Features of the Package


      ARIMA, ARFIMA, bilinear autoregressive models, nonlinear moving average models.

      Conditional heteroscedasticity models including GARCH, FIGARCH, HYGARCH, threshold ARCH (GJR), APARCH, EGARCH, and GARCH-M models, together with the obvious FIEGARCH, FIAPARCH, HYEGARCH and HYAPARCH variants.

      Regressors can be included in both the mean and variance equations. Three different modelling modes available, including error dynamics and structural dynamics.  Distributed lags easily specified in all modes, including polynomial distributed lags (PDLs).

      Error correction models, including nonlinear error correction (asymmetric, exponential smooth transition, cubic).

      Regime switching models, including simple Markov switching, Hamiltons dynamic Markov-switching models of mean and variance (SWARCH), and explained switching, where probabilities can depend on predetermined variables.

      Smooth transition (ST) regime switching implemented for any component of the model.

      All the above features (except bilinear) are available for single equations and also systems of equations including VARs, simultaneous systems, vector error correction (VECM) models, and fractional cointegration models. DCC and BEKK multivariate GARCH options for systems.

      Discrete data models including probit, logit, and ordered probit/logit, Poisson and negative binomial, also dynamic variants of these models.

      Algebraic formulation of arbitrary nonlinear equations - just type the equation into a text field in natural notation. The nonlinear model is fully integrated with other the dynamic program features.

      Almost any nonlinear model not otherwise built in can be estimated by supplying the Ox code for the required function. This feature can be used either on its own, or in conjunction with the built-in modelling components. The complete set of testing and forecasting options are available for the users model. This may be either a single equation or a system of similar equations, with cross-equation restrictions if required.

      Linear panel data models with fixed or random effects, and permitting unbalanced panels. 

Estimation Methods

      Standard (non-iterative) OLS and IV estimation of linear regressions.

      Nonlinear least squares.

      Conditional time domain MLE allowing choice of Gaussian, Students t, skewed Students t, and GED disturbances.

      Frequency domain (Whittle) MLE for ARIMA/ARFIMA models. 

      ML estimation for binary and count data models.

      LGV, FIML and 3SLS estimation for systems of equations.

      Efficient GMM estimation of nonlinear equations/systems.

Estimation Options

      Numerical optimization using BFGS with the option of the simulated annealing algorithm to provide starting values.

      Any parameter can be fixed at a preset value in estimation, or subjected to inequality constraints using a logistic map.

      Automatic regressor selection:  reports the best (on preferred model selection criterion) of  the 2N regressions with subsets of a baseline set of N regressors.

      Automatically estimates all ARMA specifications up to preset maximum orders, allowing easy model selection.

      One- and two-dimensional plotting of the concentrated criterion function.

      Nonparametric (Nadaraya-Watson) bivariate regression.

      Log-periodogram regression (Geweke-Porter-Hudak and Moulines-Soulier methods), and local Whittle ML estimation of long memory parameter. 

      Rolling and incremental estimation. Multi-step forecasts can be selected for a fixed date, so that the performance of forecasts at each range can be compared.

      Bootstrap bias correction.

Test and Forecasting Options

      Standard and user-specified diagnostic tests (LM and M principles), including common factor test, information matrix test, Nyblom-Hansen scores test, Andrews structural change test,

      Residual-based tests including Durbin-Watson, KPSS, V/S, Lo's RS, HML and cusum of squares.

      Summary statistics for data series, including the RS, V/S and KPSS tests of I(0), and ADF, Phillips-Perron and Elliott-Rothenberg-Stock tests of I(1).

      Multiple linear or nonlinear parameter restrictions can be tested by the Wald principle, and/or imposed in estimation for testing by the LM principle.

      Any test statistic can be user-programmed in Ox, based on estimation outputs.

      Multi-step ex-ante forecasts of linear-in-mean and Markov-switching models, with standard error bands adjusted for ARCH innovations.

      Multi-step forecasting by Monte Carlo of any nonlinear specification, reporting median forecasts of mean and variance, with 95% confidence bands, and empirical kernel densities for any forecast.   

      Stochastic simulation of any fitted or user-specified model, with shocks drawn from either Gaussian/Student distributions or from EDF of residuals. 

      Bootstrap p-values for diagnostic and significance tests, using the simulation module to generate bootstrap draws.

      Bootstrap equal-tailed confidence intervals.

      Johansen tests for cointegrating rank, and MINIMAL analysis on cointegrating vectors.

      Obtain test p-values with distributions tabulated by simulation.


      Standard output includes:

v     Point estimates, standard errors (robust formula by default), p-values for significance.

v     Roots of ARMA and GARCH polynomials.

v     Schwarz, Hannan-Quinn and Akaike model selection criteria.

v     Residual standard deviation, skewness, kurtosis, and Jarque-Bera statistic.

v     Residual Q statistics for residuals and squared residuals.

      Optional outputs include:

v     Full covariance matrix.

v     Choice of standard, robust and HAC standard errors and covariance matrix.

v     Correlograms of residuals and squared residuals.

v     Forecast distributions by Monte Carlo simulation. 

v     One-step ex post forecasts, with tests of model stability. 

v      Solved moving average (impulse-response) coefficients of the mean and variance processes.

v     Listings of series, including actual and fitted series, simple and ARCH-re-weighted residuals and the conditional variance series.

v     Graphics include time plots, residual correlograms, spectra, histograms and QQ-plots, and forecasts.

v     Summary statistics for data series, including Lo's R/S and KPSS tests of I(0), and ADF and Phillips-Perron tests of I(1).

Simulation and Monte Carlo Modules

      Any model that can be estimated can also be simulated, with a wide range of options for random disturbance generation.

      Monte Carlo experiments are easily set up by combining the estimation and simulation capabilities.    

      Even bootstrap tests can feasibly be studied by Monte Carlo using the 'warp speed' method. 

Graphical User Interface

      GUI operation through menus and dialogs, allows models to be specified and options selected with intuitive point-and-click interface.

      Storing and retrieval of model specifications. 

      Graphics for instant display, using gnuplot. Graphs can be saved in EPS, PNG (bitmap) and other formats. 

      A large variety of data transformations (logs, lags, differences etc. etc.), plus deleting, renaming and re-ordering of data series, dummy variable creation, and editing of individual observations.

      Integrated help system.

      Two or more data files can be merged in memory.

      Generated series (residuals, probabilities, simulations, etc.) can be retrieved for further analysis.

      Observation dates (years/quarters/months/weeks/weekdays/days) can be assigned and reported in the output.

Programming Mode 

      The kernel code module can be imported to a users Ox program. A command language allows selection of most program options for batch operation.

      Outputs can be written to program variables for further analysis instead of the screen.

       Options specified in GUI mode can be exported in text format, and then entered as command lines in programming mode. This feature makes it straightforward to learn the command language for batch operation. Text commands can also be imported into the GUI program at start-up.

Neat Utilities

      Spreadsheet editor:  not quite as flexible as Excel, but does the main jobs required for data preparation, especially of panel data .

      Calculator: evaluates numerical formulae,  and plots functions of one or two variables.

      Matrix calculator: construct second moment matrices from the data, import estimation outputs such as covariance matrices, or create matrices from scratch in the editor. Then evaluate any matrix expression or function.

      Look-up tables of probabilities and critical values for all the standard statistical distributions, including density and CDF plots.

      Front end for SsfPack state space modelling package.