# Time Series

Time series regression modeling explained in detail.

**Time Series Regression Modeling**

Time series regression is used to model the relationship between a dependent variable and time as an independent variable. It is a specialized form of regression modeling that is designed to handle data that is collected over time and exhibits temporal dependencies.

In time series regression, the goal is to estimate the parameters of a regression model that best fits the observed data, taking into account the sequential ordering of the data points in time. The time variable is used as an independent variable, and the goal is to model the relationship between the dependent variable and time, along with any other independent variables that may be included in the model. The time series regression model is Yt = β0 + β1*X1t + β2*X2t + … + βn*Xnt + εt where:

Yt is the value of the dependent variable at time t.

Xt1, Xt2, …, Xnt are the values of the independent variables at time t.

β0, β1, β2, …, βn are the coefficients, parameters, of the regression model that represent the strength and direction of the relationship between the variables.

εt is the error term or residual, which represents the unexplained variation in the dependent variable at time t that is not accounted for by the regression model.

The time series regression model can be estimated using ordinary least squares (OLS), maximum likelihood estimation (MLE), autoregressive integrated moving average (ARIMA), autoregressive integrated moving average with exogenous variables (ARIMAX), and other time series regression methods.

Time series regression can be used to forecast the future values of the dependent variable, assess the significance and direction of the relationship between variables over time, identify long-term trends, seasonal patterns, and other temporal dependencies in the data, and evaluate the performance of the model using appropriate metrics.