fBasics-package: Portfolio Modelling, Optimization and Backtesting

Description

The 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.

Arguments

A. Overview:

1. Basic Statistics Functions 2. Financial Return Distributions 3. Hypothesis Testing 4. Plotting Routines 5. Matrix Computations and Linear Algebra

6. Utility Functions

1. Basic Statistics Functions

Financial Return Statistics:

ll{ Function ________________ Description _________________________________________ basicStats Returns a basic statistics summary. File: stats-basicStats.R Function ________________ Description _________________________________________ 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. File: stats-maxdd.R } Calculation of Sample Moments: ll{ Function ________________ Description _________________________________________ sampleLmoments Computes sample L-moments. File: stats-sampleLMoments.R Function ________________ Description _________________________________________ sampleMED Returns sample median sampleIQR returns sample inter quartal range sampleSKEW returns robust sample skewness sampleKURT returns robust sample kurtosis. File: stats-sampleRobMoments.R } Bivariate Interpolation: ll{ Function ________________ Description _________________________________________ akimaInterp Interpolates irregularly spaced points akimaInterpp Interpolates and smoothes pointwise. File: stats-interpAkima.R Function ________________ Description _________________________________________ krigeInterp Kriges irregularly spaced data points. File: stats-interpKrige.R Function ________________ Description _________________________________________ linearInterp Interpolates irregularly spaced points linearInterpp Interpolates linearly pointwise. File: stats-interpLinear.R } Utility Functions: ll{ Function ________________ Description _________________________________________ 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. File: has been moved tp package timeSeries Function ________________ Description _________________________________________ 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. File: stats-rowStats.R }

2. Financial Return Distributions

Generalized Hyperbolic Distribution: ll{ Function ________________ Description _________________________________________ dgh Returns density for the GH distribution pgh returns probability for the GH distribution qgh returns quantiles for the GH distribution rgh returns random variates for the GH distribution. File: dist-gh.R Function ________________ Description _________________________________________ ghFit Fits parameters of the GH distribution. File: dist-ghFit.R Function: ________________ Description _________________________________________ ghMode Computes mode of the GH distribution. File: dist-ghMode.R Function ________________ Description _________________________________________ 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. File: dist-ghMoments.R Function ________________ Description _________________________________________ 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. File: dist-ghRobMoments.R } Hyperbolic Distribution: ll{ Function ________________ Description _________________________________________ 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. File: dist-hyp.R Function ________________ Description _________________________________________ hypFit Fits parameters of the HYP distribution. File: dist-hypFit.R Function ________________ Description _________________________________________ hypMode Computes mode of the HYP distribution. File: dist-hypMode.R Function ________________ Description _________________________________________ hypMean Returns true mean of the HYP distribution hypVar 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. File: dist-hypMoments.R Function ________________ Description _________________________________________ 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. File: dist-hypRobMoments.R } Normal Inverse Gaussian: ll{ Function ________________ Description _________________________________________ 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 C implementation of function qnig(). File: dist-nig.R Function ________________ Description _________________________________________ 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. File: dist-nigFit.R Function ________________ Description _________________________________________ nigMode Computes mode of the NIG distribution. File: dist-nigMode.R Function ________________ Description _________________________________________ 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. File: dist-nigMoments.R Function ________________ Description _________________________________________ 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. File: dist-nigRobMoments.R } Generalized Hyperbolic Student-t Distribution: ll{ Function ________________ Description _________________________________________ 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. File: dist-ght.R Function ________________ Description _________________________________________ ghtFit Fits parameters of the GHT distribution. File: dist-ghtFit.R Function ________________ Description _________________________________________ ghtMode Computes mode of the GHT distribution. File: dist-ghtMode.R Function ________________ Description _________________________________________ 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. File: dist-ghtMoments.R Function ________________ Description _________________________________________ 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. File: dist-ghtRobMoments.R } Stable Distribution: ll{ Function ________________ Description _________________________________________ 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. File: dist-stable.R Function ________________ Description _________________________________________ 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. File: dist-stableFit.R Function ________________ Description _________________________________________ stableMode Computes mode of the stable distribution. File: dist-stableMode.R } Generalized Lambda Distribution: ll{ Function ________________ Description _________________________________________ 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. File: dist-gld.R Function ________________ Description _________________________________________ 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. File: dist-gldFit.R Function ________________ Description _________________________________________ gldMode Computes mode of the GLD distribution. File: dist-gldMode.R Function ________________ Description _________________________________________ 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. File: dist-gldRobMoments.R } Spline Smoothed Distribution: ll{ Function ________________ Description _________________________________________ dssd Returns spline smoothed density function pssd returns spline smoothed probability function qssd returns spline smoothed quantile function rssd returns spline smoothed random variates. File: dist-ssd.R Function ________________ Description _________________________________________ ssdFit Fits parameters for a spline smoothed distribution. File: dist-ssdFit.R }

3. Hypthesis Testing

One Sample Tests: ll{ Function ________________ Description _________________________________________ 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 File: test-normalTest.R Function ________________ Description _________________________________________ locationTest Performs locations tests on two samples .tTest Unpaired t test for differences in mean .kw2Test Kruskal-Wallis test for differences in locations File: test-locationTest.R Function ________________ Description _________________________________________ scaleTest Performs scale tests on two samples .ansariTest Ansari-Bradley test for differences in scale .moodTest Mood test for differences in scale File: test-scaleTest.R Function ________________ Description _________________________________________ 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 File: test-variance Test.R } Two Sample Tests: ll{ Function ________________ Description _________________________________________ 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 File: test-ks2Test.R } Test Utilities: ll{ Function ________________ Description _________________________________________ '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 File: test-fHTEST.R }

4. Plotting Routines

Financial Time Series Plots: ll{ Function ________________ Description _________________________________________ seriesPlot Dispalys a time series plot cumulatedPlot displays cumulated series give returns returnPlot displays returns given cumulated series drawdownPlot displays drawdown series from returns. File: plot-seriesPlot.R } Correlation Plots: ll{ Function ________________ Description _________________________________________ acfPlot Displays tailored ACF plot pacfPlot displays tailored partial ACF plot teffectPlot displays the Taylor effect lacfPlot displays lagged autocorrelations. File: plot-acfPlot.R }

Distribution Plots: ll{ Function ________________ Description _________________________________________ histPlot Returns tailored histogram plot densityPlot returns tailored density plot logDensityPlot returns tailored log density plot. File: plot-histPlot.R Function ________________ Description _________________________________________ boxPlot Returns side-by-side standard box plot boxPercentilePlot returns box-percentile plot. File: plot-boxPlot.R Function ________________ Description _________________________________________ qqnormPlot Returns normal quantile-quantile plot qqnigPlot returns NIG quantile-quantile plot qqghtPlot returns GHT quantile-quantile plot qqgldPlot returns GLD quantile-quantile plot. File: plot-qqPlot.R } Aggregation Plots: ll{ Function ________________ Description _________________________________________ scalinglawPlot displays scaling law behavior. File: plot-scalinglawPlot.R }

5. Matrix Computations and Linear Algebra

Matrix Operations: ll{ Function ________________ Description _________________________________________ kron Returns the Kronecker product. File: matrix-kron.R Function ________________ Description _________________________________________ vec Stacks a matrix as column vector vech stacks a lower triangle matrix. File: matrix-vech.R Function ________________ Description _________________________________________ pdl Returns regressor matrix for polynomial lags. File: matrix-pdl.R Function ________________ Description _________________________________________ tslag Returns Lagged/leading vector/matrix. File: matrix-tslag.R } Linear Algebra: ll{ Function ________________ Description _________________________________________ inv Returns the inverse of a matrix. File: matrix-inv.R Function ________________ Description _________________________________________ norm Returns the norm of a matrix. File: matrix-norm.R Function ________________ Description _________________________________________ rk Returns the rank of a matrix. File: matrix-rk.R Function ________________ Description _________________________________________ tr Returns the trace of a matrix. File: matrix-tr.R } Matrix Utilities: ll{ Function ________________ Description _________________________________________ isPositiveDefinite Checks if a matrix is positive definite makePositiveDefinite forces a matrix to be positive definite. File: matrix-posDefinite.R Function ________________ Description _________________________________________ colVec Creates a column vector from a data vector rowVec creates a row vector from a data vector. File: matrix-colVec.R Function ________________ Description _________________________________________ gridVector Creates from two vectors rectangular grid. File: matrix-gridVector.R Function ________________ Description _________________________________________ triang Extracs lower tridiagonal part from a matrix Triang Extracs upper tridiagonal part from a matrix. File: matrix-triang.R } Matrix Examples: ll{ Function ________________ Description _________________________________________ hilbert Creates a Hilbert matrix. File: matrix-hilbert.R Function ________________ Description _________________________________________ pascal Creates a Pascal matrix. File: matrix-pascal.R }

6. Utility Functions

Color Utilities: ll{ Function ________________ Description _________________________________________ colorLocator Plots Rs 657 named colors for selection colorMatrix returns matrix of R's color names. File: utils-colorLocator.R Function ________________ Description _________________________________________ colorTable Table of Color Codes and Plot Colors itself. File: utils-colorTable.R Function ________________ Description _________________________________________ 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. File: utils-colorPalette.R }

Plot Utilities: ll{ Function ________________ Description _________________________________________ symbolTable Shows a table of plot symbols. File: utils-symbolTable.R Function ________________ Description _________________________________________ characterTable Shows a table of character codes. File: utils-characterTable.R Function ________________ Description _________________________________________ 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. File: utils-decor.R Function ________________ Description _________________________________________ interactivePlot Plots several graphs interactively. File: utils-interactivePlot.R } Special Function Utilities: ll{ Function ________________ Description _________________________________________ Heaviside Computes Heaviside unit step function Sign another signum function Delta computes delta function Boxcar computes boxcar function Ramp computes ramp function. File: utils-heaviside.R Function ________________ Description _________________________________________ tsHessian Computes Two Sided Hessian matrix. File: utils-hessian.R } Other Utilities: ll{ Function ________________ Description _________________________________________ .unirootNA Computes zero of a function without error exit. File: utils-unitrootNA.R Function ________________ Description _________________________________________ getCall Extracts the call slot from a S4 object 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. File: utils-getS4.R }

B. Code and Function Dependencies:

1. Dependences and Suggested Packages 2. Builtin Functions 3. Compiled Fortran and C Code

1. Dependences and Suggested Packages:

Required packages include:

ll{ Dependences _________________ Description _________________________________________ MASS R base package methods R base package timeDate Rmetrics package timeSeries Rmetrics package Suggested ___________________ Description _________________________________________ akima contributed R package spatial contributed R package RUnit contributed R package tcltk contributed R package.}

2. 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 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 timDate 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: ll{ Builtin _________________ Description _________________________________________ gelGmm gll function from gmm package gmmGMM gmm function from gmm package kweightsSandwhich kweights from sandwhich package glGld glfunctions from gld package ssdenGss ssden from the gss package hypHyperbolicDist hyp from HyperbolicDist package.}

3. Compiled Fortran and C Code:

ll{ Fortran/C _________________ Description _________________________________________ gld.c source code from gld package nig.c source code from Kersti Aas gss.f source code fromsandwhich package.}

C. Copyright and Licencies:

D. Contact Address:

www.rmetrics.org Addresses:

Description

Arguments

A. Overview:

1. Basic Statistics Functions

2. Financial Return Distributions

3. Hypthesis Testing

4. Plotting Routines

5. Matrix Computations and Linear Algebra

6. Utility Functions

B. Code and Function Dependencies:

1. Dependences and Suggested Packages:

2. Builtin Functions:

3. Compiled Fortran and C Code:

C. Copyright and Licencies:

D. Contact Address:

Details