Estimation of a time-varying parameter GARCH model based on Google Trends

In this paper, I propose to include a ‘bad news’ index based on Google search volume in a GARCH model. The resulting specification allows its parameters to vary with the level of the index via a logistic transition function. In a simulation study, I then illustrate the model’s dynamics and justify the use of maximum likelihood estimation, as well as the validity of a Likelihood Ratio Test to verify the explanatory power of the exogenous information. On a set of S&P 500 returns the test indicates that including Google search volume improves the fit significantly for the periods during and after the global financial crisis in 2008. A comparison to other GARCH specifications, including an extended GARCH and spline-GARCH, shows that the proposed model yields accurate Value-at-Risk predictions but the difference of its variance forecasts to a realized variance proxy rank behind a standard GARCH(1,1) model in both an in-sample and out-of-sample setting. Keywords: GARCH model, varying parameters, Google Trends, Likelihood Ratio Test, Realized Variance, Value-at-Risk