VAR Model Analysis: Japan GDP and Consumption per capita

Project Overview

Time series analysis of Japan's GDP per capita and consumption per capita using ARMA and VAR models to examine the dynamic relationships.

Data Source

World Bank API (1990-2023)

Repository Structure

├── data_collection.ipynb -> Data fetching and pre-processing
├── analysis.ipynb -> Time series analysis
├── japan_data.csv -> Processed Dataset
├── acf_pacf_plots.png -> Autocorrelation plots
├── requirements.txt -> Libraries required
├── .gitignore
└── README.md -> This file

Methodology

1. Data Collection

• Fetched the annual data from World Bank API for a period of 48 years from 1974 to 2022
• Variables: GDP per capita (NY.GDP.PCAP.CD) and Consumption per capita (Calculated from NE.CON.PRVT.CD / SP.POP.TOTL)

2. Growth Rate Calculation

• Growth rate calculated as percentage changes, growth rate = ((X_t - X_t-1) / X_t-1) x 100

3. Stationarity Testing

• Method: Augmented Dickey-Fuller (ADF) test
• Null Hypothesis: Series has unit root (non-stationary)
• Significance Level: 5%
• Iterative differencing applied until both series achieved stationarity

4. ARMA Model Selection

• Tested: ARMA (p,q) for p,q ∈ {1,2,3,4}
• Criteria: AIC and BIC
• Method: Box-Jenkins methodology
• Seprate models estimated for GDP growth and Consumption growth

5. VAR Model Selection

• Tested: VAR(p) for p ∈ {1,2,3,4}
• Criteria: AIC and BIC
• Multi-variate model capturing dynamic relationships between GDP and Consumption

6. Granger Causality Tests

• Tests bidirectional causality
• Maximum lags: 4
• Test Statistic: F-test
• Significance Level: 5%

Key Results

Stationarity

• GDP Growth Rate: Stationary
• Consumption Growth Rate: Stationary
• Differencing applied: 1 Time

ARMA Model Selection

GDP Growth

• Best model by AIC: ARMA(2,2)
• Best model by BIC: ARMA(1,0)

Consumption Growth

• Best model by AIC: ARMA(2,4)
• Best model by BIC: ARMA(1,0)

VAR Model Selection

• Best model by AIC: VAR(3)
• Best model by AIC: VAR(1)

Granger Causality

Question: Does consumption Granger-cause GDP or the other way around? Answer: No

Visualizations

GDP and Consumption Growth Rate Plot

ACF and PACF plots

Requirements

Python Packages

• pandas
• numpy
• matplotlib
• statsmodels
• wbgapi

Installation

pip install -r requirements.txt

Technical Notes

• Sample Size: Sufficient for reliable inference (n >= 30)
• Information Criteria: AIC tends to select more complex models, BIC penalizes complexity more
• Granger Causality Interpretation: No causality

This project was completed as part of the Time Series Analysis by Prof. Anindya S. Chakrabarti in the Post Graduate Diploma in Advanced Business Analytics program at IIM Ahmedabad.