Forecasting stock volatility

Can Google Trends help you make money?

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The goal

Who has ever watched movies or documentaries about the 2008 crisis like "The Big Short" or "Inside Job" and wondered "If only I could predict the stock market crisis and make so much money by betting against the market?"

We did.

In particular, since the recent Covid-19 crisis, where we saw in barely four trading days a plunge of 26% in the Dow Jones Industrial Average. More and more people have started trading on the stock market since then, resulting in an increase in market volatility.

Thus, one should get interested in people's behavior to be able to predict a stock or index trend. And guess what could be a good insight on what people think?
Their Google searches!

This gave us the idea to use Google Trends to improve volatility forecasting models. But first, we need to find out which search terms are relevant and how to use them.

Key insights

Efficient model

GARCH(1,1)

Only 2 keywords

crisis, Dow Jones

20% improvement

Adding Google Trends data to the GARCH model

Covid-19

Market crash: February 20th, 2020 - April 7th, 2020

Introduction

Since our goal is to predict increase in volatility because of a financial crisis, we should analyze an index rather than a particular stock because we just care about the whole market. Also, one stock could be affected by very specific reasons such as earnings report, news, lawsuits etc.

We chose the Dow Jones Industrial Average index given its reputation as a reference for financal market trends in the US.
We consider this index during the Covid-19 crisis from January until May 2020 and in particular during the stock market crash between February 20th and April 7th.

It has been shown that using Google Trends is particularly efficient during recessions for forecasting near term economic indicators and it is also the case for financial time series.

As a remark, the presented solution can be extrapolated for any stock of your choice with minimum tweaking as well as to other periods! Indeed, we didn't include specific Covid-19 data.

We do not claim any methodological advances here, certainly it is possible to build more sophisticated forecasting models than those we use but we showed how easy it is to use Google Trends to improve basic models.

What models perform the best when it comes to forecasting volatility?

First, we will analyse the daily log returns of the Dow Jones index.

Looking at the ACF and PACF, the only signficant lags seems to be 1 or 2. However, after several tests, we got that no Auto-Regressive process is necessary for the mean model. For the volatility process, the first lag is signficant. This means that the volatility of one day affects the next day.

This is all great but let's talk math now. The most efficient model we found is the GARCH(1,1) with zero mean and Student's t distributed errors. The formulas of the model are the following:

\[r_t = 0 + \epsilon_t\] \[\sigma^2_t = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2\] \[\epsilon_t = \sigma_t e_t,\,\,\, e_t \sim t_{\nu}\]

Fitting the model to the data, we got the following results:

Zero Mean - GARCH Model Results
Dep. Variable:	DJI	R-squared:	0.000
Mean Model:	Zero Mean	Adj. R-squared:	0.012
Vol Model:	GARCH	Log-Likelihood:	4.39503
Distribution:	Standardized Student's t	AIC:	-0.790064
Method:	Maximum Likelihood	BIC:	8.83681
		No. Observations:	82
Date:	Fri, Dec 18 2020	Df Residuals:	78
Time:	17:23:39	Df Model:	4

Volatility Model
	coef	std err	t	P>\|t\|	95.0% Conf. Int.
omega	1.7646e-03	1.492e-03	1.182	0.237	[-1.160e-03,4.690e-03]
alpha[1]	0.3561	7.059e-02	5.044	4.553e-07	[ 0.218, 0.494]
beta[1]	0.6439	7.236e-02	8.898	5.673e-19	[ 0.502, 0.786]

Distribution
	coef	std err	t	P>\|t\|	95.0% Conf. Int.
nu	6.9856	3.506	1.992	4.632e-02	[ 0.114, 13.857]

Covariance estimator: robust'

The performance of this GARCH model is already quite good! A mean absolute error of 0.0055! But let's see if we can further improve it using Google Trends.

What do common shareholders search on Google when they are afraid of the future?

When people are interested in a given stock, they will google its ticker and related news but also search about the market in general. We can actually know if the market is bullish or bear by looking at this searches.

In the case of the Dow Jones index which measures the stock performance of 30 large companies listed on stock exchanges in the United States, the context is more important.

Here in context of crisis, people will search for words such as
'debt','loan','job','unemployment','economics','inflation','sell','bonds','gold', 'stocks','dow jones', 'crisis','finance','risk', or'leverage'.

As we want to make the model simple and the forecasting fast, we only keep the most relevant ones.
We did proceed in the following way to select the keywords:
First, we kept only the keyword that had a spike just before or during the crisis.

We remove the seasonality from the Google Trends data before using it. We also plot the trends of these time series and the DJI price at the same scale to see clear spikes in volatility right after an increase in the queries volume for the selected keywords.
Then, from this list, we kept only the significant ones after fitting the trends model.

We are quite on the right track!

How much does adding Trends data outperform models not using it?

The most efficient model we found is the GARCH(1,1) with the selected Trends data as mean regressors and Student's t distributed errors. So the same model but we just add trends data as predictors in the mean process.
The formulas of the model are the following:

\[r_t = \mu + \text{dow jones.nsa}_t + \text{crisis.nsa}_t + \epsilon_t\] \[\sigma^2_t = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2\] \[\epsilon_t = \sigma_t e_t,\,\,\, e_t \sim t_{\nu}\]

Fitting the model to the data, we got the following results:

AR-X - GARCH Model Results
Dep. Variable:	DJI	R-squared:	0.015
Mean Model:	AR-X	Adj. R-squared:	-0.009
Vol Model:	GARCH	Log-Likelihood:	7.25056
Distribution:	Standardized Student's t	AIC:	-0.501113
Method:	Maximum Likelihood	BIC:	16.3459
		No. Observations:	82
Date:	Fri, Dec 18 2020	Df Residuals:	75
Time:	19:21:41	Df Model:	7

Mean Model
	coef	std err	t	P>\|t\|	95.0% Conf. Int.
Const	0.1675	6.888e-02	2.432	1.502e-02	[3.251e-02, 0.303]
dow jones.nsa	-1.4728e-03	6.290e-04	-2.341	1.921e-02	[-2.706e-03,-2.400e-04]
crisis.nsa	-1.8454e-03	8.000e-04	-2.307	2.106e-02	[-3.413e-03,-2.775e-04]

Volatility Model
	coef	std err	t	P>\|t\|	95.0% Conf. Int.
omega	1.7414e-03	1.614e-03	1.079	0.281	[-1.422e-03,4.905e-03]
alpha[1]	0.4291	8.899e-02	4.822	1.423e-06	[ 0.255, 0.604]
beta[1]	0.5709	7.866e-02	7.258	3.927e-13	[ 0.417, 0.725]

Distribution
	coef	std err	t	P>\|t\|	95.0% Conf. Int.
nu	8.5807	7.184	1.194	0.232	[ -5.499, 22.660]

Covariance estimator: robust

We got a mean absolute error of 0.0044.

That's 20% improvement in the forecast!

This is quite a good performance. This might help predicting future increases in volatility which could suggest an upcoming crisis. It can be used to bet against the market by shorting stocks, contracting put options with banks.

Your turn!

Feel free to use this results on another index as the NASDAQ or S&P500.

Or with a particular stock as Tesla by focusing on the keywords 'electric car', 'AV' and 'Elon Musk' searches for example.

Or if DJI is your favorite index, you can try to add more relevant keywords, it's up to you!

We can't guarantee the result, but we let you test it.

However, be careful about the fact that this model might not perform as well after the recession.

Try the code!

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