pfilter: Particle Filtering and Smoothing

In TSSS: Time Series Analysis with State Space Model

Particle Filtering and Smoothing

Description

Trend estimation by particle filter and smoother.

Usage

pfilter(y, m = 10000, model = 0, lag = 20, initd = 0, sigma2, tau2,
        alpha = 0.99, bigtau2 = NULL, init.sigma2 = 1, xrange = NULL,
        seed = NULL, plot = TRUE, ...)

Arguments

y	univariate time series.
m	number of particles.
model	model for the system noise. 0: normal distribution 1: Cauchy distribution 2: Gaussian mixture distribution \alpha N(0, \tau^2) + (1 - \alpha) N(0, T^2), where N is the normal density.
lag	lag length for fixed-lag smoothing.
initd	type of initial state distribution. 0: normal distribution 1: uniform distribution 2: Cauchy distribution 3: fixed point (default value = 0)
sigma2	observation noise variance \sigma^2.
tau2	system noise variance \tau^2 for model = 0 or dispersion parameter for model = 1.
alpha	mixture weight \alpha. (valid for model = 2)
bigtau2	variance of the second component T^2. (valid for model = 2)
init.sigma2	variance for initd = 0 or dispersion parameter of initial state distribution for initd = 2.
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 particle filtering and smoothing for the first order trend model;

x_n = x_{n-1} + v_n,	(system model)
y_n = x_n + 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 or a Cauchy distribution, and non-Gaussian distribution, respectively.

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

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)

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 Practice, Springer, New York.

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

See Also

pfilterNL performs particle filtering and smoothing for nonlinear non-Gaussian state-space model.

Examples

data(PfilterSample)
y <- PfilterSample

## Not run: 
pfilter(y, m = 100000, model = 0, lag = 20, initd = 0, sigma2 = 1.048,
        tau2 = 1.4e-2, xrange = c(-4, 4), seed = 2019071117)

pfilter(y, m = 100000, model = 1, lag = 20 , initd = 0, sigma2 = 1.045,
        tau2 = 3.53e-5, xrange = c(-4, 4), seed = 2019071117)

pfilter(y, m = 100000, model = 2, lag = 20 , initd = 0, sigma2 = 1.03,
        tau2 = 0.00013, alpha = 0.991, xrange = c(-4, 4), seed = 2019071117)

## End(Not run)

TSSS documentation built on Sept. 29, 2023, 9:07 a.m.