Astrostatistics Image Penn State University Eberly College of Science Center for Astrostatistics Center for Astrostatistics

Time series analysis

Fast Fourier Transforms
    Metasite with annotated links to libraries and source codes,benchmarks, and didactic material on various forms of the Fast Fourier Transform.  From FFTW.  These include:

    Subroutine library in C for efficient computation of the discrete Fourier transform in one or more dimension for datasets of arbitrary size. Winner of Wilkinson Prize for Numerical Software.  From Matteo Frigo and Steven G. Johnson of MIT.

FXT library
    Algorithms fast Fourier and other transforms, sorting and searching, permutations, and more with associated text book. By Jorg Arndt (Bayreuth).

Variable star software
    A variety of programs for amateur astronomers from the American Association of Variable Star Observers including: averaging, polynomial fitting, Fourier analysis, residual analysis (TS); iterative pre-whitening (CLEANest); epoch folding plots (PhasPlot); and non-stationary periodicities (WWZ).

Finding periodicities with splines
    Nonparametric method for locating periodicities in unevenly spaced univariate data based on efficient least-squares fitting of cubic B-splines. Developed for astronomy by C. Akerlof at University of Michigan

Standards Time Series and Regresion Package (STARPAC)
    Library of about 150 Fortran subroutines for time series analysis and nonlinear regression, developed at the National Institute for Standards and Technology. Includes digital filtering, complex demodulation, univariate and bivariate correlation and spectrum analysis, ARMA and ARIMA models. Old-fashioned interface.  Distributed by the National Center for Atmospheric Research. 

    Maximum-likelihood autoregressive analysis including autocorrelation functions, ARMA model fitting, windowning and filtering, noise and model simulations, spectral density, and Box-Jenkins analysis.  Accompanies volume TIMESLAB: A Time Series Analysis Laboratory by H. J. Newton (1988).  Distributed by Statlib.

    Nonlinear time series analysis package for chaotic systems. Includes linear tools (autoregressive models, power spectrum, filters), visualization tools, embedding and Poincare sections, nonlinear prediction and local polynomial models, dimensionality adn entropy estimation, Lyapunov exponents, simulations, and cross-correlation of multivariate time series. From TISEAN Project at MPI Dresden and University of Wuppertal, Germany.

Amara's Wavelet page
    Metasite with extensive description, software, bibliography, and Web sites for wavelet methods. Provides linksto nearly wavelet software packages and toolboxes (many are commercial and not public domain). Environments include UNIX, X-Windows, Windows, Macintosh, C, C++, Matlab, Maple, PV-WAVE, Khoros, Mathematica, S+, IDL and MIDAS. See also a similar site at the University of Salzburg.

Multi-Taper Spectral Analysis Methods (MTM)
    Spectral analysis with tapering to minimize spectral leakage and spurious correlations.

    Econometrics package for Windows including: variable transformations, kernel density estimation, time series analysis (cross-correlation, stationarity tests, ARIMA & GARCH modeling), linear regression models (Poisson regression, Tobit, 2-stage least squares, user-supplied nonlinear), and more by H. Bierens (Penn State).

    Package for multivariate nonparametric time series analysis by maximum likelihood polynomial expansion permitting uneven weighting, non-normality and nonlinearity. By A. R. Gallant and G. E. Tauchen, and distributed by Statlib.

    Dynamic XWindow graphical system for exploratory time series analysis including autoregressive models and Fourier analysis. Distributed by Statlib.

RQA software
    Software for Recurrence Quantification Analysis of complex (e.g. chaotic, nonlinear and nonstationary) systems. By. C. L. Webber of the Department of Physiology at Loyola University Chicago. 

Singular Spectrum Analysis - MultiTaper Method (SSA-MTM)
    Toolkit of UNIX utilities to analyze short, noisy time series testing for trend and oscillating components, and three kinds of power spectra (windowed correlogram, multi-taper method, maximum-entropy method).  From the Department of Atmospheric & Oceanic Sciences at University of California Los Angeles.

Maximum likelihood ARIMA model
    Calculates the maximum likelihood estimators of the parameters of a fractionally-differences ARIMA(p,d,q) model with covarances and correlation matrices and standard errors.  By C. Fraley of University of Washington.

Time-frequency analysis
    Package for optimal and adaptive kernel time-frequency representations for long signals with changing time-frequency characteristics.  It adapts the kernel over time for improved performance.  By R. Baraniuk (DSP Group, Rice University) and colleagues.

ARMA model
    Maximum likelihood estimation of autoregressive-moving average model by Kalman filtering.  Applied Statisistics algorithm #154 distributed by Statlib.

Goodness-of-fit test for ARMA model
    Applied Statistics algorithm #194 distributed by Statlib.

Change point for Poisson process
    Continuous-time estimation of a change-point in a Poisson process.  By. R. W. West and R. T. Ogden of University of South Carolina.

Restricted maximum likelihood estimation for unevenly spaced data
    Parameter estimation for unevenly spaced univariate time series using a first-order process with white noise.  By S. P. Smith of EA Engineering and distributed by Statlib.

CUSUM charts
    Probability and distribution functions of run lengths in a cumulative summation chart. By F. F. Gan and distributed by Statlib.