undesirable effects on the statistical estimation methods, for example, substantially impacting the sample autocorrelations. Thus, the aim of this work is to propose a semiparametric robust estimator for the fractional parameters in the seasonal autoregressive fractionally integrated moving average (SARFIMA) model, through the use of a robust periodogram at both very low and seasonal frequencies. The model and some theories related to the estimation method are discussed. It is shown by simulations that the robust methodology behaves like the classical one to estimate the long-memory parameters if there are no outliers (no contamination). On the other hand, in the contaminated scenario (presence of outliers), the standard methodology leads to misleading results while the proposed method is unaffected. The methodology is applied to model and forecast
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.