mjv2146 / stochastic-volatility

Detecting unobservable changes in standard deviation of GDP

Stochastic Volatility

Task

• Economies frequently experience large downturn beyond the scope of a 'normal' downturn.
• This project considers that the average size of a downturn can vary over time.
• I estimate this using the model

$$\begin{align} \underbrace{\log y_t}_{\text{Observed}} &= \rho_y \log y_{t-1} + \exp(\sigma_{t-1}) \epsilon_t \\\ \underbrace{\sigma_t}_{\text{Unobserved}} &= (1-\rho_\sigma) \overline{\sigma} + \rho_{\sigma} \sigma_{t-1} + \sigma_\nu \nu_t \\\ \epsilon_t &\sim \mathcal{N}(0, 1) \\\ \nu_t &\sim \mathcal{N}(0, 1). \end{align}$$

• $y_t$ is the (observed) GDP component.
• $\sigma_t$ is unobserved and determines the standard deviation of GDP innovations. As $\sigma_t$ increases, the standard deviation of $y_t$ increases.

Data

Argentina Industrial Production - Global Economic Monitor

Notebooks

Notebook	Description
Clean Data	Clean raw industrial production series to separate cycle and trend components.
Main	Estimate stochastic volatility process.

Findings

• Argentina features stochastic volatility - the standard deviation of GDP fluctuations changes over time.
• The volatility of GDP increased during recessions such as the 1998-2002 Argentine Great Depression and the 2008 Global Financial Crisis.
• Argentina experienced a 0.5% decline in GDP volatility following 1998-2002 Argentine Great Depression.

Tools

• pandas - data wrangling
• matplotlib/seaborn - visualizations
• pystan - bayesian methods