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.A probabilistic time series model is necessary for a wide variety of analysis goals ,including regression inference, forecasting, and Monte Carlo simulation. When selecting a model, aim to find the most parsimonious model that adequately describes your data. Asimple model is easier to estimate, forecast, and interpret*Specification tests help you identify one or more model families that could plausiblydescribe the data generating process.*Model comparisons help you compare the fit of competing models, with penalties for complexity.*Goodness-of-fit checks help you assess the in-sample adequacy of your model, verify that all model assumptions hold, and evaluate out-of-sample forecast performance.Model selection is an iterative process. When goodness-of-fit checks suggest model assumptions are not satisfied-or the predictive performance of the model is not satisfactory-consider making model adjustments. Additional specification tests, model comparisons, and goodness-of-fit checks help guide this process..The most important content is the following:* Econometrics Toolbox Product Description* Econometric Modeling* Econometrics Toolbox Model Objects, Properties, and Methods* Stochastic Process Characteristics* Data Transformations* Data Preprocessing* Trend-Stationary vs. Difference-Stationary Processes* Nonstationary Processes* Trend Stationary* Difference Stationary* Specify Lag Operator Polynomials* Lag Operator Polynomial of Coefficients* Difference Lag Operator Polynomials* Nonseasonal Differencing* Nonseasonal and Seasonal Differencing* Time Series Decomposition* Moving Average Filter* Moving Average Trend Estimation* Parametric Trend Estimation* Hodrick-Prescott Filter* Using the Hodrick-Prescott Filter to Reproduce Their* Original Result* Seasonal Filters* Seasonal Adjusment* Seasonal Adjustment Using a Stable Seasonal Filter* Seasonal Adjustment Using S(n,m) Seasonal Filters* Box-Jenkins Methodology* Box-Jenkins Model Selection* Autocorrelation and Partial Autocorrelation* Theoretical ACF and PACF* Sample ACF and PACF* Ljung-Box Q-Test* Detect Autocorrelation* Engle's ARCH Test* Detect ARCH Effects* Unit Root Nonstationarity* Unit Root Tests* Assess Stationarity of a Time Series* Information Criteria* Model Comparison Tests* Likelihood Ratio Test* Lagrange Multiplier Test* Wald Test* Covariance Matrix Estimation* Conduct a Lagrange Multiplier Test* Conduct a Wald Test* Compare GARCH Models Using Likelihood Ratio Test* Check Fit of Multiplicative ARIMA Model* Goodness of Fit* Residual Diagnostics* Check Residuals for Normality* Check Residuals for Autocorrelation* Check Residuals for Conditional Heteroscedasticity* Check Predictive Performance* Nonspherical Models* Plot a Confidence Band Using HAC Estimates* Change the Bandwidth of a HAC Estimator* Check Model Assumptions for Chow Test* Power of the Chow Test