# Scaling law behaviour

`plot-scalinglawPlot.Rd`

Evaluates the scaling exponent of a financial return series and plots the scaling law.

## Arguments

- x
an uni- or multivariate return series of class

`"timeSeries"`

or any other object which can be transformed by the function`as.timeSeries()`

into an object of class`"timeSeries"`

.- span
an integer value, determines for the

`qqgaussPlot`

the plot range, by default 5, and for the`scalingPlot`

a reasonable number of points for the scaling range, by default daily data with 252 business days per year are assumed.- doplot
a logical value. Should a plot be displayed?

- labels
a logical value. Whether or not x- and y-axes should be automatically labeled and a default main title should be added to the plot. By default

`TRUE`

.- trace
a logical value. Should the computation be traced?

- ...
arguments to be passed.

## Value

a list with the following components:

- Intercept
intercept,

- Exponent
the scaling exponent,

- InverseExponent
the inverse of the scaling component.

## Details

**Scaling Behavior:**

The function `scalingPlot`

plots the scaling law of financial
time series under aggregation and returns an estimate for the scaling
exponent. The scaling behavior is a very striking effect of the
foreign exchange market and also other markets expressing a regular
structure for the volatility. Considering the average absolute
return over individual data periods one finds a scaling power law
which relates the mean volatility over given time intervals
to the size of these intervals. The power law is in many cases
valid over several orders of magnitude in time. Its exponent
usually deviates significantly from a Gaussian random walk model
which implies 1/2.

## Examples

```
## data -
data(LPP2005REC, package = "timeSeries")
SPI <- LPP2005REC[, "SPI"]
plot(SPI, type = "l", col = "steelblue", main = "SP500")
abline(h = 0, col = "grey")
## teffectPlot -
# Scaling Law Effect:
scalinglawPlot(SPI)
#>
#> Scaling Law: SPI
#> Plot Intercept 0.7135344
#> Plot Slope 0.5213102
#> Plot Inverse Slope 1.918244
#>
```