Requirements

Requires GAUSS Mathematical and Statistical System 6.0 or the GAUSS Engine 6.0.

New Features

• Structures, in particular DS structures for handling data, and PV structures for handling parameters
  
• New method for testing hypotheses concerning models with constraints on parameters (Silvapule & Sen, _Constrained_Statistical_Inference_)
  
• New numerical derivatives, user-provided analytical derivatives can compute a subset of the derivatives, the rest will be computed numerically
  
• New trust region method
  
• User-provided procedure includes calculation of function and optionally derivatives--reduces calculations in common between function and derivatives
  
• General improvement in algorithms

  Platforms

Windows, LINUX and UNIX.

Requirements

Requires GAUSS Mathematical and Statistical System 6.0 or the GAUSS Engine 6.0.

CO is fast and can handle large, time-consuming problems because it takes advantage of the speed and number-crunching capabilities of GAUSS. It is thus ideal for large scale Monte Carlo or bootstrap simulations.
 

Example

A Markowitz mean/variance portfolio allocation analysis on a thousand or more securities would be an example of a large scale problem CO could handle (about 20 minutes on a 133 Mhz Pentium-based PC).

CO also contains a special technique for semi-definite problems, and thus it will solve the Markowitz portfolio allocation problem for a thousand stocks even when the covariance matrix is computed on fewer observations than there are securities.

Because CO handles general nonlinear functions and constraints, it can solve a more general problem than the Markowitz problem. The efficient frontier is essentially a quadratic programming problem where the Markowitz Mean/Variance portfolio allocation model is solved for a range of expected portfolio returns which are then plotted against the portfolio risk measured as the standard deviation:

where l is a conformable vector of ones, and where  is the observed covariance matrix of the returns of a portfolio of securities, and µ are their observed means.

This model is solved for

and the efficient frontier is the plot of  on the vertical axis against

on the horizontal axis. The portfolio weights in  describe the optimum distribution of portfolio resources across the securities given the amount of risk to return one considers reasonable.

Because of CO's ability to handle nonlinear constraints, more elaborate models may be considered. For example, this model frequently concentrates the allocation into a minority of the securities. To spread out the allocation one could solve the problem subject to a maximum variance for the weights, i.e., subject to

where  is a constant setting a ceiling on the sums of squares of the weights.

This data was taken from from Harry S. Marmer and F.K. Louis Ng, "Mean-Semivariance Analysis of Option-Based Strategies: A Total Asset Mix Perspective", Financial Analysts Journal, May-June 1993.

An unconstrained analysis produced the results below:

It can be observed that the optimal portfolio weights are highly concentrated in T-bills.

Now let us constrain w´w to be less than, say, .8. We then get:

The constraint does indeed spread out the weights across the categories, in particular stocks seem to receive more emphasis.

Efficient portfolio for these analyses

We see there that the constrained portfolio is riskier everywhere than the unconstrained portfolio given a particular portfolio return.

In summary, CO is well-suited for a variety of financial applications from the ordinary to the highly sophisticated, and the speed of GAUSS makes large and time-consuming problems feasible.

CO is an advanced GAUSS Application and comes as GAUSS source code.

GAUSS Applications are modules written in GAUSS for performing specific modeling and analysis tasks. They are designed to minimize or eliminate the need for user programming while maintaining flexibility for non-standard problems.

Platform: Windows, LINUX and UNIX.

Requirements: GAUSS/GAUSS Light version 3.2.19 or higher.

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
  
• Ability to activate and inactivate coefficients
  
• Heteroskedastic-consistent covariance matrix of coefficients
  

Bootstrap Estimation

CurveFit includes special procedures for computing bootstrapped estimates. One procedure produces a mean vector and covariance matrix of the bootstrapped coefficients. 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 unimodal 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. These plots are superior to usual methods in assessing the statistical significance of coefficients in nonlinear models.

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.

Platform: Windows, LINUX and UNIX.

Requirements: GAUSS/GAUSS Light version 3.2 or higher.

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
  
  

Platform: Windows, LINUX and UNIX.

Requirements: GAUSS/GAUSS Light version 3.2 or higher.

• Includes methods for analyzing and generating contingency
  tables and statistics for them.
• Includes new routines to compute descriptive statistics,
  including both univariate and multivariate skew and kurtosis.
• Includes support for variable names of up to 32 characters.
• Includes support for date variables where applicable.
• You can now choose between two report types-all variables
  in a single table or individual reports for each variable-and
  you can choose which statistics to include in the report and
  the order in which they appear.

• Chi-Squared (Pearson and Likelihood Ratio)
• Phi
• Cramer's V
• Spearman s Rho
• Goodman-Krustal's Gamma
• Kendall's Tau-B
• Stuart s Tau-C
• Somer's D
• Lamda

Requirements

Requires GAUSS Mathematical and Statistical System 6.0 or the GAUSS Engine 6.0.

• Is derived from the assumption that residuals have a generalized extreme value distribution and allows for a general pattern of dependence among the responses thus avoiding the IIA problem, i.e., the "independence of irrelevant alternatives."

Conditional logit model

• Includes both variables that are attributes of the responses as well as, optionally, exogenous variables that are properties of cases.

Multinomial logit model

• Qualitative responses are each modeled with a separate set of regression coefficients

• The log-odds of one category versus the next higher category is linear in the cutpoints and explanatory variables

• The coefficients of the regression in each category are linear functions of a reference regression

• Estimates model with Poisson distributed dependent variable. This includes censored models - the dependent variable is not observed but independent variables are available - and truncated models where not even the independent variables are observed. Also, a zero-inflated Poisson model can be estimated where the probability of the zero category is a mixture of a Poisson consistent probability and an excess probability. The mixture coefficient can be a function of independent variables.

• Estimates model with negative binomial distributed dependent variable. This includes censored models - the dependent variable is not observed but independent variables are available - and truncated models where not even the independent variables are observed. Also, a zero-inflated negative binomial model can be estimated where the probability of the zero category is a mixture of a negative binomial consistent probability and an excess probability. The mixture coefficient can be a function of independent variables.

Logit, probit models

• Estimates dichotomous dependent variable with either Normal or extreme value distributions

• Estimates model with an ordered qualitative dependent variable with Normal or extreme value distributions

Supports structures and n-dimensional arrays

New GARCH models

New simulation bounds method for statistical inference

FANPAC now contains a simulation bounds method for constructing confidence intervals for models with restricted parameter spaces (Andrews, D.W.K., 1999, "Estimation when a parameter is on a boundary," Econometric, 67, 1341-1383)

A special feature of FANPAC is the ability to place constraints on the parameters to enforce stationarity and invertability and positive definiteness of the conditional variances and covariances. Andrews Method is correct for these kinds of models.

Requires GAUSS Mathematical & Statistical System 5.0 or the GAUSS Engine/Engine Pro/Engine for Workgroups/Enterprise Engine 5.0.

Platform: Windows, LINUX and UNIX.

Requirements: GAUSS/GAUSS Light version 3.2 or higher.

• 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
  
  

Platform: Windows, LINUX and UNIX.

Requirements: GAUSS/GAUSS Light version 4.0 or higher.

Features

• Calculates heteroskedastic-consistent standard errors, and performs both influence and collinearity diagnostics inside the ordinary least squares routine (OLS)
  
  
• All regression procedures can be run at a specified data range
  
  
• Performs multiple linear hypothesis testing with any form
  
  
• Estimates regressions with linear restrictions
  
  
• Accommodates large data sets with multiple variables
  
  
• Stores all important test statistics and estimated coefficients in an
  efficient manner
  
  
• Both three-stage least squares and seemingly unrelated regression can be
  estimated iteratively
  
  
• Thorough Documentation
  
  
• The comprehensive user's guide includes both a well-written tutorial and an informative reference section. Additional topics are included to enrich the usage of the procedures. These include:
  
  
  • Joint confidence region for beta estimates
    
    
  • Tests for heteroskedasticity
    
    
  • Tests of structural change
    
    
  • Using ordinary least squares to estimate a translog cost function
    
    
  • Using seemingly unrelated regression to estimate a system of cost share equations
    
    
  • Using three-stage least squares to estimate Klein's Model I
    
    

Platform: Windows, LINUX, Mac, and UNIX.

Requirements: GAUSS/GAUSS Engine/GAUSS Light version 6.0 or higher.

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.

Features

• Fits a hierarchical model given fit configurations
  
  
• Will fit all 3-way hierarchical models of a table
  
  
• Provides for cell weights
  
  
• LOGLIN can estimate most of the models described in such texts as Y.M.M. Bishop, S.E. Fienberg, and P.W. Holland (1975) Discrete Multivariate Analysis, S. Haberman (1979) Analysis of Qualitative Data, Vols. 1 and 2, as well as the book by A. Agresti.
  
  

Platform: Windows, LINUX, Mac, and UNIX.

Requirements: GAUSS/GAUSS Engine/GAUSS Light version 6.0 or higher.

Major Features of Maximum Likelihood MT

• Structures
• Simple bounds
• Hypothesis testing for models with bounded parameters
• Log-likelihood function
• Algorithm
• Secant algorithms
• Line search methods
• Weighted maximum likelihood
• Active and inactive parameters
• Bounds

Platform: Windows, LINUX and UNIX.

Requirements: GAUSS/GAUSS Light version 8.0 or higher.

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 method, and from two step-length methods, a quadratic/cubic method, or the hookstep method.

Platform: Windows, LINUX, Mac, and UNIX.

Requirements: GAUSS/GAUSS Engine/GAUSS Light version 6.0 or higher.

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, BRENT, 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

Optimization 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.

Platform: Windows, LINUX and UNIX.

Requirements: GAUSS/GAUSS Light version 3.2 or higher.

Time Series MT 1.0 is the newest time series application available for GAUSS. This new product will streamline the creation of large GAUSS programs that utilize Time Series models.

Features

• LSDV - Least Squares Dummy Variable model for multivariate data with bias correction of the parameters
• Switch - Hamilton's Regime-Switching Regression model
• SVARMAX - Seasonal VARMAX model: SVARMAX(p,d,q,P,D,Q)s
• TSCS - Time Series Cross-Sectional Regression models
• Thread-safe
• Structured output

• Computes estimates of the parameters and standard errors for a regression model with autoregressive errors.

• Portmanteau Statistics
• Forecasting: Univariate and Multivariate
• Univariate Simulation

• Bayesian prior
• Constraints on transition probabilities

Additional Features

• Exact full information maximum likelihood (FIML) estimation of VARMAX and VARMA, ARIMAX, ARIMA, ECM models.
  Impose general linear and nonlinear and equality and inequality constraints on the parameters. Find Lagrangean values associated with each constraint. Return ACF indicator matrices, together with other summary information, including Akaike, Schwarz, and Bayesian information criteria. Compute forecasts from VARMAX and VARMA models.
  
  
• Exact maximum likelihood estimation of ECM models.
  Unit root and cointegration tests, DF, ADF, Phillips-Perron, and Johansen's Trace and Maximum Eigenvalue tests.
  
  
• Estimation of VAR models.
  Compute parameter estimates 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.
  
  
• ARIMA Models
  The Time Series module includes tools for estimating general ARIMA (p,d,q) models using an exact MLE procedure based on C. Ansley (Biometrika 1979, pp. 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.
  
  
• Time-Series Cross-Sectional Regression Models: TSCS
  This module provides procedures to compute estimates for "pooled time-series cross-sectional" models. The assumption is that there are multiple observations over time on a set of cross-sectional units (e.g., people, firms, countries).

  For example, the analyst may have data for a cross-section of individuals each measured over 10 time periods. While these models were devised to study a cross-section of units over multiple time periods, they also correspond to models in which there are data for groups such as schools or firms with measurements on multiple observations within the group (e.g., students, teachers, employees).
  

  The specific model that can be estimated with this program is a regression model with variable intercepts. That is, a model with individual-specific effects. The regression parameters for the exogenous variables are assumed to be constant across cross-sectional units. The intercept varies across individuals. This program provides three estimators:
  

  • Fixed-effects OLS estimator (analysis of covariance estimator)
    
  • Constrained OLS estimator
    
  • Random effects estimator using GLS
    

  A Hausman test is computed to show whether the error components (random effects) model is the correct specification. In addition to providing the analysis of computed. The first partial squared correlation shows the percentage of variation in the dependent variable that can be explained by the set of independent variables while holding constant the group variables. The second shows the extent to which variation in the dependent variable can be accounted for by the group variable after the other independent variables have been statistically held constant.
  

  A key feature of this program is that it allows for a variable number of time-series observations per cross-sectional unit. For instance, there might be 5 time-series observations for the first individual, 10 for the second, and so on. This is useful when there are missing values.
  

Platform: Windows, LINUX and UNIX.

Requirements: GAUSS/GAUSS Light version 8.0 or higher.