Modules and add-on's for GAUSS

The GAUSS AD 1.0 module is an application program for generating GAUSS procedures for computing algorithmic derivatives. A major achievement of AD is improved accuracy for optimization. Numerical derivatives invariably produce a loss of precision. The loss of precision is greater for standard errors than it is for estimates. At the default tolerance, Constrained Maximum Likelihood (CML) and Maximum Likelihood (Maxlik) can be expected generally to have four or five places of accuracy, whereas standard errors will have about two places. Accuracy essentially doubles with AD. AD works independently of any application to improve derivatives, and it can be used with any application that uses derivatives.

For some types of optimization problems, convergence is accelerated. Iterations are faster and fewer of them are needed to achieve convergence. The types of problems that will see the most improvement are those with a large amount of computation.

Constrained Maximum Likelihood 2.0.6+ and Maximum Likelihood 5.0.7+ have been updated to improve speed with AD.

CML solves the general maximum likelihood problem subject to general constraints on the parameters - linear or nonlinear, equality or inequality. CML uses the Sequential quadratic Programming method in combination with several descent methods selectable by the user - Newton-Raphson, quasi-Newton (i.e, DFP and BFGS), scaled quasi-Newton, and BHHH. There are also several selectable line search methods. A Trust Region method is also available which prevents saddle point solutions. Gradients can be user-provided or numerically calculated.

CML provides for statistical inference for constrained statistical models. Confidence limits may be computed from selected methods, bootstrap, Bayesian (using a weighted likelihood bootstrap), or inversion of three types of statistics, the Wald, the likelihood ratio, or the Lagrange Multiplier. Confidence limits from the inversion of the likelihood ratio statistic are also called profile likelihood confidence limits.

The bootstrap and Bayesian procedures generate simulated parameter sets from the bootstrap and posterior distributions respectively. Procedures may be applied to these parameter sets to either produce confidence limits, expected values, or kernel density plots of the distributions.

Constrained Optimization will solve the important Markowitz asset allocation model - which minimizes portfolio variance, s2 = x'Sx, subject to x'm = r, where x is a vector of proportions and 0 <= x <= 1, sum(x) = 1, r is the portfolio return, m is the vector of the means and S the covariance matrix of the observed returns of the portfolio securities. More significantly, however, Constrained Optimization can easily handle recent extensions of the Markowitz model that incorporate third and fourth moments of the observed returns, as well as providing the capability of adding nonlinear constraints to the model.

Features:

• Solves standard Nonlinear Programming Problem using Sequential Quadratic Programming method
• Linear and nonlinear constraints on parameters
• Equality and inequality constraints on parameters

• Solve the Markowitz asset allocation model
• Solve nonparametric extensions of Markowitz model incorporating higher moments
• Bound Coefficients to avoid undefined regions

Control Systems-Transformation and Analysis
This application allows you to transform linear system models between various representations such as pole-zero form, transfer function form and state-space form. It also allows you to build up complex multi-input-multi-output linear systems from smaller blocks. Both continuous and discrete systems are supported. On the analysis side, Module 1 allows you to analyze the system by looking at it's time response, it's frequency response, or the way the poles vary with the system gain. Singular value and eigenvalue responses are supported.

Using the analysis function to guide your choice of compensators you can carry out frequency domain and pole-zero designs with this application module. CtrlGauss Module 1 is ideal for anyone interested in analyzing the response of linear systems.

Control systems and economic models are just two possible applications. CtrlGauss and SimGauss are designed to work together. System models can be easily incorporated into SimGauss models using the state-space representation. Also, because you can change the dimensions of a SimGauss model after it is compiled, you can write a general system simulation and then quickly try various system models in it just by changing the values and sizes of the associated matrices. SimGauss will also produce a linearized model from a non-linear system. This linearized model can then be analyzed using CtrlGauss Module 1 to aid understanding of the simulation and to suggest possible control techniques.

[contact addresses] [Detailed description] [homepage] 

Nonlinear curve fitting - Given data and a procedure for computing the function, CurveFit will find a best fit of the data to the function in the least squares sense.

Special Features:

• Weight observations
• Multiple dependent variables
• Bootstrap estimation
• Histogram and surface plots of bootstrapped coefficients
• Profile t, and profile likelihood trace plots
• Levenberg-Marquardt descent method
• Polak-Ribiere Conjugate Gradient descent method
• Activate and inactivate coefficients
• Heteroskedastic-consistent covariance matrix of coefficients

Bootstrap Estimation

CurveFit includes special procedures for computing boot-strapped estimates. One procedure produces a mean vector and covariance matrix of the boot-strapped coefficients, while another generates histogram plots of the distribution of the coefficients and surface plots of the parameters in pairs. The plots are especially valuable for nonlinear models because the distributions of the coefficients may not be uni-modal or symmetric.

Profile t, and Profile Likelihood Trace Plots

Also included in the module is a procedure that generates profile t trace plots and profile likelihood trace plots using methods described in Bates and Watts, "Nonlinear Regression Analysis and its Applications". Ordinary statistical inference can be very misleading in nonlinear models, and these plots provide a means for assessing the statistical significance of coefficients in nonlinear models that is superior to the usual methods.

Descent Methods

The primary descent method for the single dependent variable is the classical Levenberg-Marquardt method. This method takes advantage of the structure of the nonlinear least squares problem, providing a robust and swift means for convergence to the minimum. If, however, the model contains a large number of coefficients to be estimated, this method can be burdensome because of the requirement for storing and computing the information matrix. For such models the Polak-Ribiere version of the Conjugate Gradient method is provided, which does not require the storage or computation of this matrix.

Multiple Dependent Variables

CurveFit allows multiple dependent variables using a criterion function permitting the interpretation of the estimated coefficients as either maximum likelihood estimates or as Bayesian estimates with a noninformative prior. This feature is useful for estimating the parameters of "compartment" models, i.e., models arising from linear first order differential equations. 

The procedures in DSTAT provide basic sample statistics of the variables in GAUSS data sets. These statistics describe the numerical characteristics of random variables, and provide information for further analysis.

Features

• Handles large data sets
• Accommodates both character and numeric variables
• All statistics calculated are accessible for later use
• Provides statistics for an entire data set or specified data range

Main Functions

• Calculates the means of a set of variables
• Calculates the extreme values of a set of variables
• Computes the covariance matrix of a set of variables
• Computes the correlation matrix of a set of variables
• Creates contingency tables
• Computes statistics and measure of fits for a contingency table
• Computes frequency distributions for a set of variables

Tests the differences of means between two groups

Discrete Choice contains a set of procedures for estimating a variety of discrete choice models, including:

• Multinomial logit model
• Adjacent category and stereotype multinomial logit models
• Conditional logit model
• Nested logit model
• Poisson, truncated, censored and zero-inflated models
• Negative binomial, truncated, censored and zero-inflated models
• Logit, probit, ordered logit and probit models

Discrete Choice has the same functionality and more as Quantal Response; however, it won't run applications developed with Quantal Response. Discrete Choice will replace Quantal Response in our Applications Bundle, but Quantal Response will still be available for purchase for those who need it.

Requires GAUSS Mathematical and Statistical System 5.0. Available for Windows, Linux, Solaris, AIX and HP-UX platforms

Features Include:

• ASCII and Excel file conversions
• Handling missing data
• Create and simulate data sets
• Create new variables
• Delete observations
• Drop variables
• Keep variables and drop all others
• Execute GAUSS commands unfiltered
• List data sets
• List variable names and types
• Merge data sets on a key variable
• Select observations
• Sort data set
• Compute statistics on data set
• Simulate using various models, e.g., probit, logit, GARCH, linear
• Impute missing data using EM algorithm

Platforms:
Available for Windows, LINUX, AIX4, HPUX11 and Sun SPARC

• Plot types supported by GAUSSplot:
  • XY Line plots
  • Bar plots
  • Polar line plots
  • 2D Cartesian plots
  • 2D Contour plots
  • 3D Cartesian plots, including
    • ability to graph 3D surfaces and solids
    • Gouraud shading
    • configurable light source intensity and location
    • surface translucency
  • 3D Contour plots
    
• Built-in curve fitting
• 3D rotation and animation
• Supports the following export file types:
  • Encapsulated PostScript (EPS)
  • PostScript
  • HPGL and HPGL/2
  • Windows Metafile Format (WMF on UNIX and Windows)
  • JPEG
  • BMP
  • PNG
  • TIFF
  • PostScript bitmap
  • Sun Raster bitmap
  • X-Window bitmap

Platforms:
Available now for Windows and Linux; coming soon for Solaris, Mac OS X, Windows Itanium 2 and Linux AMD 64.

A full-featured package for Finance and Econometrics
GAUSSX is a comprehensive analysis package for GAUSS. The new windows version is like two products in one. It is a powerful GUI enhancement for GAUSS, and a comprehensive econometrics package with state of the art analysis capabilities. GAUSSX is also available for UNIX and provides the same powerful analysis capabilities as the windows version under the familiar X-Windows GAUSS interface.

[contact addresses] [Detailed description] [homepage] 

GENO is a numerical optimizer with exceptionally wide application. It may be used to solve uni- or multi-objective optimization problems: the problem may be static or dynamic, linear or nonlinear, unconstrained or constrained (by equations or inequalities); in addition, any combination of the variables may assume real or discrete values.

[contact addresses] [Detailed description] [homepage] 

LAPACK State of the Art Numerics for GAUSS
The LALIB-386 package is an implementation of LAPACK as an extension of the GAUSS Run-time Library. The LAPACK routines for real and complex general, real symmetric, complex symmetric, and complex Hermitian matrices are implemented.

LAPACK-Linear Algebra PACKage is the long awaited update to the well known LINPACK and EISPACK software packages. For more than 20 years LINPACK and EISPACK have been the standard for numerical computation. Currently used by GAUSS and other numerical and statistical software as their core routines, LINPACK and EISPACK have now been upgraded under the direction of many of the same people who created the original software. LAPACK, not only contains the latest, state-of-the-art numerical algorithms, it also provides many new features for the serious numerical analyst. These features emphasize the most important numerical analysis issue, the accuracy and precision of the ill-conditioned problem.

An important addition is the "expert" routine. The linear equation, least squares, and eigenvalue functions have both regular and expert versions. The expert versions, in addition to returning the usual results, also provide extensive information about the problem. For example, the expert version of the linear equation solver for the real or complex square matrices equilibrates and scales the input matrices, and returns the LU factorization, the pivoting information, scaling vectors, condition estimate, and forward error bounds and relative backward error estimates.

LALIB-386 contains routines for solving linear equations, least squares problems, eigensystems, and factorizations. The following routines are included:

Linear Equations: LSOLSQ & LSOLSQX Regular and expert versions for real or complex square matrices using the LU factorization LSOLPD & LSOLPDX Regular and expert versions for real symmetric or complex Hermitian positive denite matrices using the Cholesky factorization

LSOLIN & LSOLINX Regular and expert versions for real symmetric complex symmetric, or complex Hermitian indenite matrices using the LDL factorization

LSYLV Solves Sylvester's equation, AX + XB = C

Ordinary Least Squares: LOLSQR Using QR factorization(or LQ if rows are less than columns)

LOLSOF Using complete orthogonal factorization

LOLSSVD Using singular value decomposition.

Eigensystems LALIB contains a full complement of eigensystem functions in both regular and expert versions. Subsets of eigenvalues/vectors may be computed by specifying a range of either values or indices. For square input matrices either left or right eigenvectors, or both, may be computed. There are also functions for computing the singular value decomposition and Schur form and vectors. LEIGH, LEIGHX, Eigenvalues, eigenvectors of a real symmetric, complex LEIGH1X, LEIGH2X, Hermitian matrix; eigenvalues, eigenvectors selected by LEIGHV, LEIGHVX, index or by value LEIGHV1X,LEIGHV2X

LEIG, LEIGVL, Eigenvalues, right and/or left eigenvectors of a real LEIGVRL, LEIGVX, or complex square matrix

LSVD, LSVD1, Singular value decomposition LSVD2

LSCHUR, LSCHURV, Schur form, Schur vectors. LSCHURX, LSCHURVX

Solves LALIB contains solve functions for real or complex general matrices, real or complex, symmetric or Hermitian, positive definite or indefinite matrices, as well as triangular matrices, and Sylvester's equation. The expert versions return appropriate factorizations, pivot vectors, scaling vectors, condition numbers, and forward and backward error bounds.

Factorizations LALIB implements real and complex versions of the QR, RQ, LDL, LU, and Cholesky factorizations. LQR, LQRE, LQREP, QR factorization for real or complex rectangular LQQR, LQQRE, matrices, with and without pivoting, with and LQQREP, LQYR, without Q,QY and Q'Y LQYRE, LQYREP, LQYTR, LQYTRE, LQYREP

LLU, LINV, For real or complex retangular matrices LU LLUCOND,LLUDET factorization with pivoting, inverse(for square matrices), condition number, determinant LCHOL, LINVPD, For real symmetric or comples Hermitian positive LCHCOND, LCHDET demite matrices, Cholesky factorization, inverse, condition number, determinant

LDL, LDLINV, For real or complex symmetric, complex, Hermitian LDLCOND, LDLDET indefinite matrices, LDL factorization, inverse, condition number, determinant. 

LikPak 1.0 from Econotron Software consists of over 50 likelihood functions and examples for GAUSS. LikPak is designed to be used with GAUSS optimization packages such as Constrained Maximum Likelihood MT, Maximum Likelihood, and Maximum Likelihood MT.

LikPak has been designed to complement the optimization packages; it saves the programmer from having to write the likelihood and shows how the likelihood can be parameterized for a particular problem.

LikPak is designed to be used as a template; that is, select the example that is relevant to your problem and use that example as a starting point. The functions in LikPak corespond to the set of likelihoods currently used in economics, and each function is backed up with documentation describing typical parameterizations.

The source code is written in GAUSS and will run on any platform of GAUSS or the GAUSS Engine. See Processes and Utilities below for a list of processes and utilities included in LikPak. Full documentation and examples are provided for each function.

[contact addresses] [homepage] 

Linear Covariance Structure Analysis, Simultaneous Equations, and Confirmatory Factor Analysis
LINCS computes full-information maximum likelihood (FIML) or minimum distance (MDE) estimates of linear structural models, including models with measurement error terms. Also included is a stand-alone procedure for two-stage least squares that is used by LINCS for computing start values. The MDE method is more well known by psychometricians as the Asymtotic Distribution Free, or ADF, method.

This version of LINCS will also handle data sets with missing observations in them, or alternatively, an imputed data set may be generated using MISS.

Capabilities:

Compute White's heteroskedastic-consistent standard errors; Perform Hausman-type specification tests. Permit placement of general non-linear constraints on the parameters, and computes the correct standard errors. Produce both total and indirect effects and their standard errors.

LINCS features go beyond those of LISREL, EQS, or COSAN, which estimate similar models. 

• Thread-safe Execution: Control variables are model matrices are contained in structures allowing thread-safe execution of programs.
• Sparse matrices: Linear Programming MT exploits sparse matrix technology permitting the analysis of problems with very large constraint matrices. The size of a problem that can be analyzed is dependent on the speed and amount of memory on the computer, but problems with two to three thousand constraints and more than six thousand variables have been tested on ordinary PC's.
• MPS files: procedures are available for translating MPS formatted files.

Other Product Features

LPMT is designed to solve small and large scale linear programming problems. LPMT can be initialized with a starting value, such as the solution to a previous problem which is similar to the one being solved. This feature can dramatically reduce the number of iterations required to find a feasible starting point.

Features

• Upper and lower finite bounds can be provided for variables and constraints
• Problem type (minimization or maximization)
• Constraint types (<=, >=, =)
• Choice of tolerances
• Pivoting rules

Computes

• The value of the variables and the objective function upon termination, and returns the dual variables
• State of each constraint
• Uniqueness and quality of solution
• Multiple optimal solutions if they exist
• Number of iterations required
• A final basis
• Can generate iterations log and/or final report, if requested

The Linear Regression MT application module is a set of procedures for estimating single equations or a simultaneous system of equations. This module allows constraints on coefficients, and heteroskedastsic consistent standard errors. It includes two-stage least squares, three-stage least squares, and seemingly unrelated regression procedures.

Features include:

• Performs both influence and collinearity diagnostics inside the ordinary least squares routine (OLS)
• Performs multiple linear hypothesis testing with any form
• Accommodates large data sets with multiple variables
• Estimates regressions with linear restrictions

The Loglinear Analysis MT application module contains procedures for the analysis of categorical data using loglinear analysis.

The estimation is based on the assumption that the cells of the K-way table are independent Poisson random variables. The parameters are found by applying the Newton-Raphson method using an algorithm found in A. Agresti (1984) Analysis of Ordinal Categorical Data. You may construct your own design matrix or use LOGLIN procedures to compute one for you. You may also select the type of constraint and the parameters.

MAXLIK performs maximum likelihood estimation of the parameters of statistical models. All you have to provide is a GAUSS function to calculate the log-likelihood for a set of observations, and MAXLIK does the rest.

Features

• More than 25 options can be easily specified by the user to control the optimization

• Descent algorithms include: BFGS (Broyden-Fletcher-Goldfarb-Shanno), DFP (Davidon-Fletcher-Powell), Newton, Steepest Descent, PRCG (Polak-Ribiere type Conjugate Gradient), and BHHH (Berndt-Hall-Hall-Hausman)

• Step-length methods include: STEPBT, BRENT, BHHHSTEP, and a step-halving method

• A "switching" method may also be selected which switches the algorithm during the iterations according to two criteria: number of iterations, or failure of the function to decrease within a tolerance

Improved Algorithm

MAXLIK implements the numerically superior Cholesky factorization, solve, and update methods for the BFGS, DFP, and Newton algorithms.

Event Count and Duration Regression:

COUNT is included in this module for estimating the Limited Dependent Variable model. These procedures provide maximum likelihood estimators for parametric regression models of events data, i.e., models with dependent variables that are measured either as event counts or as durations between events. 

A Statistical Environment for GAUSS
Markov is a statistical environment that makes it easy to do simple things without restricting your use of the full power of GAUSS. Experienced GAUSS programmers can work more efficiently. New users will find that Markov makes GAUSS easier and more fun to learn. A user writes: "Markov makes life a lot easier for the GAUSS users, even for people who have learned how to do things the harder way in GAUSS." Markov is ideal for classroom use where you want students to be able to get output quickly and easily, but also want them to have access to a matrix language.

How Markov Works

Markov works with a simple command structure. For example, to run a multiple regression with listwise deletion you would use the command: set dsn mydata; set lhs yvar; set rhs xvar1 xvar2; opt miss list; go reg;

After running a regression in Markov all of the results are returned to globals that can be used for additional analysis. These can be used in your own GAUSS programs, or can be used by Markov commands for further analysis. For example, to test the hypothesis that the coefficients for XVAR1 and XVAR2 were both zero, you would simply enter the command: test delete xvar1 xvar2;

Or, if you insist, use GAUSS commands to get the same answer: let q[2,3] = 0 1 0 0 0 1; let r = 0 0; qbr = q*_b; rcovbr = q*_covb*q'; f = (qbr' inv(rcovbr) * qbr)/2; print f; p = cdffc(f,2,_nobs-3); print p;

Complicated graphs can be computed just as easily, with impressive results.

Features in Markov Extensive on-line documentation and a nearly 300 page manual that includes complete descriptions of each procedure.

Statistical procedures include descriptive statistics, cross-tabulation, log-linear models, multinomial logit, probit, Poisson regression including the NEGBIN 1 model, ordered logit and probit, simultaneous equation models, and regression analysis with collinearity diagnostics, residual analysis and powerful statistical tests such as White's information matrix test.

Full data management capabilities including sorting, merging and updating. Variables in memory can be saved to GAUSS data files as simply as entering the command: WRITE X Y Z to NEWFILE Varibles from disk files can be brought into memory simply: READ WEIGHT LENGTH FROM AUTO. Enchancements to GAUSS's DATALOOP procedure make it easy to construct the types of variables most commonly used in statistical analysis.

Statistical graphics including box and whisker plots, scatterplot matrices, quantile-quantile plots, and many more. Each plot can be specified using a simple command language.

A shell for Monte Carlo simulation is built into Markov. This allows you to program the procedure you want to simulate, and Markov does all the work of keeping track of the results of the simulation. Summary statistics are displayed as the simulation proceeds. Lengthy simulations can be suspended and resumed later. Results can be easily graphed. For example, simulations done with Markov to study the behavior of the Breusch-Pagan test for heteroscedasticity in the presence of skewed errors showed the importance of a robustified test. The results are plotted on the previous page.

Finally, complete source code is provided allowing you to modify and extend Markov. 

Mercury consists of a set of utilities that extend the power of GAUSS, especially in terms of message and data communication between Gauss and an external application. Mercury has four main components:

• Provides Windows clipboard support for Gauss for both data and text.

• Provides Gauss functionality for Excel. Given a set of data in an Excel Workbook, Gauss will take the data, process it, and return the results to the specified cells in the spreadsheet.

• A set of communication and message tools for developers who need to link Gauss to an external application using custom interfaces.

• A demonstration project showing how Gauss compliant DLLs are created.

The Nonlinear Equations MT application module solves systems of nonlinear equations where there are as many equations as unknowns.

The functions must be continuous and differentiable. You may provide a function for calculating the Jacobian, if desired. Otherwise NLSYS will compute the Jacobian numerically. You can also select from two descent algorithms, the Newton method or the secant update methods, a quadratic/cubic method, or the hookstep method.

OPTMUM is intended for the optimization of functions. It has many features, including a wide selection of descent algorithms, step-length methods, and "on-the-fly" algorithm switching. Default selections permit you to use OPTMUM with a minimum of programming effort. All you provide is the function to be optimized and start values, and OPTMUM does the rest.

Features

• More than 25 options can be easily specified by the user to control the optimization

• Descent algorithms include: BFGS, DFP, Newton, Steepest Descent, and PRCG

• Step length methods include: STEPBT, and BRENT , a step-halving method may also be used

• A "switching" method may also be selected which switches the algorithm during the iterations according to two criteria: number of iterations, or failure of the function to decrease within a tolerance

Improved Algorithm

OPTMUM implements the numerically superior Cholesky factorization, solve and update methods for the BFGS, DFP, and Newton algorithms. The Hessian, or its estimate, are updated rather than the inverse of the Hessian, and the descent is computed using a solve. This results in better accuracy and improved convergence over previous methods. 

Run multiple GAUSS workspaces simultaneously on either local or remote computers with Forward Software's new Parallel GE, a networked user interface for the GAUSS Engine (and soon for GAUSS)! Increase user productivity and maximize computer resources with Parallel.

• Run GAUSS programs in multiple workspaces at the same time.
• Distribute these workspaces across networked computers.
• Write your own parallel programs easily--just three extra commands!
• Make use of your multi-processor hardware or extra computers to increase throughput.
• Continue preparing and queuing programs for execution while your program is running.
• Continue working in another workspace while your queued programs are running.
• No need to save--your work is saved as you do it.

And much more!

Available for GAUSS Engine 5.0, soon to be available for GAUSS 5.0 as well. 

Quantal Response is a statistical package which provides a set of procedures for estimating models in which the dependent variable is qualitative in some way. These models are particularly useful for researchers in the social, behavioral, and biomedical sciences, as well as economics, public choice, education, and marketing.

[Detailed description] 

A discrete simulation module for GAUSS
QueGAUSS allows you to simulate discrete systems involving queues. These include such things as phone exchanges, manufacturing processes and hospital patient services. Using QueGAUSS you can examine the statistics of waiting times, transit times and utlization of resources.

QueGAUSS consists of items, event procedures and queues. Items are the things that flow through the model. You can define any number of item types each with their own attributes (both numeric and character). Event procedures are GAUSS procedures that process the items. Queues are available to store items that are waiting to be processed. Print procedures are provided to display the contents of items and queues using user defined formats.

FEATURES:

• Basic Statistics are automatically collected for all items and queues.

• Accumulators can be defined to collect other statistics.

• Plots of the variations in statistics as well as frequency tables can also be accumulated.

• Wide range of built-in-distributions:-exponention (Poisson), Erlang, Hyper-exponential, Normal, Uniform and Integral Uniform.

• Access to all of GAUSS programming, data handling and plotting functions.

• Random samples of any distribution (discrete or continuous) can be obtained given its distribution.

• Extensive error checking built-in which can be disabled for faster runs.

• Intelligent printing functions to display items and queues.

• Verbose mode which allows you to trace backwards and forwards through the simulation's executions.

• Transit and Markitem procedures to determine the transit time of items.

• Number of items in existence at one time limited only by memory.

• Memory compaction allows unlimited number of items during the course of simulation.

• The start up phase of a simulation can be easily ignored.

• 80 page manual including tutorial, detailed examples, guidelines for writing a simulation, debugging tips, command reference and index.

SimGauss is the fast and easy way to simulate non-linear differential equations and state-space systems, such as vehicle dynamics, biological systems and economic models. SimGauss V2.0 is a major revision of SimGauss which adds a number of new features that allow you to write your model fast, run it fast and analyze and plot the results fast, all from within the GAUSS environment.

Features:

• Model code written in GAUSS Programming Language. GAUSS is fast and was designed to make it easy to write efficient code for serious numerical computation;

• All the model variables can be displayed and modified from the GAUSS command level or via the matrix editor, SGVIEW;

• Choice of 8 integration algorithms;

• Understands state vectors and vector derivative equations;

• SimGauss' vector capability can be used to efficiently investigate variations in the model's parameters. Also, because GAUSS is optimized for vector operations these runs are faster than the sum of the individual runs;

• Extensive simulation operators: Backlash, Bound, Deadband, Delay, Quantization, Limited Integration, Table Lookups and an algebraic equation solver;

• Powerful user events give you further control over your model while it is running;

• Publication Quality Graphics, high resolution (up to 4096x3120) 2D and 3D color graphics with hidden line removal, zoom and pan are available to enhance your reports;

• SimGauss can be extended by defining your own specialized procedures in the GAUSS language, or by including existing Fortran, C or Assembler code;

• The simulation can be halted at any time and the SAVEALL command used to save the compiled model code and the current model values to disk.

SSATS is a set of preprogrammed GAUSS procedures that perform all the tasks necessary to and associated with the specification, estimation, and forecasting of multivariate state space time series models. A standard state space model takes the form:

y_t = Cz _t + e_t (observation equation)
z_t+1 = Az _t + Be_t (state equation)

where y_t is an (m x 1) vector of the time series to be modeled and/or forecast, z _t is the (n x 1) state vector, e _t is an (m x 1) vector of stochastic innovations (error terms), and A, B, and C are parameter matrices to be estimated.

Masanao Aoki developed a particularly successful algorithm to estimate such models based on the balanced representation and relying heavily on results from linear systems theory. SSATS will let a researcher easily begin to implement the techniques laid out in Aoki's book, State Space Modeling of Time Series (Springer-Verlag, 1987, 1990).

SSATS will be useful to any researcher who is interested in empirical work on multivariate dynamic systems. SSATS is a valuable tool for anyone involved in the specification, estimation, and forecasting of multivariate (or univariate) time series models. The procedures can be used on their own, combined into a single command program, or used selectively in conjunction with other time series methods to aid in specification or forecast evaluation.

SSATS provides procedures to easily accomplish such tasks as:

• Scale and center data prior to estimation

• Choose the model specification (model order of the time series),

• Estimate the model coefficients A, B, and C

• Estimate covariance matrices of parameter matrices, data series, errors, and states

• Evaluate model specification with diagnostic tools

• Produce in-sample and out-of-sample forecasts

• Evaluate forecasting performance including a variety of summary statistics.

All of the forecasting evaluation procedures can be used with forecasts generated by any methods; they are not restricted to use with state space models. Similarly, the model specification procedures and statistical tests included can be used to identify the model order of a time series even if the researcher then estimates a VAR or VARMA model instead of a state space model.

The SSATS procedure module comes with:

• 19 procedures

• A complete user's guide containing descriptions and examples for all procedures

• A primer on state space models, the Aoki estimation algorithm, and tips and guidance on how to successfully model and forecast multivariate time series using state space models

• A sample program showing how to combine the procedures into a complete implementation of the procedures to specify a model, estimate it, produce forecasts, and evaluate the model's performance

A sample data set and demo output to allow researchers to insure that the programs are working properly on their systems.

Stat/Transfer is a menu driven program which allows you to transfer data files between dBase, Epi, Excel, GAUSS, HTML, JMP, LIMDEP, Lotus 1-2-3, Matlab, Minneset, MS ACCESS, ODBC, OSIRIS, Paradox, Quattro Pro, SAS, S-Plus, SPSS, Stata, Statistica, Symphony, Systat.

[Homepage] [contact addresses]

Automatic differentiation for GAUSS is now available with Econotron's Symbolic Tools package!

The Symbolic Tools package augments the numeric and graphical capabilities of GAUSS with additional mathematical functionality based on symbolic computations, including:

• Automatic differentiation
• Symbolic algebra
• Exact linear algebra
• Language extension
• User defined precision

Symbolic Tools enables GAUSS to undertake automatic differentiation, by creating procs that return analytical gradients and Hessians, which can then be used by Aptech's GAUSS Applications such as Maximum Likelihood, Constrained Maximum Likelihood, Optimization, and Nonlinear Equations. Additionally, Language Extension provides all the functionality of Maple, as well as all the symbolic arithmetic that Maple offers. Over 180 GAUSS examples are included, as well as 10 examples, including ARCH and GARCH. Requires GAUSS 4.0 or GAUSS Engine 4.0 or higher for Windows and Maple 9.

[contact addresses] [homepage] 

Time-Series Cross-Sectional Regression Models
Includes procedures to compute estimates for "pooled time-series, cross-sectional" models. Includes : Fixed-effects OLS estimator (analysis of covariance estimator)

• Constrained OLS estimator

• Random effects estimator using GLS.

Autoregression Models
Computes estimates of the parameters and standard errors for a regression model with autoregressive errors. Can be used for models for which the Cochrane-Orcutt or similar procedures are used. Also computes autocovariances and autocorrelations of the error term U.

ARIMA Models
The Time Series module also includes tools for estimating general ARIMA (p,d,l,q) models using an exact MLE procedure based on C. Ansley (Biometrika 1979, p. 59-65). Procedures for computing forecasts, theoretical autocovariances, sample autocorrelations and partial autocorrelations (using Durbin's algorithm), as well as for simulating ARIMA models are provided.

[Detailed description] 

TSAGL - Signal Processing Analysis and Display
Time Series Analysis and Graphics Library (TSAGL) is a general-purpose signal processing, analysis and display package. It contains a host of basic and complex algorithms that allow you to develop sophisticated programs based upon your specific needs. The algorithms are written as GAUSS procedures. They can therefore be accessed quickly and easily from within the GAUSS environment.

Many procedures provided in this package reflect advanced concepts in the field of signal processing. You will find in the TSAGL manual a brief description of the fundamental ideas or equations along with references to publications used to develop each procedure.

The TSAGL procedures (over 70 procedures are implemented in the current version) are gathered in the five libraries listed here:

• Standard Library

• Filter Library

• Graphics Library

• Spectrum Library

• Model Library

Time Series Analysis and Graphics Library is designed to be versatile. It is a convenient research and development tool for anyone involved in the field of signal processing and analysis. Because it is written in the form of GAUSS procedures, you can develop custom-tailored programs. 

TSM - Advanced Time Series Estimation package for Financial Analysts, Economists and Engineers
TSM is a GAUSS library for time series modeling in both time domain and frequency domain and works in conjunction with the GAUSS Application -- Optimization.

It is primarily designed for the analysis and estimation of ARMA, VARX processes, state space models, fractional processes and structural models. To study these models, special tools have been developed like procedures for simulation, spectral analysis, Hankel matrices, etc. Estimation is based on the Maximum Likelihood principle and linear restrictions may be easily imposed.
Following LÜTKEPOHL [1991], several procedures enable one to get the VAR(1) representation, roots of the reverse characteristic polynomial, the pure AR and MA representations, the matrices of the response forecast errors and the orthogonal impulses (and those of the corresponding dynamic multipliers) and the forecast error variance decomposition matrices. Two types of estimation can be performed: Conditional Maximum Likelihood (based on REINSEL,[1993] and Exact Maximum Likelihood (based on ANSLEY and KOHN [1983].
Related to ARMA processes (and to state space models), Hankel matrices may be computed. You can also determine the McMillan degree of an ARMA process (see Aoki [1987]).

State Space Models
Analysis and Estimation of state space models (SSM) are included in TSM. The SSM form corresponds to the one presented in HARVEY [1990]. Filtering, (fixed-interval) smoothing and maximum likelihood (with implicit linear restrictions) may be easily undertaken. For time invariant SSM, three additional procedures permit computing initial conditions, forecasting processes and solving the algebraic Riccati equation. Note that for structural models (local level, local linear trend, basic structural and cycle models), maximum likelihood can be performed in the frequency domain.

Spectral Analysis
TSM also contains spectral analysis procedures for the estimation of periodograms, cross-periodograms and coherencies, cross-amplitude spectra and phase spectra. Data windowing can be done in the frequency domain. The user has the choice between different lag window generators (rectangular, Hartlett, Daniell, Tukey, Parzen and Bartlett-Priestley) and may define his own generator. Note that there also exists a procedure for smoothing in the time domain, based on the Savitzky-Golay filter.
General maximum likelihood estimation can be undertaken. For ML estimation in the frequency domain (Whittle likelihood), special procedures are available. Linear restrictions may be imposed in this implicit, form-Jacobian, gradient and Hessian matrices (and information matrix in the frequency domain) allow one to easily perform Lagrange multiplier tests.
TSM also contains procedures for resampling and simulation, like bootstrap, surrogate data technique and kernel estimation.

Extensively Illustrated and Documented

More than 100 examples illustrate TSM routines. These examples are not just applications, but should be viewed as extensions of the library. They concern, for example, the optimal order of VAR models, the Kolmogorov-Smirnov statistic in the frequency domain, CUSUM and CUSUMsq tests or normality test for probit models.

This English language package includes a comprehensive 130 page manual and requires the GAUSS Application -- Optimization and GAUSS-386i v3.2 (DOS version).