Determine if there is an influence of newspaper articles on stock quotation

Question

Lets assume there is a company called "XY", which is listed in the NASDAQ. Lets further assume that newspapers are frequently reporting about company XY, either in a positive, neutral or a negative way.

I am trying to figure out whether there is an influence of positive themed newspaper articles about company XY on the stock price of company XY or not. For this reason I gathered and classified all newspaper articles about company XY. Then I created a N-dimensional data matrix (with n = 4 columns), containing the stock price of company XY as a time series (1000 days), the associated NASDAQ index for each day, a dummy variable for a positive article (1 = positive ; 0 = neutral or negative) and a dummy variable for special events (like the release of quarterly figures).

So far, I only worked with (S)ARIMA and (S)ARIMAX (including external regressors) models. I guess that the variance in stock prices is conditionally influenced by the previous variance, so I thought ARCH or GARCH would be a good model to start with. Unfortunately, I do not have the experience to judge if this is a good idea or if there are other types of models that probably can handle the described conditions better than GARCH.

So my actual questions are:

• Is is possible to include external regressors (e.g. the dummy variables) in a GARCH model?
• Is there another model class which fits the described issue better?

Answer 1

Is is possible to include external regressors (e.g. the dummy variables) in a GARCH model?

Yes, it is. The vanilla GARCH(1,1) model for a variable (e.g. stock return) $r_t$ looks like \begin{aligned} r_t &= \mu_t + u_t, \\ u_t &= \sigma_t \varepsilon_t, \\ \sigma_t^2 &= \omega + \alpha_1 u_{t-1}^2 + \alpha_2 u_{t-2}^2 + \beta_1 \sigma_{t-1}^2, \\ \varepsilon_t &\sim i.i.d.(0,1), \end{aligned} where $\mu_t$ is the conditional mean of $r_t$ which could be e.g. a constant or an ARMA process. You can trivially include an extra variable $x_{t_1}$ in the conditional variance equation like this: $$ \sigma_t^2 = \omega + \alpha_1 u_{t-1}^2 + \beta_1 \sigma_{t-1}^2 + \gamma_1 x_{t-1}. $$ In R, you can do that via the argument external.regressors inside the argument variance.model of the function ugarchspec from the "rugarch" package (see the help file). Note that if $x_t$ can be negative, you might end up with negative conditional variance. To avoid that, you may use a nonnegative transformation of $x_t$ or another flavour of GARCH like log-GARCH or EGARCH.

Is there another model class which fits the described issue better?

This is an empirical question. You might try a few different models (different flavours of GARCH; stochastic volatility; a conditional variance equation with just a constant plus the extra variable $x_t$) for your data and check which of them perform better (e.g. by looking at information criteria or at out-of-sample forecasting performance).