This study examines the informational efficiency of the bitcoin spot market by evaluating the predictive power of mechanical trading rules designed to exploit price continuation. Significant return predictability is found until the introduction of bitcoin futures in December Mar 29, · Some findings suggest that Bitcoin markets, while inefficient in their early days, transitioned into efficient markets recently. Others find support for the adaptive market hypothesis (AMH), an alternative theory that builds on evolutionary principles and assumes markets and market efficiency evolve over crypmoney.de by: 2. Aug 01, · Urquhart [ 14] studies the Bitcoin market from its beginnings in to mid and suggests that the market is inefficient but it is moving closer towards efficiency in time. Nadarajah & Chu [ 15] dispute these results and conclude that the market is in fact crypmoney.de by:
Bitcoin market efficiencyBitcoin and market-(in)efficiency: a systematic time series approach | SpringerLink
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Autocorrelation function Acf up to lag 30 for log returns left panel and of standardized model residuals right panel for Bitcoin. The MA 6 coefficient is largest, as expected, and strongly significant with a p value of 0.
Furthermore, the autocorrelation structure of the standardized model residuals in the right panel of Fig. The empirical significance level of the Ljung Box statistic of the standardized model residuals at lag six amounts to 0.
We note, also, that the peak of the autocorrelation at lag 6 seems persistent across time, so for example this number amounts to 0. We infer that the log returns of the series are subject to systematic and significant positive autocorrelation, which points towards a possible market inefficiency that could be exploited by suitable trading strategies.
The question whether the observed dependency structure is sufficient for balancing trading costs and to outperform the already impressive passive buy-and-hold strategy under these circumstances will be analyzed below. The above data analysis has revealed dependency structures which contradict the weak form EMH and which could be exploited by suitable forecast techniques.
We propose three variants: moving-average filters, frequently found in momentum trading strategies, ARMA time series models and neural nets. Whereas the former two can exploit the statistically significant linear dependency structure of the log returns, the latter can account for possible non-linearity in the data, additionally.
Momentum trading is a technique in which traders buy or sell an asset according to the direction of its trend. Given the different characteristics of these filters, we are faced with the problem of selecting a pertinent design and we propose to base our decision upon signal extraction principles.
For that purpose, consider the following simple local linear level model:. Harvey This model-based perspective justifies heavy smoothing in the case of noisy data, which would suggest applications to first differences or log returns of the original prices. We infer that the usage of EqMAs, as applied to log returns of Bitcoin data, could be justified based on signal extraction principles and use this design for our momentum trading strategy.
The previous EqMA-designs apply equal weights to current and past observations. A potentially more refined weighting scheme, at least in terms of forecasting, could be obtained by relying on the MA 6 -model 1 proposed in the previous section. The model can be inverted into its infinite autoregressive representation. For simplicity of exposition, we here restrict the analysis to feedforward nets with two hidden layers of dimensions six and three, see Fig.
Their outputs. The decision for the above net configuration is based on our data analysis input layer accounts for the first six lags of the data as well as on a suitable compromise between flexibility and simplicity requirements classic mean-square loss function as well as traditional sigmoid activation function : the results obtained by the above structure are representative for a fairly broad range of alternative net specifications or software implementations.
Feedforward net with two hidden layers applied. The six dimensions of the first hidden layer correspond to the first six lags of the Bitcoin log returns. As we have discussed above, under the EMH none of the above trading strategies could be persistently profitable and in fact they should all lead to systematic losses when accounting for the bid-ask spread at the corresponding trading time points. We will now challenge these claims, equipped with linear and non-linear filter techniques.
The previous analysis of prices, log prices, and log returns in Sect. In particular, the autocorrelation function in Fig.
Therefore, we propose to apply a simple EqMA 6 filter. Top panel: log returns black and filtered series red. Bottom panel: cumulated log- performances of the momentum strategy based on EqMA 6 for Bitcoin color figure online. Note that trading costs are ignored here for simplicity see below for corresponding results. The empirical significance level of a test for whether the two Sharpe ratios differ significantly amounts to 6. Continuing our performance analysis, we compute in Fig. First of all, our results show strictly positive returns over the entire period which itself is impressive.
This points to the fact that the Bitcoin market inefficiency becomes more accentuated in the last period of our sample, which contrasts with previous findings in Urquhart , Kurihara and Fukushima , and Bariviera stating increased efficiency after around though it is fair to mention that our data sample stretches two years further to the right than theirs.
A test of the hypothesis that the drift of the resulting performance is larger than zero Footnote 2 leads to a value of the corresponding t statistic of 3. To conclude, we note that the above results may claim out-of-sample validity since the only freely determined parameter, namely the filter length, was obtained from a straightforward analysis of the autocorrelation function whose main feature, the peak at lag 6, is pretty stable over time as shown in Sect. We here rely on the forecast filter derived from the MA 6 -model 1.
Specifically, we buy or sell the Bitcoin depending on the sign of the forecasts. Cumulated performances of the resulting strategy are displayed in Fig. Except for a short contraction, coinciding with the drawdown of Bitcoin in early , model-performances are fairly regular over the observed time span.
The time series model beats buy-and-hold on all accounts, but the extent is less marked than for the previous simpler EqMA 6 strategy. The trading strategy applied in this section builds on a return forecast through a neural net time series model outlined in Sect. Analogously to the previous strategy, which used a classic time series model for return forecasting, the sign of our Bitcoin return forecast again indicates whether we buy or sell.
In contrast to the previous linear approaches, fitting of unknown parameters is generally more challenging for neural nets because the numerical optimization tends being trapped into local minima.
Therefore, parameter estimates ordinarily depend upon suitable initial values for these parameters. In this context, it is common to rely on random initializations of biases and weights: each random seed thus generates a new random net whose parameters may differ substantially from realization to realization.
In order to illustrate the extent of this problem on trading outcomes, we compare cumulated in-sample left panel and out-of-sample right panel performances of random nets in Fig. Cumulated performances of random nets applied to log returns of Bitcoin: in-sample left panel and out-of-sample right panel.
A quick glance at both graphs illustrates the effect of the random seed on trading performances: for example annualized Sharpe ratios vary in a range from 0. In-sample performances are overly optimistic due to overfitting, as expected.
Interestingly, out-of-sample gains seem to be quite substantial, in the mean over all realizations, even after the breakdown of the Bitcoin in early The out-of-sample results in Fig.
At this stage of the analysis, we may be interested in finding out if in-sample numbers trading performances or forecast performances are informative about future out-of-sample performances.
Specifically, the correlation between in-sample and out-of-sample Sharpe ratios amounts to 0. Overcoming these conflicting evidences, we could rely on a simple ensemble average, the cross-sectional mean, of all performances as shown in Fig.
Average cumulated out-of-sample performances across random nets for the neural net forecast model red versus MA 6 forecast model blue strategies for Bitcoin color figure online. Indeed, a quick glance at both curves suggests fairly similar performances, except perhaps for the heavier drawdown of the classic model at the beginning of Buy-and-hold and the MA 6 -model are systematically outperformed by the other two strategies for the considered time span.
To verify significance of the above out-of-sample performances, we compute the t test for positive trading performances: the empirical significance levels are 0. We may infer from Fig. To conclude, we briefly analyze the effects of trading costs, by crossing the spread between bid and ask prices at each trade.
We here restrict the analysis to EqMA filters, since results are similar across all three approaches. Effect of trading costs crossing the bid-ask spread on performances of the momentum strategy based on EqMA 6 for Bitcoin. We may infer that the effect of the spread is negligible even for filters with relatively short holding periods, such as the EqMA 6. Our aim was to check pertinence of the EMH for the Bitcoin. Data analysis suggested evidence for a violation of this assumption by revealing systematic significant positive serial correlation of the log returns, which unfolded after accounting for volatility clustering.
We then proposed three different trading strategies relying on simple equally weighted moving average filters, derived from signal extraction principles, as well as on classic ARMA forecast models and non-linear neural nets. Our trading results confirmed the previous data analysis, by highlighting a filter of length 6, or an EqMA 6 , as the most effective momentum strategy.
Its performances were strongly statistically significant and the course of the yearly return series suggested increasing market inefficiency towards the sample end Januar 10, Similar results were obtained for the two forecast approaches with a slight edge in favor of the ensemble average of random neural nets.
A comparison of their trading performances out-of-sample suggested only modest departure from linearity, possibly during the drawdown of the Bitcoin at the beginning of Statistical significance could be established for all but the MA 6 -model which marginally missed the mark due to the aforementioned drawdown.
Finally, we extended our performance analysis to the inclusion of trading costs by crossing the spread between bid and ask prices at each trade. Confirming the overall positive cumulative performances, our results were only marginally affected by accounting for trading costs.
In summary, our findings strongly reject the EMH for the Bitcoin market throughout the entire sample period and in particular in recent times.
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