coconots-package {coconots}

Concolution-closed Models for Time Series

Description

Functions to analyse time series consisting of low counts are provided. The focus in the current version is on practical models that can capture first and higher-order dependence based on the work of Joe (1996). Both equidispersed and overdispersed marginal distributions of data can be modelled. Regression effects can be included. Fast and efficient procedures for likelihood based inference and probabilistic forecasting are provided as well as useful tools for model validation and diagnostics.

Details

The package allows simulation of convolution-closed count time series models with the cocoSim function. Model fitting is performed with the cocoReg routine. By passing a cocoReg-type object, the S3 method predict computes the one-step ahead forecasting distribution. cocoBoot, cocoPit, cocoScore, and cocoResid provide routines for model assessment. The main usage of the package is illustrated within the cocoReg function chapter. For more details and examples of the functions see the respective sections within this vignette.

By default, our functions make use of an RCPP implementation. However, users with a running Julia installation can choose to call Julia in the background to run their functions by specifiying it in the R function input. This option is particularly useful for the regression (cocoReg), where a complex likelihood function must be numerically evaluated to obtain parameter estimates. By leveraging Julia's automatic differentiation capabilities, our functions can take advantage of numerical gradients, leading to increased numerical stability and faster convergence.

As we find both, the Julia and RCPP implementations produce qualitatively similar results in all our tests, we have decided to use the RCPP implementation as the default option to make our package accessible to non-Julia users.

Author(s)

Maintainer: Manuel Huth <[e-mail]>

References

Czado, C., Gneiting, T. and Held, L. (2009) Predictive model assessment for count data. Biometrics 65, 1254–61.

Gneiting, T. and Raftery, A. E. (2007) Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association, 102:359-378.

R.C. Jung, A.R. Tremayne (2006) Coherent forecasting in integer time series models. International Journal of Forecasting 22, 223–238

Jung, R. C. and Tremayne, A. R. (2011) Convolution-closed models for count time series with applications. Journal of Time Series Analysis, 32, 3, 268–280.

Jung, Robert C., Brendan P. M. McCabe, and Andrew R. Tremayne. (2016). Model validation and diagnostics. In Handbook of Discrete Valued Time Series. Edited by Richard A. Davis, Scott H. Holan, Robert Lund and Nalini Ravishanker. Boca Raton: Chapman and Hall, pp. 189–218.

Joe, H. (1996) Time series models with univariate margins in the convolution-closed infinitely divisible class. Journal of Applied Probability, 664–677.

Tsay, R. S. (1992) Model checking via parametric bootstraps in time series analysis. Applied Statistics 41, 1–15.

Westgren, A. (1916) Die Veraenderungsgeschwindigkeit der lokalen Teilchenkonzentration in kollioden Systemen (Erste Mitteilung). Arkiv foer Matematik, Astronomi och Fysik, 11, 1–24.