Visualizing The Madness of Crowds with Python

At the same time we’re going to create a new column for each of our assets which will capture the change in the ‘Adj Close’ price feature from one period to the next.The new column will be called ‘Adj_Close_Change’, and by definition it’s the difference between the ‘Adj Close’ shifted forward by one period and the current ‘Adj Close’ — also known as the first-difference of a series.Although Bitcoin and MoviePass price histories don’t go back nearly as far as the S&P 500, the visuals still reveal important insights.First, the time series plot of S&P 500 reveals a long-term upward trend.Second, if we compare the means of the ‘Adj Close’ price for S&P 500 from the time period (1980–1995) against the time period (1996–2018), there’s a drastic difference in the magnitudes.What these two observations tell us is that the time series data for S&P 500 falls into a category of time series data called non-stationary data.The two defining characteristics of non-stationary data are:Non-constant means across different time periodsNon-constant means even when taking the difference of means from period to period, so the change in means are also non-constantTime series data that are non-stationary due to different means across different time periods can be made stationary if the change in means are constant (fluctuate around the same point up and down for a long time).Why is this important?Because stationary time series, as opposed to non-stationary, revert to the mean and therefore can be analyzed with statistical methods for things like forecasting.If you examine the adjusted closing price for Bitcoin from 2011–2017, it resembles what’s known as a random walk with no clear trend until you get to the 2017–2018 period.The same situation applies to the adjusted closing price of MoviePass stock from about 2003 to 2018.As described above, a way to tell if a time series can be made stationary and therefore mean reverting is to look at the first-differences in prices as we do here.As the above plots show, the means for S&P 500 Index is clearly non-stationary as even the first-difference has an increasing trend.Also, there appears to be some strong evidence that both Bitcoin and MoviePass stock are stationary and therefore mean reverting for most of their price histories.Thus, for the average investor, it may not be prudent to invest in assets that possess:Long-run mean-reverting properties andGoes up in price by magnitudes previously unseen (hockey-stick pattern) without good reasons andHighly volatileIn the final analysis, the ultimate power of visuals is not that they provide conclusive evidence, but rather that they give us the necessary guidance for directing our research and provide the common person with readily understandable information.. More details

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