acfPlot autocorrelation function plot,
pacfPlot partial autocorrelation function plot,
ccfPlot cross correlation function plot,
lacfPlot lagged autocorrelation function plot,
lmacfPlot long memory autocorrelation function plot,
logpdfPlot logarithmic density plots,
qqgaussPlot Gaussian quantile quantile plot,
scalinglawPlot scaling behavior plot,
teffectPlot Taylor effect plot. }acfPlot(x, labels = TRUE, ...)
pacfPlot(x, labels = TRUE, ...)
ccfPlot(x, y, lag.max = max(2, floor(10*log10(length(x)))), type =
c("correlation", "covariance", "partial"), labels = TRUE, ...)
lacfPlot(x, n = 12, lag.max = 20, labels = TRUE, ...)
lmacfPlot(x, lag.max = max(2, floor(10*log10(length(x)))), ci = 0.95,
type = c("both", "acf", "hurst"), labels = TRUE, details = TRUE, ...)
logpdfPlot(x, n = 50, type = c("lin-log", "log-log"), doplot = TRUE,
labels = TRUE, ...)
qqgaussPlot(x, span = 5, col = "steelblue4", labels = TRUE, ...)
scalinglawPlot(x, span = ceiling(log(length(x)/252)/log(2)), doplot = TRUE,
labels = TRUE, details = TRUE, ...)
teffectPlot(x, deltas = seq(from = 0.2, to = 3, by = 0.2), lag.max = 10,
ymax = NA, standardize = TRUE, labels = TRUE, ...)"steelblue".TRUE.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 witx be standardized?"correlation", "covariance",
or "partial" denoting which type of correlation should be
plotted,
[lmacf] -
a character string, either "both", as.vector into a numeric vector.is.na(ymax) TRUE, then
the value is selected automatically.logpdfPlot
returns a list with the following components: breaks,
histogram mid-point breaks; counts, histogram counts;
fbreaks, fitted Gaussian breaks; fcounts, fitted
Gaussian counts.
qqgaussPlot
returns a Gaussian Quantile-Quantile Plot.
scalingPlot
returns a list with the following components: exponent,
the scaling exponent, a numeric value; fit, a list with
the coefficients returned by lsfit, i.e. intercept
and X.
acfPlot, pacfplot, ccfPlot
return an object of class "acf", see acf.
lmacfPlot
returns a list with the following elements: fit, a list
by itself with elements Intercept and slope X,
hurst, the Hurst exponent, both are numeric values.
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.logpdfPlot and qqgaussPlot are two simple functions
which allow a quick view on the tails of a distribution.
The first creates a logarithmic or
double-logarithmic density plot and returns breaks and counts.
For the double logarithmic plot, the negative side of the distribution
is reflected onto the positive axis.
The second creates a Gaussian Quantile-Quantile plot.
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.
Autocorrelation Functions:
The functions acfPlot, pacfPlot, and ccfPlot
plots and estimate autocorrelation, ACF, partial autocorrelation,
PACF, and cross-covariance and cross-correlation functions, CCF.
The functions allow to get a first view on correlations in and
between time series. The functions are synonyme function
calls for R's acf, pacf, and ccf from the
the ts package.
Long Memory Autocorrelation Function:
The function lmacfPlot plots and estimates the
long memory autocorrelation function and computes from the
plot the Hurst exponent of a time series. The volatility of
financial time series exhibits (in contrast to
the logarithmic returns) in almost every financial market a slow
ecaying autocorrelation function, ACF. We talk of a long memory
if the decay in the ACF is slower than exponential, i.e. the
correlation function decreases algebraically with increasing
(integer) lag.
Thus it makes sense to investigate the decay on a double-logarithmic
scale and to estimate the decay exponent. The function
lmacf calculates and plots the autocorrelation function of
the vector x. If the time series exhibits long memory
behaviour, it can easily be seen as a stright line in the plot.
This double-logarithmic plot is displayed and a linear regression
fit is done from which the intercept and slope ar calculated.
From the slope the Hurst exponent is derived.
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.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.
## SOURCE("fBasics.3B-StylizedFacts")
par(ask = FALSE)
## data -
# require(MASS)
plot(SP500, type = "l", col = "steelblue", main = "SP500")
abline(h = 0, col = "grey")
## qqgaussPlot -
# Lagged Correlations:
qqgaussPlot(SP500)
## teffectPlot -
# Taylor Effect:
teffectPlot(SP500)Run the code above in your browser using DataLab