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. A simple model is easier to estimate, forecast, and interpret.
Specification tests help you identify one or more model families that could plausibly describe 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.
Econometrics Toolbox Features
|Modeling Questions||Features||Related Functions|
|What is the dimension of my response variable?||
|Is my time series stationary?||
|Does my time series have a unit root?||
|How can I handle seasonal effects?||
|Is my data autocorrelated?||
|What if my data is heteroscedastic (exhibits volatility clustering)?||
|Is there an alternative to a Gaussian innovation distribution for leptokurtic data?||
|How do I decide between several model fits?||
|Do I have two or more time series that are cointegrated?||
|What if I want to include predictor variables?||
|What if I want to implement regression, but the classical linear model assumptions might not apply?||
|What if observations of a dynamic process include measurement error?|
Standard, linear state-space modeling is available in this toolbox.
- Select ARIMA Model for Time Series Using Box-Jenkins Methodology
- Detect Autocorrelation
- Detect ARCH Effects
- Unit Root Tests
- Time Series Regression I: Linear Models
- Time Series Regression II: Collinearity and Estimator Variance
- Time Series Regression III: Influential Observations
- Time Series Regression IV: Spurious Regression
- Time Series Regression V: Predictor Selection
- Time Series Regression VI: Residual Diagnostics
- Time Series Regression VII: Forecasting
- Time Series Regression VIII: Lagged Variables and Estimator Bias
- Time Series Regression IX: Lag Order Selection
- Time Series Regression X: Generalized Least Squares and HAC Estimators