SDD: AnRPackage for Serial Dependence Diagrams

Abstract

Detecting and measuring lag-dependencies is very important in time-series analysis. This study is commonly carried out by focusing on the linear lag-dependencies via the well-known autocorrelogram. However, in practice, there are many situations in which the autocorrelogram fails because of the nonlinear structure of the serial dependence. To cope with this problem, in this paper the R package SDD is introduced. Among the available approaches to analyze the lag-dependencies in an omnibus way, the SDD package considers the autodependogram and some of its variants. The autodependogram, defined by computing the classical Pearson χ 2-statistic at various lags, is a graphical device recently proposed in the literature to analyze lag-dependencies. The concept of reproducibility probability, and several density-based measures of divergence, are considered to define the variants of the autodependogram. An application to daily returns of the Swiss Market Index is also presented to exemplify the use of the package.

Bivariate discrete beta Kernel graduation of mortality data

“…An alternative approach for obtaining a bivariate discrete beta kernel could have been to parametrize, with respect to the mode, one of the various versions of the bivariate beta distribution available in the literature (see, e.g., Olkin andLiu 2003 andGupta et al 2011), and discretize it on the support X × Y. Instead, for the sake of simplicity, we have preferred the product kernel given by (3); this is not a restriction if we think that when Gaussian kernels are used in the bivariate case, the product of two simple univariate Gaussian distributions is often favored (see, e.g., Härdle 1990, Scott 1992, and Bagnato et al 2014a). …”