tsDyn (version 11.0.4.1)

aar: Additive nonlinear autoregressive model

Description

Additive nonlinear autoregressive model.

Usage

aar(x, m, d=1, steps=d, series)

Value

An object of class nlar, subclass aar, i.e. a list with mostly internal structures for the fitted gam object.

Arguments

x

time series

m, d, steps

embedding dimension, time delay, forecasting steps

series

time series name (optional)

Author

Antonio, Fabio Di Narzo

Details

Nonparametric additive autoregressive model of the form: $$ x_{t+s} = \mu + \sum_{j=1}^{m} s_j(x_{t-(j-1)d}) $$

where \(s_j\) are nonparametric univariate functions of lagged time series values. They are represented by cubic regression splines. \(s_j\) are estimated together with their level of smoothing using routines in the mgcv package (see references).

References

Wood, mgcv:GAMs and Generalized Ridge Regression for R. R News 1(2):20-25 (2001)

Wood and Augustin, GAMs with integrated model selection using penalized regression splines and applications to environmental modelling. Ecological Modelling 157:157-177 (2002)

Examples

#fit an AAR model:
mod <- aar(log(lynx), m=3)
#Summary informations:
summary(mod)
#Diagnostic plots:
plot(mod)