Matlab`s Econometrics Toolbox is great for forecasting, modelling, estimating, and simulating
As I read this, this Matlab Econometrics toolbox is so powerful for these uses using GARCH, the help file includes some very solid examples which are read from Nasdaq source files. Charts and plots are also showcased for quick analysis and understanding. There are heavy uses of GARCH to make all this happen. One powerful function is called garchset.
The help files even includes examples on showing how to:
use the default GARCH(1,1) model to model the Deutschmark/British pound foreign-exchange series.
This simulates both on a single path or multiple path.
Presampling data is also shown with simulations as well.
There are even capabilities to do optimization termination on estimation data.
A great New York Stock Exchange example is used to demonstrate Estimating ARMA(R,M) Parameters. Lower bounder restrained were also included.
As for forecasting capabilities with this Econmetrics toolbox, Asymptotic Behavior can be done as well. Regression in forecasting can be done via:
Using Forecasted Explanatory Data
Generating Forecasted Explanatory Data
Regression in Monte Carlo using some Matlab functions like:
There are various multiple time series models supported as well. These include:
Vector Autoregressive VAR(p)
Vector Moving Average VMA(q)
Vector Autoregressive Moving Average VARMA(p, q)
Vector Autoregressive Moving Average with eXogenous inputs VARMAX(p, q, r)
Structural Vector Autoregressive Moving Average with eXogenous inputs SVARMAX(p, q, r)
There is also coverage of Scholastic Differential Equation which includes:
SDE Class Hierarchy
Example: Simulating Equity Prices
Example: Simulating Interest Rates
Example: Stratified Sampling
There are various data set names out of the box regarding this Matlab Econometrics toolbox. This includes:
Data_EquityIdx U.S. equity indices, 1990–2001
Data_FXRates Currency exchange rates, 1979–1998
Data_GDP U.S. Gross Domestic Product, 1947–2005
Data_GlobalIdx1 Global large-cap equity indices, 1993–2003
Data_GlobalIdx2 Global large-cap equity indices and Euribor rates, 2001–2006
Data_GNP U.S. Gross National Product, 1947–2005
Data_Income1 Simulated data on income and education
Data_Income2 Average annual earnings by educational attainment in eight workforce age categories
Data_MarkPound Deutschmark/British Pound foreign-exchange rate, 1984–1991
Data_NelsonPlosser Macroeconomic series of Nelson and Plosser
Data_SchwertMacro Macroeconomic series of Schwert
Data_SchwertStock Indices of U.S. stock prices
Data_TBill Three-month U.S. treasury bill secondary market rates
Data_USEconModel Macroeconomic series for Demo_USEconModel
Data_VARMA22 Two-dimensional VARMA(2,2) specification