R: Scaling Law Bahaviour

ScalingLawPlot {fBasics} | R Documentation

## Scaling Law Bahaviour

### Description

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

### Usage

    scalinglawPlot(x, span = ceiling(log(length(x)/252)/log(2)), doplot = TRUE,
        labels = TRUE, trace = TRUE, ...)

### Arguments

`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`.
`span` | an integer value, determines for the `qqgaussPlot` the plot range, by default 5, and for the `scalingPlot` a reasonable number of of points for the scaling range, by default daily data with 252 business days per year are assumed.
`trace` | a logical value. Should the computation be traced?
`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`.
`...` | arguments to be passed.

### 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.

### Value

returns a list with the following components: `Intercept`, `Exponent` the scaling exponent, and `InverseExponent` its inverse value.

### Author(s)

Diethelm Wuertz for the Rmetrics R-port.

### References

Taylor S.J. (1986); Modeling Financial Time Series, John Wiley and Sons, Chichester.

### Examples

    ## data -
       SPI <- LPP2005REC[, "SPI"]
       plot(SPI, type = "l", col = "steelblue", main = "SP500")
       abline(h = 0, col = "grey")

    ## teffectPlot -
       # Scaling Law Effect:
       scalinglawPlot(SPI)

[Package fBasics version 3042.89 Index]