TSSS (version 1.3.1)

pfilterNL: Particle Filtering and Smoothing for Nonlinear State-Space Model

Description

Trend estimation by particle filter and smoother via nonlinear state-space model.

Usage

pfilterNL(y, m = 10000, lag = 20, sigma2, tau2, xrange = NULL, seed = NULL,
          plot = TRUE, ...)

Value

An object of class "pfilter" which has a plot method. This is a list with the following components:

llkhood

log-likelihood.

smooth.dist

marginal smoothed distribution of the trend \(T(i,j)\) \((i = 1,...,n, j = 1,...,7)\), where \(n\) is the length of y.

	j = 4:	50% point
	j = 3, 5:	1-sigma points (15.87% and 84.14% points)
	j = 2, 6:	2-sigma points (2.27% and 97.73% points)
	j = 1, 7:	3-sigma points (0.13% and 99.87% points)

Arguments

y

univariate time series.

m

number of particles.

lag

lag length for fixed-lag smoothing.

sigma2

observation noise variance.

tau2

system noise variance.

xrange

specify the lower and upper bounds of the distribution's range.

seed

arbitrary positive integer to generate a sequence of uniform random numbers. The default seed is based on the current time.

plot

logical. If TRUE (default), marginal smoothed distribution is plotted.

...

graphical arguments passed to the plot method.

Details

This function performs paricle filtering and smoothing for the following nonlinear state-space model;

\(x_n = \frac{1}{2} x_{n-1} + \frac{25 x_{n-1}}{x_{n-1}^2 + 1} + 8cos(1.2n) + v_n,\)	(system model)
\(y_n = \frac{x_n^2}{10} + w_n,\)	(observation model)

where \(y_n\) is a time series, \(x_n\) is the state vector. The system noise \(v_n\) and the observation noise \(w_n\) are assumed to be white noises which follow a Gaussian distribution and \(v_0\) ~ \(N(0, 5)\).

The algorithm of the particle filtering and smoothing are presented in Kitagawa (2020). For more details, please refer to Kitagawa (1996) and Doucet et al. (2001).

References

Kitagawa, G. (1996) Monte Carlo filter and smoother for non-Gaussian nonlinear state space models, J. of Comp. and Graph. Statist., 5, 1-25.

Doucet, A., de Freitas, N. and Gordon, N. (2001) Sequential Monte Carlo Methods in Praactice, Springer, New York.

Kitagawa, G. (2020) Introduction to Time Series Modeling with Applications in R. Chapman & Hall/CRC.

See Also

pfilter performs particle filtering and smoothing for linear non-Gaussian state-space model.

Examples

data(NLmodel)
x <- NLmodel[, 2]
pfilterNL(x, m = 100000, lag = 20 , sigma2 = 10.0, tau2 = 1.0,
          xrange = c(-20, 20), seed = 2019071117)