Stationarity and Autocorrelation
A series is stationary if its statistical properties do not depend on when you look: constant mean, constant variance, and autocovariance depending only on the lag.
This is the precondition for nearly every time series method, and the failure to check it is the most common serious error in financial data analysis.
Why it matters: spurious regression
Regress two independent random walks on each other and you will typically find a high and a highly significant slope.
Nothing connects them. The apparent relationship comes entirely from both series trending, and the usual t-statistics are invalid because the errors are non-stationary.
This is not a rare pathology. It is what happens by default when regressing price levels, which is exactly what an inexperienced analyst does first.
Prices are non-stationary; returns approximately are. Analysing prices directly produces relationships that look strong, test significant, and mean nothing.
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