trend: Trend Estimation

Description

Estimate the trend by state space model.

Usage

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

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.

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.

References

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

Examples

Run this code

# 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)

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