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Getting Started

Getting Started
STSA, The Statistical Time Series Analysis Toolbox is installed in your O-Matrix installation directory. For example, \omwin\STSA. The individual functions of the toolbox are divided into the ten sub-directories: ARMA, BAYES, FILTER, NONLIN, NONPAR, OPTIMIZE, POD, SPECTRAL, RNG, and STATS. These represent the main categories of functionality for the toolbox.

The STSA Toolbox is an extensive collection of O-Matrix functions for performing time series related analysis and visualization. These functions will simplify and accelerate the development efforts of anyone working with time dependent observations. The toolbox provides extensive capabilities for ARMA, Bayesian, non-linear, spectral analysis, optimization, and random number generation.

The examples directory of your installation, (omwin\stsa\examples) includes numerous application examples that provide in depth illustrations of the STSA Toolbox capabilities. These may also serve as a good starting point for your own specific requirements.

ARMA Directory
The functions in this directory can be used in the modeling (fitting, evaluation and forecasting) of univariate and multivariate stationary time series. For univariate time series analysis this directory has an extensive variety of functions for preliminary transformations, smoothing, testing for Gaussianity, descriptive statistics, order selection, estimation, residual diagnostics and forecasting. There is a complete set of functions for doing ARMA analysis according to the well known Box-Jenkins methodology. Many of these univariate analysis functions can be used, when applied in one variable at a time, in the context of multivariate time series analysis as well. For multivariate analysis there are functions for the classes of transfer function models and vector autoregressive models. A function for performing bivariate Granger-type causality analysis is also included. There are also two generic, unrestricted optimization functions, one for nonlinear least squares (gauss_newton) and one for nonlinear maximum likelihood (bhhh_ml) that can be used with a user-defined function for solving the corresponding estimation problems. The gauss_newton function is similar to the nlsq function of O-Matrix but it provides additional output, useful in the context of estimation.

Note I: The transfer function class is currently restricted to bivariate time series (one output time series with one input time series). Note II: See references [1] through [5] for extensive documentation for these classes of models.

The functions provided for univariate time series analysis can: The functions provided for multivariate time series analysis can: There are a number of auxiliary functions that can be used either for residual diagnostic analysis or to any time series directly. These include functions for:

BAYES Directory
This directory provides functions for the modeling (fitting and forecasting) of univariate time series following the Bayesian methodology outlined in reference [6]. The generic normal Dynamic Linear Model (DLM) and two of its simpler versions (first order polynomial DLM and regression through the origin DLM) are supported. With the functions provided the user can:

FILTER Directory
Functions for filtering and forecasting of univariate time series

NONLIN Directory
This directory provides functions for the modeling of some nonlinear univariate time series. Currently the directory supports the following: estimation of the parameters of GARCH model using maximum likelihood with either the Gaussian or Student's t-distribution (with fixed degrees of freedom), testing for linearity using an omnibus F-type test, bootstrapping a time series using the maximum entropy bootstrap, using the Kolmogorov-Smirnov test statistic in the context of time series, estimating a sign autoregressions and specifying and estimating a self-exciting threshold autoregressive (SETAR) model with a single threshold point. The SETAR model is a parametric model while a number of alternative semi- and non-parametric models are given in the NONPAR directory (see below). References [1], [4], [5], [7], [8], [9] an [11] contain extensive discussions and illustrations for these types of models. With the functions provided the user can:

NONPAR Directory
The functions in this directory are an important addition to the STSA capabilities. This directory has redesigned functions for some of the previous non-parametric modeling capabilities that were in the NONLIN directory and has a number of additional functions that automate the specification, estimation and forecasting using advanced non-parametric models. Most of the models are directly designed and cross-tested using the material in reference [11]. The functions in this directory have two specific modeling advantages: they allow for the automated, data-dependent selection of the smoothing parameter (bandwidth) for non-parametric estimation using generalized or multifold cross-validation and they provide immediate forecasts from a number of alternative non-parametric models. In addition, there are functions for computing the density, distribution function and conditional density of a time series, as well as a function for extracting (and forecasting) conditional quantiles. Most of the functions have a plot option that allow for fast, easy plotting of some of the results. Estimation of all models is carried out with the Epanechnikov "optimal" kernel function although we retained the gaussian_kernel and optimal_kernel functions of the previous version for user-defined functions. Numerous new examples illustrate these functions.

SPECTRAL Directory
There are 18 functions in this directory. They can be used to perform standard univariate spectral analysis and analysis of long-memory time series. See references [1], [4], [5] and [10]. In particular, with the functions provided the user can: The vector of the appropriate Fourier frequencies for plotting and evaluation is provided as output by these procedures.

RNG Directory
Functions for generating random numbers from various statistical distributions.

OPTIMIZE Directory
Functions for nonlinear optimization not available in the main O-Matrix distribution

STATS Directory
Various functions that aid in the analysis of time series data. This directory greatly extends the statistical capabilities of the main O-Matrix distribution.