trend {TSSS}

Trend Estimation

Description

Estimate the trend by state space model.

Usage

trend(y, trend.order = 1, tau2.ini = NULL, delta, plot = TRUE, ...)

Arguments

y

a univariate time series.

trend.order

trend order.

tau2.ini

initial estimate of variance of the system noise \tau^2. If tau2.ini = NULL, the most suitable value is chosen in \tau^2 = 2^{-k}.

delta

search width (for tau2.ini is specified (not NULL)) .

plot

logical. If TRUE (default), trend component and residuals are plotted.

...

graphical arguments passed to plot.trend.

Details

The trend model can be represented by a state space model

x_n = Fx_{n-1} + Gv_n,

y_n = Hx_n + w_n,

where F, G and H are matrices with appropriate dimensions. We assume that v_n and w_n are white noises that have the normal distributions N(0,\tau^2) and N(0, \sigma^2), respectively.

Value

An object of class "trend", which is a list with the following components:

trend

trend component.

residual

residuals.

tau2

variance of the system noise \tau^2.

sigma2

variance of the observational noise \sigma^2.

llkhood

log-likelihood of the model.

aic

AIC.

cov

covariance matrix of smoother.

References

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

Examples

# The daily maximum temperatures for Tokyo
data(Temperature)
trend(Temperature, trend.order = 1, tau2.ini = 0.223, delta = 0.001)

trend(Temperature, trend.order = 2)