Abstract
State space modelling is an efficient and flexible method for statistical inference of a broad class of time series and other data. This paper describes an R package KFAS for state space modelling with the observations from an exponential family, namely Gaussian, Poisson, binomial, negative binomial and gamma distributions. After introducing the basic theory behind Gaussian and non-Gaussian state space models, an illustrative example of Poisson time series forecasting is provided. Finally, a comparison to alternative R packages suitable for non-Gaussian time series modelling is presented.
Highlights
State space models offer a unified framework for modeling several types of time series and other data
Structural time series, autoregressive integrated moving average (ARIMA) models, simple regression, generalized linear mixed models, and cubic spline smoothing are just some examples of the statistical models which can be represented as a state space model
Assuming that the prior distribution of β is defined as diffuse, the diffuse likelihood of this state space model corresponds to a restricted maximum likelihood (REML)
Summary
State space models offer a unified framework for modeling several types of time series and other data. Petris and Petrone (2011) and Tusell (2011) introduce and review some of the contributed R (R Core Team 2017) packages available on the Comprehensive R Archive Network (CRAN) for Gaussian state space modeling. Several new additions have emerged on CRAN Most of these packages use one package or multiple packages reviewed in Tusell (2011) for filtering and smoothing and add new user interfaces and functionality for certain types of models. In this paper we first introduce the basic theory related to state space modeling, and proceed to show the main aspects of KFAS in more detail, illustrate its functionality by applying it to real life datasets, and make a short comparison between KFAS and other potentially useful packages for non-Gaussian time series modeling
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