# PCT: Percentage Change Transformation In TSPred: Functions for Benchmarking Time Series Prediction

## Description

The `PCT()` function returns a transformation of the provided time series using a Percentage Change transformation. `PCT.rev()` reverses the transformation.

## Usage

 ```1 2 3``` ```PCT(x) PCT.rev(p,x0) ```

## Arguments

 `x` A numeric vector or univariate time series of class `ts`. `p` A numeric vector or univariate time series of percentage changes. Possibly returned by `PCT()`. `x0` Initial value/observation of `x` (`x[1]`). First known non-transformed value used to recursively obtain the original series.

## Details

The Percentage Change transformation is given approximately by

log( x[2:n] / x[1:(n-1)] ) = log( x[2:n] ) - log( x[1:(n-1)] )

where `n=length(x)`.

## Value

A vector of length `length(x)-1` containing the transformed values.

## Author(s)

Rebecca Pontes Salles

## References

R.H. Shumway and D.S. Stoffer, 2010, Time Series Analysis and Its Applications: With R Examples. 3rd ed. 2011 edition ed. New York, Springer.

`DIF`,`detrend`, `MAS`, `LT`, `BCT`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```data(NN5.A) ts <- na.omit(NN5.A[,10]) length(ts) pct <- PCT(ts) length(pct) x0 <- ts[1] pct.rev <- PCT.rev(pct,x0) x <- c(x0,pct.rev) all(round(x,4)==round(ts,4)) ```