LPTime: Fits Vector Autoregressive model on LP transformed time series data
Description
Accepts possibly non-Gaussian non-linear univariate (stationary) time
series data; converts it to multivariate LP-transformed series and fits a vector autoregressive
(VAR) model.
Usage
LPTime(z, exo = NULL, m = 3, p = 10)
Arguments
z
Endogenous time series to be included in the VAR model.
exo
Exogenous time series to be included in the VAR model.
m
The number of required LP-transformations.
p
Lag-order of autoregression.
Value
A matrix of the estimated autoregressive coefficients obtained from
LP-VAR model.
Details
LPTime algorithm models univariate stationary nonlinear process $X(t)$ via
linear modelling of the multivariate time series:
$$\mbox{Vec}(X)(t) = [\mbox{T}_{1}[X](t),\ldots, \mbox{T}_{m}[X](t)]^{T},$$
where each of the time series components $\mbox{T}_{j}[X](t)$ are polynomials of
rank transformed $X(t)$.
It fits vector autoregressive model of the form
$$\mbox{ Vec(T}[X])(t) = \sum_{k=1}^{p} A(k ; p)\, \mbox{Vec(T}[X])(t-k) \;+\; \epsilon(t).$$
where $\epsilon(t)$ is multivariate mean zero Gaussian white noise with covariance $\Sigma_{p}$.
References
Mukhopadhyay, S. and Parzen, E. (2013).Nonlinear time series
modeling by LPTime, nonparametric empirical learning. arXiv:1308.0642.