# knsmooth: Estimation of Nonparametric Trend Functions via Kernel... In smoots: Nonparametric Estimation of the Trend and Its Derivatives in TS

 knsmooth R Documentation

## Estimation of Nonparametric Trend Functions via Kernel Regression

### Description

This function estimates the nonparametric trend function in an equidistant time series with Nadaraya-Watson kernel regression.

### Usage

knsmooth(y, mu = 1, b = 0.15, bb = c(0, 1))


### Arguments

y

a numeric vector that contains the time series data ordered from past to present.

mu

an integer 0, 1, 2, ... that represents the smoothness parameter of the second order kernel function that will be used; is set to 1 by default.

 Number (mu) Kernel 0 Uniform Kernel 1 Epanechnikov Kernel 2 Bisquare Kernel 3 Triweight Kernel ... ...
b

a real number 0 < b < 0.5; represents the relative bandwidth that will be used for the smoothing process; is set to 0.15 by default.

bb

can be set to 0 or 1; the parameter controlling the bandwidth used at the boundary; is set to 0 by default.

 Number (bb) Estimation procedure at boundary points 0 Fixed bandwidth on one side with possible large bandwidth on the other side at the boundary 1 The k-nearest neighbor method will be used

### Details

The trend is estimated based on the additive nonparametric regression model for an equidistant time series

y_t = m(x_t) + \epsilon_t,

where y_t is the observed time series, x_t is the rescaled time on the interval [0, 1], m(x_t) is a smooth and deterministic trend function and \epsilon_t are stationary errors with E(\epsilon_t) = 0.

This function is part of the package smoots and is used for the estimation of trends in equidistant time series. The applied method is a kernel regression with arbitrarily selectable second order kernel, relative bandwidth and boundary method. Especially the chosen bandwidth has a strong impact on the final result and has thus to be selected carefully. This approach is not recommended by the authors of this package.

### Value

The output object is a list with different components:

b

the chosen (relative) bandwidth; input argument.

bb

the chosen bandwidth option at the boundaries; input argument.

mu

the chosen smoothness parameter for the second order kernel; input argument.

n

the number of observations.

orig

the original input series; input argument.

res

a vector with the estimated residual series.

ye

a vector with the estimates of the nonparametric trend.

### Author(s)

• Yuanhua Feng (Department of Economics, Paderborn University),
Author of the Algorithms

• Dominik Schulz (Research Assistant) (Department of Economics, Paderborn University),
Package Creator and Maintainer

### References

Feng, Y. (2009). Kernel and Locally Weighted Regression. Verlag für Wissenschaft und Forschung, Berlin.

### Examples

# Logarithm of test data
test_data <- gdpUS
y <- log(test_data$GDP) #Applied knmooth function for the trend with two different bandwidths trend1 <- knsmooth(y, mu = 1, b = 0.28, bb = 1)$ye
trend2 <- knsmooth(y, mu = 1, b = 0.05, bb = 1)\$ye

# Plot of the results
t <- seq(from = 1947, to = 2019.25, by = 0.25)
plot(t, y, type = "l", xlab = "Year", ylab = "log(US-GDP)", bty = "n",
lwd = 2,
main = "Estimated trend for log-quarterly US-GDP, Q1 1947 - Q2 2019")
points(t, trend1, type = "l", col = "red", lwd = 1)
points(t, trend2, type = "l", col = "blue", lwd = 1)
legend("bottomright", legend = c("Trend (b = 0.28)", "Trend (b = 0.05)"),
fill = c("red", "blue"), cex = 0.6)
title(sub = expression(italic("Figure 1")), col.sub = "gray47",
cex.sub = 0.6, adj = 0)



smoots documentation built on Sept. 11, 2023, 9:07 a.m.