Assumptions underlying the VAR model
VAR analysis is subject to several assumptions and requirements to ensure the validity and reliability of the results:
- Linearity: Relationships between variables are linear.
- Stationarity: Time series data are stationary.
- No Perfect Multicollinearity: No perfect linear relationships exist between variables.
- No Autocorrelation in Residuals: Residuals are not serially correlated.
- Homoscedasticity: Residual variance is constant.
- No Endogeneity: Variables are not affected by omitted factors.
- Exogeneity: Explanatory variables are not influenced by other variables.
- Sufficient Observations: Adequate data for parameter estimation.
- Weak Exogeneity: Some variables may be endogenous but not contemporaneously correlated with errors.
Vector Autoregression (VAR) for Multivariate Time Series
Vector Autoregression (VAR) is a statistical tool used to investigate the dynamic relationships between multiple time series variables. Unlike univariate autoregressive models, which only forecast a single variable based on its previous values, VAR models investigate the interconnectivity of many variables. They accomplish this by modeling each variable as a function of not only its previous values but also of the past values of other variables in the system. In this article, we are going to explore the fundamentals of Vector Autoregression.
Table of Content
- What is Vector Autoregression?
- Mathematical Intuition of VAR Equations
- Assumptions underlying the VAR model
- Steps to Implement VAR on Time Series Model
- Step 1: Importing necessary libraries
- Step 2: Generate Sample Data
- Step 3: Function to plot time series
- Step 4: Function to check stationarity
- Step 5: VAR analysis
- Output Explanation
- Applications of VAR Models