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:
acfPlot | autocorrelation function plot, |
pacfPlot | partial autocorrelation function plot, |
lacfPlot | lagged autocorrelation function plot, |
teffectPlot | Taylor effect plot. |
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, ...)
for acfPlot and pacfplot,
an object of class "acf", see acf;
for teffectPlot, a numeric matrix
of order deltas by max.lag with
the values of the autocorrelations;
for lacfPlot, a list with the following two elements:
the autocorrelation function,
the lagged correlations.
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.
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.
an integer value, the number of lags.
maximum lag for which the autocorrelation should be calculated, an integer.
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: exp(colCumsums(x))
the exponents, a numeric vector, by default ranging from 0.2 to 3.0 in steps of 0.2.
maximum y-axis value on plot. If NA, then the value is
selected automatically.
a logical value. Should the vector x be standardized?
arguments to be passed.
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 synonym 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.
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.
## data
data(LPP2005REC, package = "timeSeries")
SPI <- LPP2005REC[, "SPI"]
plot(SPI, type = "l", col = "steelblue", main = "SP500")
abline(h = 0, col = "grey")
## Taylor Effect:
teffectPlot(SPI)
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