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Assumptions underlying the VAR model

Mathematical Intuition of VAR Equations

Steps to Implement VAR on Time Series Model

VAR analysis is subject to several assumptions and requirements to ensure the validity and reliability of the results:

  1. Linearity: Relationships between variables are linear.
  2. Stationarity: Time series data are stationary.
  3. No Perfect Multicollinearity: No perfect linear relationships exist between variables.
  4. No Autocorrelation in Residuals: Residuals are not serially correlated.
  5. Homoscedasticity: Residual variance is constant.
  6. No Endogeneity: Variables are not affected by omitted factors.
  7. Exogeneity: Explanatory variables are not influenced by other variables.
  8. Sufficient Observations: Adequate data for parameter estimation.
  9. 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

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What is Vector Autoregression?

Vector Autoregression was first presented in the 1960s by economist Clive Granger. Granger’s significant discoveries laid the framework for understanding and modeling the dynamic interactions that exist among economic factors. VAR models acquired significant momentum in econometrics and macroeconomics during the 1970s and 1980s....

Mathematical Intuition of VAR Equations

VAR models are mathematically represented as a system of simultaneous equations, where each equation describes the behavior of one variable as a function of its own lagged values and the lagged values of all other variables in the system....

Assumptions underlying the VAR model

VAR analysis is subject to several assumptions and requirements to ensure the validity and reliability of the results:...

Steps to Implement VAR on Time Series Model

The code conducts Vector Autoregression (VAR) analysis on randomly generated time series data, including stationarity testing, VAR modeling, forecasting, and visualization of the forecasted outcomes....

Applications of VAR Models

Economic Forecasting: VAR models are widely used in economics to forecast the behavior of economic variables such as GDP, inflation, and interest rates. Causal Inference: By studying the impulse responses generated by VAR models, researchers can infer the causal impact of one variable on another. This is particularly valuable in policy evaluation.Financial Markets: VAR models can be used to predict financial indices, stocks and asset prices....

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Mathematical Intuition of VAR Equations

Steps to Implement VAR on Time Series Model