Taking the pulse of society with unprecedented frequency and focus has become possible thanks to the massive flux of data from on-line services. As a consequence, such data have been used to predict the present [Choi and Varian, 2012] (called nowcasting by Castle et al. [2009] ), that is, to improve estimates of quantities that are being created but whose figures are to be revealed at the end of a given period. The latter include unemployment, travel and consumer confidence figures [Choi and Varian, 2012] , quarterly company earnings (from searches about their salient products) [Da et al., 2011] , GDP estimates [Castle et al., 2009 ] and influenza epidemics [Ginsberg et al., 2008] .
The case of asset prices is of particular interest, for obvious reasons. It seems natural that the on-line activity of people who have actually traded is related in some way to contemporaneous price changes. However, forecasting asset price changes with such data is a much harder task. The idea is by no means recent (see e.g. Antweiler and Frank [2004] ). The literature investigates the mood of traders in forums devoted to finance [Antweiler and Frank, 2004, Rechenthin et al., 2013] , newspapers [Gerow and Keane, 2011] , tweets , blogs [Gilbert and Karahalios, 2010] , or a selection of them . Determining the mood of traders requires however to parse the content of the posts and to classify them as positive or negative.
A simpler approach consists in using Google Trends (GT thereafter) which reports historical search volume interest (SVI) of chosen keywords and to relate SVIs to financial quantities of interest trading volume, for instance price volatility or price returns [Da et al., 2011 , Gerow and Keane, 2011 , Wang, 2012 , Bordino et al., 2012 , Takeda and Wakao, 2013 , Kristoufek, 2013 . Findings can be summarized as follows: using this kind of data to predict volume or volatility is relatively easy, but the correlation with future price returns is much weaker. Incidentally, this matches the daily experience of practitioners in finance who use price returns instead of fancy big data.
Here we discuss what can go wrong in every step required to backtest a trading strategy based on GT data. We then use an industry-grade backtest system based on non-linear machine learning methods to show the near-equivalence of the exploitable information content between SVI and historical price returns. We therefore conclude that price returns and GT contain about the same amount of predictive information, at least with the methods we have used and challenge to community to do any better.
2 Backtesting a speculative strategy based on Google Trends data Price returns are believed to be unpredictable by a sizable fraction of academics. Unconditional raw asset prices are certainly well described by suitable random walks that contain no predictability whatsoever. Our experience as practitioners suggest that predictability is best found conditionally and that linear regressions are not the most efficient tools to uncover non-randomness in this context. There is essentially no linear price return auto-correlation; however some significant cross-correlation are found (in sample) between changes of SVI and future price returns. One would be tempted to conclude that GT data do contain more exploitable information than price returns. In our opinion, using such methods prevents one to ask the right question and to assess properly the predictability content of either type of data. We propose that one should first build a non-linear prediction algorithm and then feed it with either past returns, GT data, or both, and finally compare the respective performance of each case.
Before reporting such comparisons, we review some dangers associated with the use of GT data for prediction. As the saying goes, prediction is hard, especially about the future. But prediction about the future in the past is even harder because it often seem easier than it should. It is prone to many kinds of biases that may significantly alter its reliability, often positively [Freeman, 1992 , Leinweber, 2007 . Most of them are due to the regrettable and possibly inevitable tendency of the future to creep into the past. Any small leak from the future may empower an unbiased random strategy into a promising candidate for speculative trading. Let us now look closely at how this happens when trying to find predictability in GT data. The procedure goes as follows: The rest of the paper is devoted to discuss each of the above steps.
This must be done first, since otherwise one would backtest all kinds of strategies until one stumbles on good-looking strategy. Academic papers often test and report fixed relationships between an increase of SVI and future price returns. For instance assume that an increase in SVI with respect to its moving average should be followed by a negative return. The same kind of strategies is found in Kristoufek [2013] who proposes to build a portfolio whose asset weights decrease as a function of their respective SVI. All this is unsatisfactory. There is no reason indeed why a given relationship should hold for the whole period (they do not, see below) and for all stocks. For instance it is easy to find two assets with consistently opposite reactions to SVI changes.
Linear strategies are out for the reasons exposed above. One is then faced with the problem of choosing a family of strategies that will not overfit the input: there may be many keyword SVIs and functions thereof as inputs. We choose therefore to use ensemble learning as a tool to relate different kinds of information and to avoid in-sample overfitting as much possible. Note, however, that this is only one layer of stock selection and investment decision in the backtest system that one of us has implemented.
The propensity of academic papers to either stop or start their investigations in 2008, even those written in 2011 [Gerow and Keane, 2011] , is intriguing. Kristoufek [2013] uses the whole available length and clearly shows that the relationship between SVI and future returns has dramatically changed in 2008. What this means is that one must properly backtest a strategy with sliding in and out of sample windows [Leinweber, 2007] . Computer power used to be an issue, but the advent of very cheap cloud computing power has solved it.
Most papers are interested in predicting future price returns of a set of assets, for instance the components of some index (e.g. a subset of Russell 3000 [Da et al., 2011] , Dow Jones Industrial average [Kristoufek, 2013] ), while some focus on predicting the index itself . We focus here on the components of the S&P 100 index. The reason why one should work with many assets is to profit from the power of the central limit theorem: assuming that one has on average a small edge on each asset price, this edge will become apparent much faster than if one invests in a single asset (e.g. an index) at equal edge.
This is a crucial ingredient and the most likely cause of overfitting because one may introduce information from the future into the past without even noticing it. A distressing number of papers use keywords from the future to backtest strategies, for instance , Choi and Varian [2012] , Janetzko [2014] . One gross error is to think of the keywords that could have been relevant in the recent past, for instance debt, AIG, crisis, etc. instead of trying to think of ones which will be relevant. But a much more subtle error is common: to take a set of keywords that is vague enough and eternally related to finance, for instance finance, and to find related keywords with Google Sets [Preis et al., 2013, Choi and Varian, 2012] . This service suggests a collection of keywords related to a given set of keywords and is accessible in a spreadsheet from docs.google.com. We entered a single keyword, finance, and asked for related keywords. We did not obtain any fancy keywords (restaurant, color, cancer, etc.) as in , but did find the celebrated keyword debt, among others. The problem is that one cannot ask Google Sets in 2014 what was related to finance in 2004. As a consequence, the output of Google Sets introduces information from the future into a backtest. Since, as far as we know, Google Sets does not provide a wayback machine, it must not be used at all to augment one's set of keywords used to backtest a strategy. This shows that the choice of keywords is a crucial ingredient.
In addition, the use of Google was not stationary during the whole period, which may introduce significant biases into the backtest results. Correcting them needs at least a null hypothesis, i.e. a null set of keywords known before the start of the backtest period. This is why we collected GT data for 200 common medical conditions/ailments/illnesses, 100 classic cars and 100 all-time best arcade games that we trust were known before 2004 (cf. appendix A) and applied the strategy described in with k = 10. Table 1 reports the t-statistics (t-stats henceforth) of the best three positive and negative performances (the latter can be made positive by inverting the prescription of the strategy, transaction costs permitting) for each set of keywords, including the one from . Our brain is hard-wired to make sense of noise and is very good at inferring false causality. We let the reader ponder about what (s)he would have concluded if bone cancer or Moon Patrol were more finance-related. This table also illustrates that the best t-stats associated to the keyword set of are not significantly different from what one would obtain by chance: the t-stats reported here being a mostly equivalent to Gaussian variables for time series longer than, say, 20, one expects 5% of their absolute values to be larger that 1.95. One notes that debt is not among the three best keywords when applied to SPY from Monday to Friday: its performance is unremarkable and unstable, as shown in more details below. This issue is discussed in more details in ?.
Google Trends data are biased in two ways. First, GT data were not reliably available before 6 August 2008, being updated randomly every few months [Wikipedia, 2013] . Backtests at previous dates include an inevitable part of science fiction, but are still useful to calibrate strategies.
The second problem is that these data are constantly being revised, for several reasons. The type of data that GT returns was tweaked in 2012. It used to be made of real numbers whose normalization was not completely transparent; it also gave uncertainties on these numbers. Quite consistently, the numbers themselves would change within the given error bars every time one would download data for the same keyword. Nowadays, GT returns integer numbers between 0 and 100, 100 being the maximum of the time-series and 0 its minimum; small changes of GT data are therefore hidden by the rounding process (but precision is about 5% anyway) and error bars are no more available. This format change is very significant: for instance, the process of rounding final decimals of prices sometimes introduces spurious predictability, which is well known for FX data [Johnson, 2005] . In the case of GT data, any new maximum increases the granularity of the data, thereby making it even less reliable. It is one of the reasons members of quantopedian.com could not replicate the results of before the GT data set was released by the authors [Cuantopian.com, 2014] . This problem can be partly solved by downloading data for smaller overlapping time periods and joining the resulting time series.
GT data have a weekly resolution by default; most academic papers make do with such coarse resolution. Note that one downloads them trimester by trimester, GT data have a daily resolution. As a somewhat logic consequence, they try to predict weekly price returns. In our experience, this is very ambitious and predictability will emerge more easily if one times one's investment, if only for instance because of day-of-the-week effect [Gibbons and Hess, 1981 ].
Most trading strategies have tunable parameters. Each set of parameters, which include keywords, defines one or more trading strategies. Trying to optimize parameters or keywords is equivalent to data snooping and is bound to lead to unsatisfactory out-of-sample performance. When backtest results are presented, it is often impossible for the reader to know if the results suffer from data snooping. A simple remedy is not to touch a fraction of historical data when testing strategies and then using it to assess the consistence of its performance, but only once (cross-validation) [Freeman, 1992] . More sophisticated remedies include White's reality check [White, 2000] (see e.g. Sullivan et al. [1999] for an application of this method). Data snooping is equivalent to having no outof-sample, even when backtests are properly done with sliding in-and out-ofsample periods.
Let us perform some in-sample parameter tuning on the strategy proposed in . Figure 1 reports the t-stat of the performance associated with the keyword debt as a function of k, the length of the reference simple moving average. Its sign is relatively robust against changes over the range of k ∈ 2, · · · , 30 but its typical value in this interval is not particularly exceptional. Let us take now the absolute best keyword from the four sets, Moon Patrol.
Both the values and stability range of its t-stat are much better than those of debt (see Figure 1 ), but this is entirely due to pure chance. One solution to avoid parameter overfitting is to average the performance of a strategy over a reasonable range of parameters. Let us take k = 1, · · · , 100 for each keyword of each list introduced above. Since all the keywords act on a single asset, we use for each list an equally weighted scheme and hence compute the mean position over all keywords and all ks. The resulting cumulated performance net of transaction costs set at 2bps per transaction (which subtracts about 15% to the performance computed over the period considered) is reported in Fig. 2 . It is rather random for random keywords but slightly positive for the biased keywords of , which is consistent with the overall positive bias of t-stats that they report. It is however not very appealing, with an annualized zero-interest rate Sharpe ratio of about 0.12 and a t-stat of 0.37, which are far from being significant. In addition, its performance is flat from 2011 onwards, i.e. out of sample.
We follow the good idea to choose as keywords company tickers and names (see e.g. Da et al. [2011] , Kristoufek [2013] ) but add also other simple, nonoverfitting, keywords of our own invention. Weekly GT data has been down- loaded on 2013-04-21. At first, we do not attempt to predict pure weekly returns but time the investment period. Feeding our backtest system with GT data and returns yields the leftmost plot of Figure 3 : there is some exploitable information in these data. Calibration window length is about 6 months, which appears in 2008 and 2009 when the system first learns to take short positions only and then reverts to long positions. This takes much time and shows the difficulty one is faced with when calibrating trading strategies with weekly signals. Summary statistics are reported in Table 2 . It is important to be aware that these backtests are much affected by tool bias, as they use heavy computational methods and powerful computers that were not available for most of the backtest period.
Let us now compare the performance of predictors based on GT data only or past returns only (Fig. 3) . We find essentially the same performance (see Table 2 ); the value of the Wilcox rank sum test p-value is 0.72: they are not very different. This may be due to the fact that the backtest system just learns to recognize trends unconditionally, in other words, that the predictors are simply equally useless. We therefore remove some information content from the predictors. This is done for example by computing a rolling median of each predictor; a value of the predictor is now reduced to a binary number which encodes which side of the previous median it belongs to. We then use exactly the same backtesting system as before with the same parameters. The performance associated to GT data and price returns is now unambiguous (Fig. 4) . The machine learning method used here could exploit less predictability from GT inputs (at least those we could think of) than from inputs based on price returns; however, other machine learning methods yield the opposite result.
Finally, Figure 5 reports the result of the same method applied on weekly returns, which shows how hard prediction may be in this case even without transaction costs.
We have not been able to show that Google Trends data contain more exploitable information than price returns themselves. Assuming that this is not due to us not using the right method, our findings suggest that Google Trends data are equivalent to price return themselves. They do share indeed many properties with price returns: they are aggregate signals created by many individuals, they reflect something related to the underlying assets. In addition both are very noisy: the uncertainty about GT data, gathered from their previous file format, is about 5%. From this point of view, there is nothing miraculous or ground-breaking about GT data. We had to use sophisticated non-linear methods coupled with a careful backtest procedure, which contrasts with the much simpler approaches usually seen in current academic literature. Why it was needed at all is probably because it is hard to guess at first what an increase in SVI means, since it may be related to good news (e.g. higher interest from potential customers), or bad ones (e.g. worry about the company itself), or both, or neither. Indeed, such data include too many searches unrelated to the financial assets for a given keyword, and even many more unrelated to actual trading. As a consequence, adding another signal based on the change of the number of news related to a given asset helps to interpret what a change of SVI means [Wang, 2012 , Cahan, 2012 . Another possibility is to use other sources of data, such as Twitter or Wikipedia , which have the invaluable advantage of being available at a much higher frequency. At any rate, we challenge the community to show that for a given backtest system, predictors based on weekly Google Trends data only are able to outperform predictors based on price that themselves yield about 17bps per week including 2bps transaction costs.
We acknowledge stimulating discussions with Frédéric Abergel, Marouanne Anane (Ecole Centrale) and Thierry Bochud (Encelade Capital).