Econometrics Toolbox provides functions for modeling economic data. You can select and estimate economic models for simulation and forecasting. For time series modeling and analysis, the toolbox includes univariate Bayesian linear regression, univariate ARIMAX/GARCH composite models with several GARCH variants, multivariate VARX models, and cointegration analysis. It also provides methods for modeling economic systems using state-space models and for estimating using the Kalman filter. You can use a variety of diagnostics for model selection, including hypothesis tests, unit root, stationarity, and structural change. Two characteristics of financial time series that conditional variance models address are: - Volatility clustering. Volatility is the conditional standard deviation of a time series. Autocorrelation in the conditional variance process results in volatility clustering. The GARCH model and its variants model autoregression in the variance series. - Leverage effects. The volatility of some time series responds more to large decreases than to large increases. This asymmetric clustering behavior is known as the leverage effect. The EGARCH and GJR models have leverage terms to model this asymmetry. The generalized autoregressive conditional heteroscedastic (GARCH) model is an extension of Engle's ARCH model for variance heteroscedasticity. If a series exhibits volatility clustering, this suggests that past variances might be predictive of the current variance. The GARCH(P, Q) model is an autoregressive moving average model for conditional variances, with P GARCH coefficients associated with lagged variances, and Q ARCH coefficients associated with lagged squared innovations. The exponential GARCH (EGARCH) model is a GARCH variant that models the logarithm of the conditional variance process. In addition to modeling the logarithm, the EGARCH model has additional leverage terms to capture asymmetry in volatility clustering. The EGARCH(P, Q) model has P GARCH coefficients associated with lagged log variance terms, Q ARCH coefficients associated with the magnitude of lagged standardized innovations, and Q leverage coefficients associated with signed, lagged standardized innovations. The GJR model is a GARCH variant that includes leverage terms for modeling asymmetric volatility clustering. In the GJR formulation, large negative changes are more likely to be clustered than positive changes. The GJR model is named for Glosten, Jagannathan, and Runkle. Close similarities exist between the GJR model and the threshold GARCH (TGARCH) model-a GJR model is a recursive equation for the variance process, and a TGARCH is the same recursion applied to the standard deviation process. The GJR(P, Q) model has P GARCH coefficients associated with lagged variances, Q ARCH coefficients associated with lagged squared innovations, and Q leverage coefficients associated with the square of negative lagged innovations. This book develops ARCH, GARCH, EGARCH, TGARCH and GJR time series models.