## 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:

- 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.

## 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.

- 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, Mallows 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.

## Examine the Fitness of Statistical Models Using Confirmatory Factor Analysis

The Factor Analysis feature in SYSTAT 13 now includes Confirmatory Factor Analysis (CFA).

- 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, McDonalds measure of Certainty, and Non-normal Fit Index (NNFI).

## Try SYSTAT 13s 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.

## Add Polish to Your Research with Stunning 2D and 3D Graphs

SYSTAT 13 renders visually compelling 2D graphics perfect for publication, and incredible 3D graphics that bring an incredible wow-factor to any research or business presentation. SYSTAT 13 comes packed with new graphical editing features, such as:

**Richer Color Choices:** Specify any color for your graphs from their red, green and blue component values.
**New Editing Capabilities:** Edit graph size, color, axes, legends, border display, etc. using interactive dialog boxes.
**New Color Gradient Editing:** SYSTAT 13 gives you precise control over gradient color and style on 3D graph surfaces.
**New Graph Labeling Features:** Generate numeric case labels in plots, multivariate displays and maps. Label the dots in dot plots.

## Explore SYSTAT 13s Improvements to Its Existing Statistical Methods

Enjoy more robust testing, regression and cross-tabulation features with SYSTAT 13. The Analysis of Variance feature now provides:

- Levenes test based on median for testing homogeneity of variances.
- A SUBCAT command that categorizes the desired factors just for the purpose of the analysis.

## Basic Statistics Upgrades

The Basic Statistics updates in SYSTAT 13 include:

- Standard error and confidence interval for the trimmed mean.
- Winsorized mean, its standard error and confidence interval.
- Sample mode and mode based on kernel density estimate of data.
- Interquartile range

## Bootstrap Analysis Upgrades

In previous versions, SYSTAT has analysis of the bootstrap outputs, summarizing the key parts of the outputs by histograms, computing various types of bootstrap estimates, their biases, standard errors, confidence intervals, and p-values. In SYSTAT 13, this facility is added to Hypothesis Testing and enhanced in Least-Squares Regression.

- In Hypothesis Testing, SYSTAT 13 provides bootstrap-based p-values and histograms of the test statistic obtained from the bootstrap samples. Apart from the usual p-values of the tests, users can now request bootstrap-based p-values in all tests for mean (one-sample z, one-sample t, two- sample z, two-sample t, paired t, Poisson) and variance (single variance, two variances and several variances)
- In Least-Squares Linear Regression, a choice of bootstrapping residuals has been included. Bootstrap estimates of the regression coefficients, their biases, standard errors, and confidence intervals are then computed based on these.

## Crosstabulation Upgrades

Updates provided in the Crosstabulation (XTAB) feature include the following:

- Relative Risk: In a 2 x 2 table, the relative risk is the ratio of the proportions of cases having a positive outcome in the two groups defined by row or column. Relative Risk is a common measure of association for dichotomous variables.
- Mode: SYSTAT 13 gives an option to list only the first N categories in a one-way table (frequency distribution). This is done by adding a MODE = N option to the PLENGTH command within XTAB.
- Output categorized appropriately based on the type of table, and reorganized table of measures.

## Hypothesis Testing Upgrades

The Hypothesis Testing feature has been strengthened by adding tests for mean vectors of multivariate data.

- One-sample Hotellings T2 test for mean vector of multivariate data equal to a known vector.
- Two-sample Hotellings T2 test for equality of two mean vectors of multivariate data.

For two-sample z, two-sample t, and test for two variances, users can now directly input data in a layout where the data across the samples appear in different columns. This is in addition to the current indexed layout.

**Logistic Regression**

SYSTAT 13 offers more intuitive ways of analyzing binary, multinomial, conditional, and discrete choice models. Specifically:

- Simplified and easy user interface and command line structure to analyze binary, multinomial, conditional, and discrete choice models separately.
- Option to specify the reference level for the binary and multinomial response models.
- Simpler form of input data to analyze matched sample case-control studies with one case and any number of controls per set.
- For Discrete choice models, SYSTAT 13 provides two data layouts: Choice set and By choice to model an individuals choices in response to the characteristics of the choices.

## Nonparametric Tests

Updates in Nonparametric tests include:

- Jonckeere-Terpstra test as an alternative to Mann-Whitney test: The test is used when the treatments are ordered in terms of the response. This test is based on the sum of the k(k-1)/2 Mann-Whitney counts (for k treatments).
- Fligner-Wolfe test as an alternative to Mann-Whitney test: The test is used when one of the treatments acts as a control, to test equality of response to control vis- -vis all other treatments, with a one-sided alternative. This is a Mann-Whitney test with two groups when the control is one group and all other treatments together form another.
- Post hoc (multiple comparisons) tests of Dwass-Steel-Critchlow-Fligner and of Conover-Inman which can be used as a follow-up when a Kruskal-Wallis test shows significance.
- A multiple comparison test due to Conover as a follow-up of Friedman test showing significance.