Forecasting Volatility with Empirical Similarity and Google Trends

Transcription

1 Forecasting Volatility with Empirical Similarity and Google Trends Moritz Heiden with Alain Hamid University of Augsburg ISF / 17

2 Volatility and investor attention Idea: Investors react on news or information of unknown source and focus their interest on a market prior to acting on it. Noise traders/ retail investors have limited information, they react differently from professional investors and their uncertainty induces volatility (e.g. agent-based literature, Lux and Marchesi, 1999). Traditional approaches: Volume and turnover are correlated with volatility, but have no predictive content (Brooks, 1998; Donaldson and Kamstra, 2005). 2 / 17

3 Measuring retail investors attention Following recent literature (Da et. al, 2011; Andrei and Hassler, 2013) we suggest using google search volume as a measure of retail investors attention. Google data accounted for 84.73% of all search queries worldwide in The search engine is a contemporary data source. Searching for a specific term itself is undoubtably a measure of attention. 3 / 17

4 Data Google Trends 4 / 17

5 Data Google Trends Realized Volatility Google Trends Data Jan Jan Jul Jan Jul Jan Figure: Weekly Google Search Volume and Realized Volatility of Dow Jones (Oxford Man database) 5 / 17

6 Data Google Trends Figure: Crosscorrelation lagged Google Search Volume and Realized Volatility of Dow Jones Lag 6 / 17

7 The concept of empirical similarity Predict Y t with the help of explanatory variables X t = ( Xt 1,..., Xt m ) ( and a database consisting of historical cases X 1 i,..., Xi m ), Y i for i = 1,..., t 1, based on the similarity s of historical cases and the current situation with characteristics X t. Y t = Yt s i<t = s (X i, X t ) Y i i<t s (X + ε t, (1) i, X t ) 7 / 17

8 The concept of empirical similarity In our case: Predict realized volatility v t with help of Google Search Volume g t, based on the similarity of previous volatility and investor attention: v t = ω 0 + β t (g t 1, v t 1 ; ω 1 ) v t 1 + ε t, t = 1,..., n (2) with similarity function β t : β t (g t 1, v t 1 ; ω 1 ) = exp (ω 1 (g t 1 v t 1 )) (3) 8 / 17

9 The concept of empirical similarity beta ar1 Jan Jan Jul Jan Jul Jan Figure: Similarity function vs. AR(1) parameter full sample 9 / 17

10 Forecast comparison Out-of-sample forecasting Moving window of 250 obs., first forecast for the week from , weekly re-estimation. Benchmark models: AR(1), ARFIMA, HAR and versions of the models with Google component. Methods of comparison: Mincer-Zarnowitz regressions, Model Confidence Set based on QLIKE loss functions, VaR forecasting framework. 10 / 17

11 Forecast comparison Out-of-sample losses and Mincer-Zarnowitz regressions Weekly out-of-sample average losses model MSE QLIKE MZ R 2 ES AR AR G ARFIMA ARFIMA G HAR HAR G / 17

12 Forecast comparison Model Confidence Set p-values Subsampling: Two crisis periods (100 obs.), October 2008 and June Out-of-sample forecasts MCS p-values model Full sample Crisis 1 Crisis 2 ES AR AR G ARFIMA ARFIMA G HAR HAR G / 17

13 Forecast comparison Model Confidence subsamples Realized Volatility Google Trends Data MCS ES Leading Okt Okt Apr Okt Apr Okt Apr Okt Apr Sep Figure: MCS during crisis subsamples 13 / 17

14 Forecast comparison VaR summary statistics VaR forecast comparison Idea: punish overpredictions with reverse QLIKE loss function. VaR t (0.99) summary statistics and average losses model % exc. no. exc. Exceedance loss Benchmark loss ES AR AR G ARFIMA ARFIMA G HAR HAR G / 17

15 Forecast comparison VaR MCS p-values VaR t (0.99) forecasts MCS p-values model Exceedance loss Benchmark loss ES AR AR G ARFIMA ARFIMA G HAR HAR G / 17

16 Forecast comparison VaR MCS p-values Results: Google Search Volume leads to smaller average losses and significant better forecasts based on the Empirical Similarity approach. Higher forecasting accuracy in volatile periods translates into better forecasts of the VaR and less overpredictions. Handle the data with care: Simply adding a linear term in a regression might result in a mixture of different dynamics. Standardization of the Google Data is problematic, daily data did not improve forecasts. 16 / 17

17 Forecast comparison VaR MCS p-values Literature: Brooks, Chris Predicting stock index volatility: can market volume help? Journal of Forecasting 17(1) Da, Zhi, Joseph Engelberg, Pengjie Gao In search of attention. Journal of Finance 66(5) Dimpfl, Thomas, Stephan Jank Can internet search queries help to predict stock market volatility. Working paper. Donaldson, R. Glen, Mark J. Kamstra Volatility forecasts, trading volume, and the arch versus option-implied volatility trade-off. Journal of Financial Research 28(4) Lieberman, Offer A similarity-based approach to time-varying coefficient non-stationary autoregression. Journal of Time Series Analysis 33(3) / 17