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What is the best way (most common) to discover if a stock is trending or not? (Despite drawing a line). A hurst exponent? A linear regression maybe?

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See the average directional movement index (ADX):-

"At its most basic the Average Directional Index (ADX) can be used to determine if a security is trending or not."

http://stockcharts.com/school/doku.php?id=chart_school%3atechnical_indicators%3aaverage_directional_#trend_strength

It's easy to calculate. There is an example spreadsheet on the link page.

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As in the answer by Chris Degen, various technical indicators for trend estimation exist (just to mention one additional: the moving average and moving average cross over).

In this free ebook by Rob Hyndman and George Athana­sopou­los present various time series techniques for forecasting. These are ARIMA models and exponential smoothing methods. They can be used to estimate a trend in time series.

But be careful if I remember correctly then they state that stock prices are hard to forecast (if not impossible).

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