S4U - SYSTAT (More Statistics)

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Forecast Time Series Error Variance with ARCH and GARCH
Conventional time series analysis procedures assume that the variance of the random (error) terms in the series is constant over time. In practice, however, certain series, especially in the financial domain, exhibit volatility with different levels of variance in different periods. In order to capture and model this phenomenon, Autoregressive Conditional Heteroskedasticity (ARCH) models have been developed. Here the variance at each point of the series is modeled using the past disturbances in the series. The ARCH model generally requires a large number of parameters to successfully capture the dynamics of the error variance. The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, by introducing additional autoregressive terms of the error variance helps achieve parameter parsimony in the modeling.

SYSTAT 13’s Time Series Analysis update provides the following:

Find the Best Predictors with Best Subsets Regression
In the development of a multiple (linear) regression model, it would be nice if the number of predictors in the model developed is small without sacrificing predictive power. The best subsets regression addresses this issue.

•	Hypothesis tests for ARCH effects: Well-known McLeod and Lagrange Multiplier tests are provided for this purpose.
•	Estimation of ARCH and GARCH model parameters by different implementations (BHHH, BFGS, and Newton-Raphson) of the maximum likelihood method with various options for convergence criteria.
•	Forecasts for error variances using the parameter estimates.
•	The Jarque-Bera test for normality of errors.

•	SYSTAT 13 finds best models (choice of predictors) for a given number of predictors, the number varying from one to the total number available in the data set.
•	The best model is identified by various criteria such as R2, Adjusted R2, Mallow’s Cp, MSE, AIC, AICC and BIC.
•	SYSTAT 13 then offers to carry out a complete regression analysis on the data set chosen by the user (same as the training set or different) on the best model selected by any of the criteria.

•	CFA can be used to test the postulated factor structure based on a priori knowledge about the relationship between the observed (manifest) variables and the latent variables.
•	With CFA, SYSTAT allows users to specify the observed variables, a set of latent variables, and their variance-covariance structure.
•	A path diagram can be used to specify the hypothesized model.
•	SYSTAT 13 estimates the parameters of the CFA model using one of the following estimation options: Maximum likelihood, Generalized least-squares, and Weighted least-squares.
•	SYSTAT 13 provides a wide of variety of goodness-of-fit indices to measure the degree of conformity of the postulated factor model to the data. Some of the well-known indices provided are: Goodness-of-Fit Index (GIF), Root Mean Square Residual (RMR), Parsimonious Goodness-of- fit Index (PGFI), AIC, BIC, McDonald’s measure of Certainty, and Non-normal Fit Index (NNFI).

Try SYSTAT 13's Newest Regression Capability: Polynomial Regression
SYSTAT 13 provides a direct computation of polynomial regression on a single independent variable. The key features are:

•	The order of the polynomial can be up to 8.
•	Besides fitting polynomials in standard forms, SYSTAT 13 provides orthogonal polynomial regression.
•	SYSTAT 13 reports goodness-of fit-statistics (R2 and adjusted R2) and ANOVA with p-values for all models, starting from the order specified by the user, down to linear (order = 1).
•	SYSTAT 13 provides confidence and prediction interval plots along with estimates, and a plot of residuals versus predicted values, as Quick Graphs.