Vector Autoregession Model

Multivariate Time Series Analysis

A univariate time series data contains only one single time-dependent variable while a multivariate time series data consists of multiple time-dependent variables. We generally use multivariate time series analysis to model and explain the interesting interdependencies and co-movements among the variables. In the multivariate analysis — the assumption is that the time-dependent variables not only depend on their past values but also show dependency between them. Multivariate time series models leverage the dependencies to provide more reliable and accurate forecasts for a specific given data, though the univariate analysis outperforms multivariate in general. In this repository, we apply a multivariate time series method, called Vector Auto Regression (VAR) on real-world datasets obtained from expert databases and official economic data agreed upon by subject matter experts.

Vector Auto Regression (VAR)

VAR model is a stochastic process that represents a group of time-dependent variables as a linear function of their own past values and the past values of all the other variables in the group. For instance, we can consider a bivariate time series analysis that describes a relationship between hourly temperature and wind speed as a function of past values:

temp(t) = a1 + w11 * temp(t-1) + w12 * wind(t-1) + e1(t-1)

wind(t) = a2 + w21 * temp(t-1) + w22 * wind(t-1) + e2(t-1)

where a1 and a2 are constants; w11, w12, w21, and w22 are the coefficients; e1 and e2 are the error terms.

Dataset

Statmodels is a python API that allows users to explore data, estimate statistical models, and perform statistical tests. It contains time series data as well. We download a dataset from the API.

EDA and General Analysis

Jupyter Notebook file real-world-VAR.ipynb show step by step illustrations on VAR based analysis and Bayesain Structured Time Series models.

Python Based VAR Model for Potential Deployment

1. Tests functions on ordinary least squares regressions (OLS)    
`https://github.com/xxl4tomxu98/econometrics-gdp-dpi-VAR/test-VAR.py`

  -  Auto-Correlation of Residuals for Persistence of the Model (ACF and PACF)
  -  Homoscedasticity of Residuals (Arch)
  -  Normality of Residual Distributions (Normality)
  -  Stationarity of Residuals (ADF)

2. Accumulative Python File Constructing VAR Model and Call Tests Functions 
`https://github.com/xxl4tomxu98/econometrics-gdp-dpi-VAR/real-world-VAR.py`