Time Series Modelling 4.26 by James Davidson
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The Package
This powerful and flexible time series modelling package
(formerly known as TSMod, now TSM) estimates and forecasts ARIMA
and ARFIMA models, several GARCH, FIGARCH, APARCH and EGARCH variants,
bilinear models, Markov-switching and smooth transition models. Most model
features can be freely combined. User-supplied Ox code can be integrated
with the other features of the package to allow complete flexibility in
model specification. Dynamic equations systems can be specified and estimated
easily, options including VARs, simultaneous systems, error correction systems, multivariate GARCH
and regime switching.
A comprehensive set of diagnostic tools is implemented including Q tests, LM tests, moment tests and parameter stability tests. Other features include nonparametric regression, log-periodogram regression, recursive and rolling estimation, automated ARMA order selection, Monte Carlo forecasting of general nonlinear time series models, and parametric bootstrap tests and confidence intervals. Cointegration analysis options include Johansen's rank tests, and MINIMAL analysis of restrictions on the cointegrating space. Monte Carlo experiments to be performed on any model that can be specified in the program. Data can be input from suitably formatted text files and spreadsheet formats such as .xls, .wks or .in7 (GiveWin format), and transformed and edited interactively.
The program comes with a platform-independent graphical user interface (GUI) — see the screenshots — and comprehensive graphics capabilities. Alternatively, TSM can be called from a user's Ox program and returns the results.
Compared to the leading commercial econometrics packages, TSM is a bargain. It has virtually all the facilities one would expect of a standard regression package, and is very easy to use. More important, it offers a unique range of time series models, techniques and special features.
Ø ARIMA, ARFIMA, bilinear autoregressive models.
Ø Conditional heteroscedasticity models including GARCH, FIGARCH, HYGARCH (see Davidson 2004a), threshold ARCH (GJR), APARCH, EGARCH, and GARCH-M models, together with the obvious FIEGARCH, FIAPARCH, HYEGARCH and HYAPARCH variants.
Ø 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).
Ø Error correction models, including nonlinear error correction (asymmetric, exponential smooth transition, cubic).
Ø Regime switching models, including simple Markov switching, Hamilton’s dynamic Markov-switching models of mean and variance (SWARCH), and explained switching, where probabilities can depend on predetermined variables.
Ø Smooth transition (ST) regime switching implemented for any component of the model.
Ø 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 option for systems.
Ø Discrete data models including probit, logit, Poisson and negative binomial.
Ø Almost any other nonlinear model 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 user’s model. This may be either a single equation or a system of similar equations, with cross-equation restrictions if required.
Ø Standard (non-iterative) OLS and IV estimation of linear regressions.
Ø Nonlinear least squares.
Ø Conditional time domain MLE allowing choice of Gaussian, Student’s t, skewed Student’s t, and GED disturbances.
Ø Frequency domain (Whittle) MLE for ARIMA/ARFIMA models.
Ø ML estimation for binary and count data models.
Ø LGV, FIML and 3SLS estimation for systems of equations.
Ø Efficient GMM estimation of nonlinear equations/systems.
Ø Numerical optimization using BFGS with the option of the simulated annealing algorithm to provide starting values.
Ø Any parameter can be fixed at a preset value in estimation, or subjected to inequality constraints using a logistic map.
Ø Automatically estimates all ARMA specifications up to preset maximum orders, allowing easy model selection.
Ø One- and two-dimensional plotting of the concentrated criterion function.
Ø Nonparametric (Nadaraya-Watson) bivariate regression.
Ø Log-periodogram regression for long memory series (Geweke-Porter-Hudak and Moulines-Soulier methods).
Ø 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.
Ø Bootstrap bias correction.
Ø Standard and user-specified diagnostic tests (LM and M principles), including common factor test and information matrix test.
Ø Multiple linear parameter restrictions can be tested by the Wald principle, and/or imposed in estimation for testing by the LM principle.
Ø Multi-step ex-ante forecasts of linear-in-mean and Markov-switching models, with standard error bands adjusted for ARCH innovations.
Ø 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.
Ø Stochastic simulation of any fitted or user-specified model, with shocks drawn from either Gaussian/Student distributions or from EDF of residuals.
Ø Bootstrap p-values for diagnostic and significance tests, using the simulation module to generate bootstrap draws.
Ø Bootstrap equal-tailed confidence intervals.
Ø Johansen tests for cointegrating rank, and MINIMAL analysis on cointegrating vectors.
Ø 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.
Ø 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 Durbin-Watson statistic.
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).
Ø GUI operation through menus and dialogs, allows models to be specified and options selected with intuitive point-and-click interface.
Ø Storing and retrieval of model specifications.
Ø Graphics for instant display, using gnuplot. Graphs can be saved in EPS, PNG (bitmap) and other formats.
Ø 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.
Ø Integrated help system.
Ø Two or more data files can be merged in memory.
Ø Generated series (residuals, probabilities, simulations, etc.) can be retrieved for further analysis.
Ø Observation dates (years/quarters/months/weeks/weekdays/days) can be assigned and reported in the output.
Ø The kernel code module can be imported to a user’s Ox program. A command language allows selection of most program options for batch operation.
Ø Outputs can be written to program variables for further analysis instead of the screen.
Ø 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.