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You need to get the open of the first candle, the high and low over all candles in the time frame and the close of the last candle. R has a package for this, your language of choice might have it as well.

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The number of up moves of the stock $S$ after 100 days follows binomial distribution. To calculate expected value of the stock we have to weight values by probability mass function. After 100 days we have $k$ up moves of $1+10\%$ and $100-k$ down moves of $1-10\%$ i.e. the value of the stock is $S_0*(1+10\%)^k*(1-10\%)^{(100-k)}$ with probability ${100}\... 3 It is not negative returns that are an issue. Assume the following prices in two periods:$P_o = 100$;$P_1 = 99\$ Standard percent calc: $$\frac{P_1}{P_0}-1 = -0.01$$ which is -1% . Using the natural logarithm you get $$ln(99)-ln(100) = -0.01005$$ which is essentially identical. Negative prices are an issue - but these are not observed for many economic ...

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Providing an example: I believe the best way to verify how the roots of the characteristic equation relates to covariance stationarity of the time-series process, is through an example in the form of an AR(1) process. In a vague sense, using the lag-operator in order to obtain the characteristic equation, offers a transformation of the Autoregressive process ...

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