smoots | R Documentation |

The `smoots`

package provides different applicable functions for the
estimation of the trend or its derivatives in equidistant time series.
The main functions include an automated bandwidth selection method for time
series with short-memory errors. With package version 1.1.0 several
functions for forecasting as well as linearity tests were added.

The `smoots`

functions are either meant for calculating nonparametric
estimates of the trend of a time series or its derivatives.

`msmooth`

is the central function of the package. It allows
the user to conduct a local polynomial regression of the trend based on
an optimal bandwidth that is obtained by an iterative plug-in algorithm.
There are also different algorithms implemented concerning the inflation rate
and other factors that can be chosen from (see also: `msmooth`

).

`dsmooth`

is a function that calculates the derivatives of the
trend after obtaining the optimal bandwidth by an iterative plug-in
algorithm. The estimates are obtained for rescaled time points on the
interval `[0, 1]`

(see also: `dsmooth`

).

`tsmooth`

is similar to `msmooth`

as it also calculates the trend
of the series. Instead of using the name of a predefined algorithm that
settles the inflation rate (and other factors), these factors can be manually
and individually adjusted as arguments in the function (see also:
`tsmooth`

).

`gsmooth`

is a standard smoothing function that applies the local
polynomial regression method. A bandwidth can be chosen freely. The estimates
are obtained for rescaled time points on the interval `[0, 1]`

(see also: `gsmooth`

).

`knsmooth`

is a standard smoothing function that applies the kernel
regression method. A bandwidth can be chosen freely
(see also: `knsmooth`

).

With the publication of the package version 1.1.0, new functions were added. These include functions for forecasting and functions for testing linearity of the deterministic trend.

`rescale`

helps rescaling the estimates of the derivatives of the
nonparametric trend function, because the estimates are obtained for rescaled
time points on the interval `[0, 1]`

and not for the actual time points
(see also: `rescale`

).

`critMatrix`

is a quick tool for the calculation of information criteria
for ARMA(`p,q`

) models with different order combinations `p`

and
`q`

. The function returns a matrix with the obtained values of the
selected criterion for the different combinations of `p`

and `q`

(see also: `critMatrix`

).

`optOrd`

is useful in combination with `critMatrix`

. It
reads a matrix equal in structure to the ones returned by `critMatrix`

and returns the optimal orders p and q. Furthermore, additional restrictions
for the selection can be imposed (see also: `optOrd`

).

`normCast`

provides means to obtain point forecasts as well as
forecasting intervals for a given series under the assumption that it follows
an ARMA(`p,q`

) model and that its innovations are normally distributed
(see also: `normCast`

).

`bootCast`

can also be used to calculate point forecasts and forecasting
intervals, if the series of interest follows an ARMA(`p,q`

) model.
However, the main difference is that this function should be applied, if the
distribution of the innovations is unknown or explicitly non-Gaussian,
because the underlying bootstrap process does not need a distribution
assumption. In spite of this advantage, it also needs significantly more
computation time. Therefore, with version 1.1.1, the bootstrap can now be
conducted in parallel for an improved performance (see also:
`bootCast`

).

`trendCast`

uses a `smoots`

object that is the output of a trend
estimation and calculates point forecasts of the trend. Forecasting intervals
are omitted for reasons that are explained within the function's
documentation (see also: `trendCast`

).

`modelCast`

calculates the point forecasts and forecasting intervals of
a trend-stationary series. Based on a `smoots`

object that is the output
of a trend estimation, `trendCast`

is applied to the estimated trend,
whereas either `normCast`

or `bootCast`

is applied to the
residuals (see also: `modelCast`

).

`rollCast`

is a backtesting function for Semi-ARMA models. A given
series is divided into in-sample and out-of-sample observations, where the
in-sample is used to fit a Semi-ARMA model. One-step rolling forecasts and
the corresponding forecasting intervals are then obtained for the
out-of-sample observations. The quality of the model is then assessed via
a comparison of the true out-of-sample observations with the point forecasts
and forecasting intervals. Different quality criteria are calculated and
returned (see also: `modelCast`

).

`confBounds`

calculates the confidence bounds of the estimated trend
or of the estimated derivative of the trend at a predefined confidence
level. A graphic of the confidence bounds alongside a previously chosen
constant or parametric illustration of the estimated series is created. With
this plot it can be tested graphically if the deterministic trend is constant
or if it follows a parametric polynomial model. Furthermore, it can also be
tested, if the derivatives of the trend are constant (see also:
`confBounds`

).

The package includes four datasets: `gdpUS`

(see also:
`gdpUS`

) that has data concerning the quarterly US GDP between
Q1 1947-01 and Q2 2019, `tempNH`

(see also: `tempNH`

) with
mean monthly Northern Hemisphere temperature changes from 1880 to 2018,
`dax`

(see also: `dax`

) with daily financial time series
data of the German stock index (DAX) from 1990 to July 2019 and `vix`

(see also: `vix`

) with daily financial time series data of the
CBOE Volatility Index (VIX) from 1990 to July 2019.

The package is distributed under the General Public License v3 ([GPL-3](https://tldrlegal.com/license/gnu-general-public-license-v3-(gpl-3))).

Yuanhua Feng (Department of Economics, Paderborn University),

Author of the Algorithms

Website: https://wiwi.uni-paderborn.de/en/dep4/feng/Dominik Schulz (Research Assistant) (Department of Economics, Paderborn University),

Package Creator and Maintainer

Feng, Y., Gries, T. and Fritz, M. (2020). Data-driven local polynomial for the trend and its derivatives in economic time series. Journal of Nonparametric Statistics, 32:2, 510-533.

Feng, Y., Gries, T., Letmathe, S. and Schulz, D. (2019). The smoots package in R for semiparametric modeling of trend stationary time series. Discussion Paper. Paderborn University. Unpublished.

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