# Tag Info

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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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In practice, for heavily traded assets (above 60% quantile of average daily dollar volume), individual asset return is pretty scalable across different time frame by a factor of $\sqrt{T}$. However, for covariance among different assets, moving between different time frame is not linearly scalable (although it should be in math). This is known as "Epps ...

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This paper states that heteroskedasticity is a stylized fact in daily as well as intra-day returns: https://statistik.econ.kit.edu/download/doc_secure1/HandbookITandFinan.pdf

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There are several ways to do this: If you need the price for June 11 and the market is closed on that day, you can use the price for June 10th (which is known on June 11th). I would advise against using the price of June 12th because it is not known on the 11th, so you would be "looking into the future" which is a bad idea and can lead to subtle fallacies ...

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You can apply the Kolmogorov-Smirnov test. I simply quote from the entry: "The two-sample K–S test is one of the most useful and general nonparametric methods for comparing two samples, as it is sensitive to differences in both location and shape of the empirical cumulative distribution functions of the two samples." There is an R-implementation too.

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The CAPM model is based on the relationship existing between an asset and its benchmark market; assuming that the bitcoin could be thought as a currency, according to me, you should take the mean of returns over all the currencies traded and then regress the BTCUSD on the the average currency market returns. Indeed, although the EURUSD is one of the most ...

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True this is a stackoverflow question but have you tried the fool around with the package Pandas? You can do in Python import pandas as pd data = pd.read_csv('filepath/file.csv') That's the easiest way.

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Do you want to model the returns in a risk-neutral framework (for derivatives) or in the real world measure (for risk analysis/portfolio construction)? For the first approach (say modelling under $Q$) you should go to the literature on bond and FX-derivatives. I would go more into detail if this is your aim. The formulation $N(\mu-\sigma^2/2,\sigma)$ ...

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The arithmetic average of +100% in Year 1 and -100% in Year 2 is 0%, but I we all know the result is not a 0% return. So arithmetic returns are absurd to use in any real life context. Maybe in another universe they can serve some purpose.

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