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STSA - The Time Series Analysis Toolbox for O-Matrix

Scatterplot with Non-Parametric Fit

New: STSA Version 2.1 Enhancements

The STSA (Statistical Time Series Analysis) Toolbox is an extensive collection of O-Matrix functions for performing time series and statistics related analysis and visualization. The STSA toolbox provides capabilities for ARMA and ARFIMA, Bayesian, non-linear and spectral analysis related models. Extensive time series filtering functions and spectral analysis functions are provided. Numerous random number generators are included for both time series, and general statistical analysis.

The STSA toolbox aids in the rapid solution of many time series problems, some of which cannot be easily dealt with using a canned program or are not directly available in most analysis software packages. For example, the NONLIN directory provides functions for model selection, estimation and forecasting for the class of functional coefficient autoregressive models: this is a state-of-the-art class of powerful and flexible non-parametric models that can be used in forecasting nonlinear time series. And, in the SPECTRAL directory the user can find functions for simulating, estimating and forecasting long-memory time series, a class of time series that is encountered in such diverse fields as hydrology and finance. The BAYES directory includes functions for Bayesian modeling and forecasting of time series that are not typically available in a commercial statistical package. The Bayesian techniques of this directory offer a greater degree of flexibility than traditional linear models and can handle a large number of forecasting tasks.

A few areas of application of the STSA toolbox include:

  1. Financial and economic forecasting.
  2. Sales forecasting and inventory control.
  3. Modeling and forecasting of physical time series (hydrology, earth sciences, astronomy, oceanography and marine biology)
  4. Simulation of time series models and examination of their properties.
  5. Filtering and smoothing of any type of time series.
  6. Statistical estimation of parameters of time series models, either linear or nonlinear, with several types of optimization methods.
The STSA toolbox can be used by practitioners in a variety of disciplines. It can also be used for classroom instruction, as it allows the instructor to concentrate on the actual application of time series concepts and not on programming.

The STSA toolbox offers a complete solution for doing time series analysis: from simulation, to estimation, to residual analysis, to forecasting, complete with many auxiliary statistical functions for descriptive statistics, statistical plots, trend forecasting, time series smoothing and others. The toolbox comes with extensive documentation and numerous examples. The provided examples provide illustrations using both real-world and simulated data that can be used as a starting point for immediately using the power of STSA.

STSA Functional Categories Synopsis:
The following list enumerates some of the primary STSA capabilities

  • ARMA Analysis
    • Univariate Analysis Functions
      • Simulate a Gaussian ARMA model
      • Compute the theoretical autocovariances of an ARMA model
      • Compute and plot the sample autocorrelation, partial correlation and cross-correlation functions
      • Compute the best linear predictors and innovations using theoretical autocovariances and the Durbin-Levinson-Whittle algorithm
      • Estimate the parameters of an ARMA model using non-linear least squares
      • Perform the Diebold-Mariano test for competing forecasting model
      • Compute the Grange causality tests
      • Estimate the parameters of a bivariate transfer function model
      • Estimate the parameters of a multivariate VAR model
      • Forecast using the estimates from a VAR model
      • Create a matrix of sequential lags of a time series
      • Estimate and plot the autocovariance function (ACVF), autocorrelation function (ACF) and partial autocorrelation function (PACF)
      • Compute the roots of the characteristic polynomials of an estimate ARIMA/ARFIMA model
      • Compute the coefficients in the infinite AR or MA representation of an ARIMA/ARFIMA model
      • Forecast (predict) future observations of the time series using an estimated model
      • Filter a time series using an estimated model
      • Validate a model using a variety of residual diagnostics
    • Multivariate Analysis Functions
      • Estimate the cross-correlation function (CCF) between pairs of time series
      • Estimate by conditional, nonlinear least squares parameters of a TF model
      • Select the order of a VAR model using two model selection criteria
      • Estimate by conditional linear least squares the parameters of a VAR model
      • Forecast (predict) future observations of the time series using an estimated model
      • Validate a model using a variety of residual diagnostics applied to each individual residual series
  • Bayesian Analysis
    • Simulate a first order polynomial DLM
    • Initialize the Bayesian recursions using arbitrary priors or reference priors
    • Automatically check the observability of a DLM
    • Fit a generic time series DLM
    • Automatically construct the system and observation matrices for a number of popular DLMs, including DLMs for seasonal time series
    • Fit a variety of DLM models to a time series
    • Perform out of sample forecasting using the fitted DLM
    • Compute interval forecasts and standardized forecast errors
    • Construct the trend and seasonal matrices for the generic DLM
    • Evaluate the forecasting performance of a DLM using the mean squared and mean absolute values of the forecast errors
  • Filter Functions
    • Smoothing a time series using simple and exponential moving averages
    • Smoothing and forecasting a time series using the Holt-Winters recursions
    • Filter a time series using a generic finite impulse response filter
    • Model, filter and forecast a time series using any time-invariant state-space model with the Kalman filter
    • Estimate, filter and forecast a time series based on a trend+cyclical structural model
  • Non-Linear Analysis
    • Bootstrap a time series using the maximum entropy bootstrap
    • Compute the empirical probability density and cumulative density of a time series
    • Compute a Kolmogorov-Smirnoff type test for the equality of a distribution between two time series
    • Compute a regression-base F-test for linearity of a time series
    • Compute a non-parametric regression
    • Forecast using a non-parametric autoregressive model
    • Model selection, estimation and forecasting using a Self-Exciting Threshold AutoRegressive model
    • Model selection, estimation and forecasting using a Functional Coefficient AutoRegressive model
    • Simulation and Estimation of ARMA models with Generalized AutoRegressive Conditional Heteroskedasticity (ARMA-GARCH models)
  • Optimization Functions
    • BHHH algorithm for nonlinear maximum likelihood optimization problems
    • Gauss-Newton optimization for nonlinear least squares
    • Quasi-Newton (BFGS algorithm)
  • Singular Spectrum Analysis
    • Construct and decompose the trajectory matrix of a time series
    • Plot the eigenvalues and eigenvectors of the decomposition
    • Reconstruct one or more components or the whole time series
    • Extract trend and seasonal components, perform deseasonalization
    • Forecast any component of the decomposition or the whole time series
  • Spectral Analysis
    • Simulate a fractional Gaussian noise time series
    • Simulate a fractionally differenced time series
    • Compute and plot the Fourier transform and periodogram of a time series
    • Compute and plot the power spectrum of a time series using the smoothed periodogram, an autoregressive approximation or autocovariances
    • Compute the cross-spectrum, the squared coherency, the amplitude and phase of two time series
    • Compute the impulse response coefficients between two time series
    • Fractionally difference a time series
    • Estimate the fractional order (Hurst exponent) of a time series (GPH regression and Whittle likelihood methods)
    • Estimate and forecast using a fractional ARMA model (ARFIMA)
  • Random Number Generators, (RNGs)
    • Cauchy distribution
    • Exponential distribution
    • Gaussian distribution
    • Gumbel (Extreme value) distribution
    • Logistic distribution
    • t (Student) distribution
    • Uniform distribution
  • Specialized Statistics
    • Compute the sample central moments of any order
    • Compute the optimal Box-Cox transformation near Gaussianity
    • Transform a time series using the optimal Box-Cox exponent
    • Compute empirical percentiles
    • Test for Gaussianity using the QQ correlation coefficient
    • Estimate regression model using linear least squares and rolling linear least squares
    • Estimate a regression model using least absolute deviations
    • Perform principal component analysis (PCA)
    • Perform factor analysis based on principal components
    • Estimate polynomial and exponential trend functions

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