Portfolio modelling, optimization and backtesting
00fBasics-package.RdThe Rmetrics fBasics package is a collection of functions to explore and to investigate basic properties of financial returns and related quantities.
The covered fields include techniques of explorative data analysis and the investigation of distributional properties, including parameter estimation and hypothesis testing. Evenmore there are several utility functions for data handling and management.
Author
Diethelm Wuertz [aut] (original code), Tobias Setz [aut], Yohan Chalabi [aut], Martin Maechler [ctb] (<https://orcid.org/0000-0002-8685-9910>), Georgi N. Boshnakov [cre, ctb], CRAN Team [ctb]
Maintainer: Georgi N. Boshnakov <georgi.boshnakov@manchester.ac.uk>
Details
Note by the maintainer (GNB): Some of the information on this overview page may be outdated. The documentation website https://geobosh.github.io/fBasicsDoc/ of the package (generated with pkgdown) provides up-to-date help pages, arranged by topic.
1 Introduction
The fBasics package contains basics tools often required in computational finance and financial engineering. The topics are: basic statistics functions, financial return distributions, hypothesis testing, plotting routines, matrix computations and linear algebra, and some usefule utility functions.
2 Basic Statistics Functions
Financial Return Statistics
basicStats Returns a basic statistics summary
Distribution Function of Maximum Drawdowns
dmaxdd Density function of mean Max-Drawdowns
pmaxdd Probability function of mean Max-Drawdowns
rmaxdd Random Variates of mean Max-Drawdowns
maxddStats Expectation of Drawdowns for BM with drift
Calculation of Sample Moments
sampleLmoments Computes sample L-moments
sampleMED Returns sample median
sampleIQR returns sample inter quartal range
sampleSKEW returns robust sample skewness
sampleKURT returns robust sample kurtosis
Bivariate Interpolation:
akimaInterp Interpolates irregularly spaced points
akimaInterpp Interpolates and smoothes pointwise
krigeInterp Kriges irregularly spaced data points
linearInterp Interpolates irregularly spaced points
linearInterpp Interpolates linearly pointwise
Utility Statistics Functions:
colStats Computes sample statistics by col
colSums Computes sums of values in each col
colMeans Computes means of values in each col
colSds Computes standard deviation of each col
colVars Computes sample variance by col
colSkewness Computes sample skewness by col
colKurtosis Computes sample kurtosis by col
colMaxs Computes maximum values in each col
colMins Computes minimum values in each col
colProds Computes product of values in each col
colQuantiles Computes product of values in each col
rowStats Computes sample statistics by row
rowSums Computes sums of values in each row
rowMeans Computes means of values in each row
rowSds Computes standard deviation of each row
rowVars Computes sample variance by row
rowSkewness Computes sample skewness by row
rowKurtosis Computes sample kurtosis by row
rowMaxs Computes maximum values in each row
rowMins Computes minimum values in each row
rowProds Computes product of values in each row
rowQuantiles Computes product of values in each row
3 Financial Return Distributions
Generalized Hyperbolic Distribution:
dghReturns Density for the GH distribution
pghreturns Probability for the GH distribution
qghreturns Quantiles for the GH distribution
rghreturns Random variates for the GH distribution
ghFitFits Fits parameters of the GH distribution
ghMode Computes mode of the GH distribution.
ghMean Returns true mean of the GH distribution
ghVar Returns true variance of the GH distribution
ghSkew Returns true skewness of the GH distribution
ghKurt Returns true kurtosis of the GH distribution
ghMoments Returns true n-th moment of the GH distribution
ghMED Returns true median of te GH distribution
ghIQR Returns true inter quartal range of te GH
ghSKEW Returns true robust skewness of te GH
ghKURT Returns true robust kurtosis of te GH
Hyperbolic Distribution:
dhyp Returns density for the HYP distribution
phyp Returns probability for the HYP distribution
qhyp Returns quantiles for the HYP distribution
rhyp Returns random variates for the HYP distribution
hypFit Fits parameters of the HYP distribution
hypMode Computes mode of the HYP distribution
hypMean Returns true mean of the HYP distribution
hypVar R Returns true variance of the HYP distribution
hypSkew Returns true skewness of the HYP distribution
hypKurt Returns true kurtosis of the HYP distribution
hypMoments Returns true n-th moment of the HYP distribution
hypMED Returns true median of the HYP distribution
hypIQR Returns true inter quartal range of the HYP
hypSKEW Returns true robust skewness of the HYP
hypKURT Returns true robust kurtosis of the HYP
Normal Inverse Gaussian:
dnig Returns density for the NIG distribution
pnig Returns probability for the NIG distribution
qnig Returns quantiles for the NIG distribution
rnig Returns random variates for the NIG distribution
.pnigC fast C Implementation of function pnig()
.qnigC fast CImplementation of function qnig()
nigFit Fits parameters of a NIG distribution
.nigFit.mle Uses max Log-likelihood estimation
.nigFit.gmm Uses generalized method of moments
.nigFit.mps Maximum product spacings estimation
.nigFit.vmps Minimum variance mps estimation
nigMode Computes mode of the NIG distribution
nigMean Returns true mean of the NIG distribution
nigVar Returns true variance of the NIG distribution
nigSkew Returns true skewness of the NIG distribution
nigKurt Returns true kurtosis of the NIG distribution
nigMoments Returns true n-th moment of the NIG distribution
nigMED Returns true median of the NIG distribution
nigIQR Returns true inter quartal range of the NIG
nigSKEW Returns true robust skewness of the NIG
nigKURT Returns true robust kurtosis of the NIG
Generalized Hyperbolic Student-t Distribution:
dght Returns density for the GHT distribution
pght Returns probability for the GHT distribution
qght Returns quantiles for the GHT distribution
rght Returns random variates for the GHT distribution
ghtFit Fits parameters of the GHT distribution
ghtMode Computes mode of the GHT distribution
ghtMean Returns true mean of the NIG distribution
ghtVar Returns true variance of the GHT distribution
ghtSkew Returns true skewness of the GHT distribution
ghtKurt Returns true kurtosis of the GHT distribution
ghtMoments Returns true n-th moment of the GHT distribution
ghtMED Returns true median of the GHT distribution
ghtIQR Returns true inter quartal range of the GHT
ghtSKEW Returns true robust skewness of the GHT
ghtKURT Returns true robust kurtosis of the GHT
Stable Distribution:
dstable Returns density for the stable distribution
pstable Returns probability for the stable distribution
qstable Returns quantiles for the stable distribution
rstable Returns random variates for the dtsble distribution
stableFit Fits parameters of a the stable distribution
.phiStable Creates contour table for McCulloch estimators
.PhiStable Contour table created by function .phiStable()
.qStableFit Estimates parameters by McCulloch's approach
.mleStableFit Estimates stable parameters by MLE approach
.stablePlot Plots results of stable parameter estimates
stableMode Computes mode of the stable distribution
Generalized Lambda Distribution:
dgld Returns density for the GLD distribution
pgld Returns probability for the GLD distribution
qgld Returns quantiles for the GLD distribution
rgld Returns random variates for the GLD distribution
gldFit Fits parameters of the GLD distribution
.gldFit.mle fits GLD using maximum log-likelihood
.gldFit.mps fits GLD using maximum product spacings
.gldFit.gof fits GLD using Goodness of Fit statistics
.gldFit.hist fits GLD using a histogram fit
.gldFit.rob fits GLD using robust moments fit
gldMode Computes mode of the GLD distribution.
gldMED Returns true median of the GLD distribution
gldIQR Returns true inter quartal range of the GLD
gldSKEW Returns true robust skewness of the GLD
gldKURT Returns true robust kurtosis of the GLD
Spline Smoothed Distribution:
dssd Returns spline smoothed density function
pssd Returns spline smoothed probability function
qssd Returns spline smoothed quantile function
rssd Returns spline smoothed random variates.
ssdFit Fits parameters for a spline smoothed distribution
4 Hypthesis Testing
One Sample Nornality Tests:
ksnormTest One sample Kolmogorov-Smirnov normality test
shapiroTest Shapiro-Wilk normality test
jarqueberaTest Jarque-Bera normality test
normalTest Normality tests S-Plus compatible call
dagoTest D'Agostino normality test
adTest Anderson-Darling normality test
cvmTest Cramer-von Mises normality test
lillieTest Lilliefors (KS) normality test
pchiTest Pearson chi-square normality test
sfTest Shapiro-Francia normality test
jbTest Finite sample adjusted JB LM and ALM test
One Sample Location, Scale and variance Tests:
locationTest Performs locations tests on two samples
.tTest Unpaired t test for differences in mean
.kw2Test Kruskal-Wallis test for differences in locations
scaleTest Performs scale tests on two samples
.ansariTest Ansari-Bradley test for differences in scale
.moodTest Mood test for differences in scale
varianceTest Performs variance tests on two samples
.varfTest F test for differences in variances
.bartlett2Test Bartlett's test for differences in variances
.fligner2Test Fligner-Killeen test for differences in variances
Two Sample Tests:
ks2Test Performs a two sample Kolmogorov-Smirnov test
correlationTest Performs correlation tests on two samples
pearsonTest Pearson product moment correlation coefficient
kendallTest Kendall's tau correlation test
spearmanTest Spearman's rho correlation test
Test Utilities:
'fHTEST' S4 Class Representation
show.fHTEST S4 Print Method
.jbALM Jarque Bera Augmented Lagrange Multiplier Data
.jbLM Jarque-Bera Lagrange Multiplier Data
.jbTable Finite sample p values for the Jarque Bera test
.jbPlot Plots probabilities
.pjb Returns probabilities for JB given quantiles
.qjb Returns quantiles for JB given probabilities
5 Plotting Routines
Financial Time Series Plots:
seriesPlot Dispalys a time series plot
cumulatedPlot Displays cumulated series give returns
returnPlot Displays returns given cumulated series
drawdownPlot Displays drawdown series from returns
Correlation Plots:
acfPlot Displays tailored ACF plot
pacfPlot Displays tailored partial ACF plot
teffectPlot Displays the Taylor effect
lacfPlot Displays lagged autocorrelations
Distribution Plots:
histPlot Returns tailored histogram plot
densityPlot Returns tailored density plot
logDensityPlot Returns tailored log density plot
boxPlot Returns side-by-side standard box plot
boxPercentile Plotreturns box-percentile plot
qqnormPlot Returns normal quantile-quantile plot
qqnigPlot Returns NIG quantile-quantile plot
qqghtPlot Rreturns GHT quantile-quantile plot
qqgldPlot Returns GLD quantile-quantile plot
Time Series Aggregation Plots:
scalinglawPlot Displays scaling law behavior
5. Matrix Computations and Linear Algebra
Elementar Matrix Operation Addons:
kron Returns the Kronecker product
vec Stacks a matrix as column vector
vech Stacks a lower triangle matrix
pdl Returns regressor matrix for polynomial lags
tslag Returns Lagged/leading vector/matrix
Linear Algebra Addons:
inv Returns the inverse of a matrix
norm Returns the norm of a matrix
rk Returns the rank of a matrix
tr Returns the trace of a matrix
General Matrix Utility Addons:
isPositiveDefinite Checks if a matrix is positive definite
makePositiveDefinite Forces a matrix to be positive definite
colVec Creates a column vector from a data vector
rowVec Creates a row vector from a data vector
gridVector Creates from two vectors rectangular grid
triang Extracs lower tridiagonal part from a matrix
Triang Extracs upper tridiagonal part from a matrix
Selected Matrix Examples:
hilbert Creates a Hilbert matrix
pascal Creates a Pascal matrix
6 Utility Functions
Color Utilities:
colorLocator Plots Rs 657 named colors for selection
colorMatrix Returns matrix of R's color names.
colorTable Table of Color Codes and Plot Colors itself
rainbowPalette Contiguous rainbow color palette
heatPalette Contiguous heat color palette
terrainPalette Contiguous terrain color palette
topoPalette Contiguous topo color palette
cmPalette Contiguous cm color palette
greyPalette R's gamma-corrected gray palette
timPalette Tim's Matlab like color palette
rampPalette Color ramp palettes
seqPalette Sequential color brewer palettes
divPalette Diverging color brewer palettes
qualiPalette Qualified color brewer palettes
focusPalette Red, green blue focus palettes
monoPalette Red, green blue mono palettes
Graphics Utilities:
symbolTable Shows a table of plot symbols
characterTable Shows a table of character codes
decor Adds horizontal grid and L shaped box
hgrid Adds horizontal grid lines
vgrid Adds vertical grid lines
boxL Adds L-shaped box
box Adds unterlined box
.xrug Adds rugs on x axis
.yrug Adds rugs on y axis
copyright Adds copyright notice
interactivePlot Plots several graphs interactively
Special Function Utilities:
Heaviside Computes Heaviside unit step function
Sign Another signum function
Delta Computes delta function
Boxcar Computes boxcar function
Ramp Computes ramp function
tsHessian Computes Two Sided Hessian matrix
Other Utilities:
.unirootNA Computes zero of a function without error exit
getModel Extracts the model slot from a S4 object
getTitle Extracts the title slot from a S4 object
getDescription Extracts the description slot
getSlot Extracts a specified slot from a S4 object
About Builtin Functions
Builtin functions are borrowed from contributed R packages and other sources. There are several reasons why we have modified and copied code from other sources and included in this package.
* The builtin code is not available on Debian, so that Linux users have no easy acces to this code.
* The original code conflicts with other code from this package or conflicts with Rmetrics design objectives.
* We only need a very small piece of functionality from the original package which may depend on other packages which are not needed.
* The package from which we builtin the code is under current development, so that the functions often change and thus leads to unexpectect behavior in the Rmetrics packages.
* The package may be incompatible since it uses other time date and time series classes than the 'timeDate' and 'timeSeries' objects and methods from Rmetrics.
We put the code in script files named builtin-funPackage.R where "fun" denotes the (optional) major function name, and "Package" the name of the contributed package from which we copied the original code.
Builtin functions include:
gelGmm gll function from gmm package
gmmGMM gmm function from gmm package
kweightsSandwhich kweights from sandwhich package
glGld gl functions from gld package
ssdenGss ssden from the gss package
hypHyperbolicDist hyp from HyperbolicDist package