Forecasting Function for Nonparametric Trend Functions
an object returned by either
the forecasting horizon; the values m(n + 1) to m(n + h)
will be predicted; is set to
the forecasting method;
a logical value; if set to
additional arguments for the standard plot function, e.g.,
This function is part of the
smoots package and was implemented under
version 1.1.0. The underlying theory is based on the additive nonparametric
y_t = m(x_t) + ε_t,
where y_t is the observed time series with equidistant design, 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.
The purpose of this function is the forecasting of future values based on a nonparametric regression model. Following the proposition in Fritz et al. (2020), point predictions can be conducted separately for the nonparametric trend function m(x_t) and the stationary part ε_t. The sum of both forecasts is then the forecast of y_t. With this function, only the forecast with respect to m(x_t) is computable. Now assume that the variance of the error in the local polynomial forecasts is negligible when calculating the forecasting intervals. We define the forecast for time point n + k, k = 1, 2, ..., h, by
hat[m](x_[n + k]) = hat[m](x_n) + Dk * δ_m,
where δ_m is equal to hat[m](x_n) - hat[m](x_[n - 1]) and D is a dummy variable. If D = 1, a linear extrapolation is applied. For D = 0, hat[m](x_n) is the predicted value.
To make use of this function, an object of class
smoots can be given
as input. However, since the discussed approach is only valid for the
estimated trend function, only objects created by
the trend was estimated, will be appropriate input objects.
With the input argument
h, a positive integer can be given to the
function that represents the forecasting horizon, i.e. how many future values
are to be estimated. Via the argument
np.fcast the value of the dummy
variable D can be specified and thus the forecasting method. For
np.fcast = "lin", D = 1 is applied, whereas for
np.fcast = "const", D is set to 0.
By means of the argument
plot that can be either set to the logical
FALSE, a simple plot of the original series
alongside the local polynomial estimates as well as the forecasted values can
be either generated or suppressed.
The function always returns a vector of forecasted values ordered from
n + 1 to n + h. Depending on the setting of the argument
plot, a generic plot of the results may be generated. Furthermore,
additional arguments of the standard plot function can be passed to this
function as well to adjust the generated plot.
A numeric vector is always returned with the forecasted values. Depending on the setting for the argument plot, a generic plot might be created.
Yuanhua Feng (Department of Economics, Paderborn University),
Author of the Algorithms
Dominik Schulz (Research Assistant) (Department of Economics, Paderborn
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.
Feng, Y., Gries, T., Fritz, M., Letmathe, S. and Schulz, D. (2020). Diagnosing the trend and bootstrapping the forecasting intervals using a semiparametric ARMA. Discussion Paper. Paderborn University. Unpublished.
Fritz, M., Forstinger, S., Feng, Y., and Gries, T. (2020). Forecasting economic growth processes for developing economies. Unpublished.
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