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I am actually doing some research on bitcoin for my bachelor thesis. I have daily data on the price of bitcoin from here. I calculated with python:

df["Price Change (in %)"] = (df["Close"] - df["Open"])/df["Open"]*100

df["Mittel"] = df["Price Change (in %)"].rolling(30).mean()

df["Vola"] = df["Price Change (in %)"].rolling(30).std()

The data frame looks like this: enter image description here

enter image description here enter image description here

Can I just interprete these data points by:

df["Price Change (in %)"].mean()
df["Price Change (in %)"].std()

And then apply the formula for margin of error?

1.96*(df["Price Change (in %)"].std() / math.sqrt(df["Price Change (in %)"].count()))
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You can always interpret mean and standard deviation and margin of error, but in time series they do not have too much useful interpretation.

  1. Mean will tell you what the average bitcoin price change was in your time interval. If the mean is 0.10% that means between your start and end date on average the bitcoin price changed by 10%. Only other useful information this tells you is whether during the time interval there was some positive or negative linear trend.

  2. Standard deviation will just give you some measure of dispersion of values in your sample, but that has little use in itself since you have nothing to compare it to. If you want to analyze how the volatility of bitcoin changes you need to estimate time varying volatility with some model like ARCH/GARCH.

  3. You can calculate confidence interval but it doesn't have much interpretation besides putting some confidence interval on your mean estimate.

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  • $\begingroup$ I wanted to build a ADL model for bitcoin price volatility, here the rolling 30 day standard deviation. $\endgroup$
    – BlankerHans
    Commented May 15, 2023 at 6:44
  • $\begingroup$ @BlankerHans you should use GARCH model that estimates time varying volatility, ADL with 30 day rolling standard deviation makes no sense $\endgroup$
    – csilvia
    Commented Jun 17, 2023 at 12:39
  • $\begingroup$ Why not? Isn't the ADL model just like a standard multiple linear regression with some lagged variables? $\endgroup$
    – BlankerHans
    Commented Jun 19, 2023 at 12:57
  • $\begingroup$ @BlankerHans precisely, and do you know what is one of the assumptions of such regression? That standard deviation is constant across observations. With price of any stock, currency, cryptocurrency or commodity that will not be true because you will often observe volatility clustering. You need to use here some ARCH type model my best guess would be GARCH. You can google it, that is what people use in this case not ARDL $\endgroup$
    – csilvia
    Commented Jun 27, 2023 at 9:25
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    $\begingroup$ @BlankerHans happy to help, also based on your comment my answer seems to solve your issue, if an answer solves your issue you should accept it $\endgroup$
    – csilvia
    Commented Aug 2, 2023 at 11:31

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