fBasics (version 2110.79)

acfPlot: Autocorrelation Function Plots

Description

Returns plots of autocorrelations including the autocorrelation function ACF, the partial ACF, the lagged ACF, and the Taylor effect plot. The functions to display stylized facts are: ll{ acfPlot autocorrelation function plot, pacfPlot partial autocorrelation function plot, lacfPlot lagged autocorrelation function plot, teffectPlot Taylor effect plot.}

Usage

acfPlot(x, labels = TRUE, ...)
pacfPlot(x, labels = TRUE, ...) 
lacfPlot(x, n = 12, lag.max = 20, type = c("returns", "values"),
    labels = TRUE, ...)
teffectPlot(x, deltas = seq(from = 0.2, to = 3, by = 0.2), lag.max = 10, 
    ymax = NA, standardize = TRUE, labels = TRUE, ...)

Arguments

deltas

the exponents, a numeric vector, by default ranging from 0.2 to 3.0 in steps of 0.2.

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.

lag.max

maximum lag for which the autocorrelation should be calculated, an integer.

n

an integer value, the number of lags.

standardize

a logical value. Should the vector x be standardized?

type

[lacf] - a character string which specifies the type of the input series, either "returns" or series "values". In the case of a return series as input, the required value series is computed by cumulating the financial returns:

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.

ymax

maximum y-axis value on plot, is.na(ymax) TRUE, then the value is selected automatically.

...

arguments to be passed.

Value

• acfPlot, pacfplot, return an object of class "acf", see acf. lacfPlot returns a list with the following two elements: Rho, the autocorrelation function, lagged, the lagged correlations. teffectPlot returns a numeric matrix of order deltas by max.lag with the values of the autocorrelations.

Details

Autocorrelation Functions: The functions acfPlot and pacfPlot, plot and estimate autocorrelation and partial autocorrelation function. The functions allow to get a first view on correlations within the time series. The functions are synonyme function calls for R's acf and pacf from the the ts package. Taylor Effect: The "Taylor Effect" describes the fact that absolute returns of speculative assets have significant serial correlation over long lags. Even more, autocorrelations of absolute returns are typically greater than those of squared returns. From these observations the Taylor effect states, that that the autocorrelations of absolute returns to the the power of delta, abs(x-mean(x))^delta reach their maximum at delta=1. The function teffect explores this behaviour. A plot is created which shows for each lag (from 1 to max.lag) the autocorrelations as a function of the exponent delta. In the case that the above formulated hypothesis is supported, all the curves should peak at the same value around delta=1.

References

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

Ding Z., Granger C.W.J., Engle R.F. (1993); A long memory property of stock market returns and a new model, Journal of Empirical Finance 1, 83.

Examples

## data - 
   # require(MASS)
   plot(SP500, type = "l", col = "steelblue", main = "SP500")
   abline(h = 0, col = "grey")

## teffectPlot -
   # Taylor Effect:
   teffectPlot(SP500)