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

## Description

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

## Usage

 `1` ```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) + ε_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 ε_t are stationary errors with E(ε_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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```# 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 Oct. 10, 2021, 1:09 a.m.