GARCH Volatility Persistence - Quant Trader Interview Question
Difficulty: Hard
Category: Statistics & Regression
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Topics: GARCH, volatility, time-series, statistics, persistence
Problem Description
You are analyzing the volatility of a stock using a GARCH(1,1) model. The model is defined as: $ \sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2 $ where:
$ \sigma_t^2 $ is the conditional variance at time t.
$ \omega $ is a constant.
$ \epsilon_{t-1} $ is the error term at time t-1.
$ \sigma_{t-1}^2 $ is the conditional variance at time t-1.
If the estimated parameters result in $ \alpha + \beta $ being very close to 1, what does this imply about the volatility
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