rescale | R Documentation |

The estimation functions of the `smoots`

package estimate the
nonparametric trend function or its derivatives on the rescaled
time interval `[0, 1]`

. With this function the derivative estimates can
be rescaled in accordance with a given vector with time points.

```
rescale(y, x = seq_along(y), v = 1)
```

`y` |
a numeric vector or matrix with the derivative estimates obtained
for time points on the interval |

`x` |
a numeric vector of length |

`v` |
the order of derivative that is implemented for |

The derivative estimation process is based on the additive time series model

`y_t = m(x_t) + \epsilon_t,`

where `y_t`

is the observed time series with equidistant design,
`x_t`

is the rescaled time on `[0, 1]`

, `m(x_t)`

is a smooth and
deterministic trend function and `\epsilon_t`

are stationary errors
with E(eps_[t]) = 0 (see also Beran and Feng, 2002). Since the estimates of
the main smoothing functions in `smoots`

are obtained with regard to the
rescaled time points `x_t`

, the derivative estimates returned by these
functions are valid for `x_t`

only. Thus, by passing the returned
estimates to the argument `y`

, a vector with the actual time points to
the argument `x`

and the order of derivative of `y`

to the argument
`v`

, a rescaled estimate series is calculated and returned. The function
can also be combined with the numeric output of `confBounds`

.

Note that the trend estimates, even though they are also obtained for the
rescaled time points `x_t`

, are still valid for the actual time points.

A numeric vector with the rescaled derivative estimates is returned.

Dominik Schulz (Research Assistant) (Department of Economics, Paderborn University),

Package Creator and Maintainer

```
data <- smoots::gdpUS
Xt <- log(data$GDP)
time <- seq(from = 1947.25, to = 2019.5, by = 0.25)
d_est <- smoots::dsmooth(Xt)
ye_rescale <- smoots::rescale(d_est$ye, x = time, v = 1)
plot(time, ye_rescale, type = "l", main = "", ylab = "", xlab = "Year")
```

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