pfilterNL | R Documentation |
Trend estimation by particle filter and smoother via nonlinear state-space model.
pfilterNL(y, m = 10000, lag = 20, sigma2, tau2, xrange = NULL, seed = NULL,
plot = TRUE, ...)
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 |
... |
graphical arguments passed to the |
This function performs particle 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).
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
|
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 Practice, Springer, New York.
Kitagawa, G. (2020) Introduction to Time Series Modeling with Applications in R. Chapman & Hall/CRC.
pfilter
performs particle filtering and smoothing for linear
non-Gaussian state-space model.
data(NLmodel)
x <- NLmodel[, 2]
pfilterNL(x, m = 100000, lag = 20 , sigma2 = 10.0, tau2 = 1.0,
xrange = c(-20, 20), seed = 2019071117)
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