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It's no bad but you have to backtest the method out-of-sample. Say you have discovered an indicator that works 100% in history, you still cannot be sure if it works next time. Another advise is you might want to investigate the distribution of loss when your system fails to work. If your system delivers 1% every time you trade, and loses 10% each time it ...


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In the long term you will underperform buy & hold because you need an accuracy of at least 65%. See these papers for more: Bauer, R.; Dahlquist, J.: „Market Timing and Roulette Wheels Revisited“, CFA Institute, 2012. http://www.cfapubs.org/doi/pdf/10.2469/irpn.v2012.n1.10 Sharpe, W.: “Likely Gains from Market Timing”, Financial Analysts Journal, ...


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It's not unusual to find a financial time series with positive trend samples biased between 55-60%, depending on the period sampled. Stocks tend to have an upward drift over the long run. When you account for the drift, I would say, that number is really not much better than chance. A better way to verify your question would be to make certain to build ...


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Directional forecast is insufficient. You could have a signal that has 100% accuracy and you would not necessarily be able to profit from it because of transaction cost, implementation etc.


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There are different methodologies to detect a change in the market efficiency, both in the market and firm-specific cases. In the FIRM-SPECIFIC case, the most common procedure is the event study methodology; you can find how to construct an event-study case explained in Kothari & Warner (2006), who collected all the event study methodology implemented ...


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Let $S_t$ and $B_t$ be respectively the stock price and the money market account value at time $t$. Then $S_t/B_t$ is called the discounted stock price. Note that \begin{align*} E\left(\frac{S_N}{S_0}\right) &= E\left(\frac{S_N}{B_N} \frac{B_N}{B_0}\right)\frac{B_0}{S_0}\\ &= E\left(\frac{S_N}{B_N}\right) E\left(\frac{B_N}{B_0}\right)\frac{B_0}{S_0} ...


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Do you mean the "realize measure" of volatility using the intraday Transaction-and-Quote data? If that's the case, just trade data, or mid-quote would be sufficient. Looking at Level II and level III data really introduces a lot of noises (hudge cancellation rates, orders placed by HFT blindly to gain time-priority advantage). Using those data to calculate ...


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Possibly you might be able to first estimate the bid-ask spread from execution prices, using the method of Roll (1984), and then adjust the volatility for this. Essentially the bid-ask bounce adds to the underlying volatility, so knowing an estimate of the b/a and the apparent volatility, the underlying volatility could be recovered by subtraction. ...


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If high frequency returns are iid and the mean and variance are finite and vthe variance is greater than zero then the Central Limit theorem holds Then, regardless of the distribution of the high returns, when aggregated over time the aggregated returns will tend in distribution to a Normal distribution. The Lindeberg-Lévy-Feller version of the Central Limit ...


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My main reference will be "Dan Xu, Christian Beck - Transition from lognormal to chi-square superstatistics for financial time series" Non-equilibrium statistical mechanics (more specifically, superstatistics) gives some ideas of explaining the relation between time frame and its distribution: "...to regard the time series as a superposition of local ...


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Surely, there is; search for aggregational gaussianity in Google Scholar or ScienceDirect. In fact, 5 minutes returns are leptokurtic and fat-tailed; then as you increase timeframe, returns become more and more normal. Yearly data is almost normal, if you have enough points.


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Quote: Starting in 2003, the NYSE started disseminating automatically, with a software called autoquote, any change in the best quotes in its listed stocks. Before that specialists had to update manually new inside quotes in the LOB. This implementation considerably accelerated the speed at which algorithmic traders receive information Endquote Source: ...


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Of course this does not make sense. But the problem is not the total return index but (most likely) the range of historical values used in the calibration. In a Solvency II setting we are talking about annual VaR on the 99.5% level. As a quick reality check assume you are a well versed extreme event modeller. In fact you just need at least 5 events. ...


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Maybe this is rather a comment then an answer but three points: GBM is a stochastic model for stock prices. It is used to price derivatives in an arbitrage free setting. In this case you look at a process whose expected return is just the risk free rate (due to no-arbitrage). Forecast this price is trivial. It is debatable how forecastable stock prices ...


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There is probably nothing wrong with your code although I did not check it in Mathematica. Normally, Geometric Brownian motion is just a model. Here, you simulate lots of paths and then average over it. The first plot gives something like $$ E(S_t) = S_0*\exp(\mu t) $$ with $S_0$ the initial stock price. However, because of the simulation, you do not get ...



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