Time series regression is a statistical method for predicting a future response based on the response history (known as autoregressive dynamics) and the
transfer of dynamics from relevant predictors. Time series regression can help you understand and predict the behavior of dynamic systems from
experimental or observational data. Time series regression is commonly used for modeling and forecasting of economic, financial, and biological systems.
You can start a time series analysis by building a design matrix (X), which can include current and past observations of predictors ordered by time (t). Then,
apply ordinary least squares (OLS) to the multiple linear regression (MLR) model to get an estimate of a linear relationship of the response (y) to the design
matrix. β represents the linear parameter estimates to be computed and urepresents the residual terms. The residual terms can be extended in the MLR
model to include heteroscedasticity or autocorrelation effects.
Other models that capture dynamics more explicitly include:
• Autoregressive integrated moving average with exogenous predictors (ARIMAX)
• Regression models with ARIMA time series errors
• Distributed lag models
Sample Solution
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