On nonparametric density estimation for multivariate linear long-memory processes

ABSTRACT

We consider nonparametric estimation of the density function and its derivatives for multivariate linear processes with long-range dependence. In a first step, the asymptotic distribution of the multivariate empirical process is derived. In a second step, the asymptotic distribution of kernel density estimators and their derivatives is obtained.

KEYWORDS:

• Kernel density estimation
• Linear process
• Long-range dependence
• Multivariate
• Multivariate time series

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G07
• 62H12
• 62M09
• 62M10

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