
STSA  The Time Series Analysis Toolbox for OMatrix


New: STSA Version 2.1 Enhancements
The STSA (Statistical Time Series Analysis) Toolbox is an extensive
collection of OMatrix functions for performing time
series and statistics related analysis and visualization.
The STSA toolbox provides
capabilities for ARMA and ARFIMA, Bayesian,
nonlinear 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
stateoftheart class of powerful and flexible
nonparametric 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 longmemory 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:
 Financial and economic forecasting.
 Sales forecasting and inventory control.
 Modeling and forecasting of physical time series (hydrology,
earth sciences, astronomy, oceanography and marine biology)
 Simulation of time series models and examination of their properties.
 Filtering and smoothing of any type of time series.
 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 realworld 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
crosscorrelation functions
 Compute the best linear predictors and innovations using theoretical
autocovariances and the DurbinLevinsonWhittle algorithm
 Estimate the parameters of an ARMA model using nonlinear least squares
 Perform the DieboldMariano 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 crosscorrelation 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 HoltWinters recursions
 Filter a time series using a generic finite impulse response filter
 Model, filter and forecast a time series using any timeinvariant statespace
model with the Kalman filter
 Estimate, filter and forecast a time series based on a trend+cyclical
structural model
 NonLinear Analysis
 Bootstrap a time series using the maximum entropy bootstrap
 Compute the empirical probability density and cumulative density of
a time series
 Compute a KolmogorovSmirnoff type test for the equality of a distribution
between two time series
 Compute a regressionbase Ftest for linearity of a time series
 Compute a nonparametric regression
 Forecast using a nonparametric autoregressive model
 Model selection, estimation and forecasting using a SelfExciting
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 (ARMAGARCH models)
 Optimization Functions
 BHHH algorithm for nonlinear maximum likelihood optimization problems
 GaussNewton optimization for nonlinear least squares
 QuasiNewton (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 crossspectrum, 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 BoxCox transformation near Gaussianity
 Transform a time series using the optimal BoxCox 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
System Requirements
Pricing and Ordering Information
