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I'm very much a Stata and linear regression newbie. I am running a linear regression with Bitcoin price as the dependent variable and using independent variables such as the S&P500, SSE, and FTSE closing prices, the U.S. CPI, the U.S. GDP, U.S exchange rates with CNY and the Euro, the 10yr maturity rate, and google trend data. I want to analyze the effect that these independent variables have on Bitcoin prices if any at all. All data is recorded at the monthly frequency.

I have a few questions regarding the data and how to use it in linear regression:

1) Should I use a time series or a normal linear regression analysis?

2) Should I use the % change for my data points as opposed to just the prices and going rates? If not, why shouldn't I?

Any and all help is appreciated. If there are any useful links you know of that would be great as well. Thanks!

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  • $\begingroup$ Just a suggestion: when you’re starting out with basic methods, don’t use financial data. Predicting a financial pattern like you propose will be difficult, and you’re unlikely to learn much about how the basic techniques work when those models have abysmal performance. $\endgroup$ – Dave Nov 7 '19 at 3:53
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Yes, set up your data with months as rows and assets as columns.

For the bitcoin, SP500, or any price-based values, you need to transform the price into the log-returns for each time period: $y_t=\log(y_t)- \log(y_{t-1})$. Thus, this month's log-return value for bitcoin is the log of bitcoin's price this month minus the log of bitcoin's price last month. FYI, log-returns are equal to $y_t=\log(\frac{y_t}{y_{t-1}})$, since $\log(a/b) = \log(a) - \log(b)$. When done, you won't have a log-return value for the 1st-month values.

Log-returns have to be used because they are normally-distributed, whereas prices themselves are log-normally distributed and inappropriate for linear models.

For the CPI etc. just use the data.

Then run a regression, and you should be good to go.

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