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.
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.
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.
Jupyter Notebook file real-world-VAR.ipynb show step by step illustrations on VAR based analysis.
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`