Quote from steve46:
A stationary time series is one in which the underlying rules that generate the series do not change over time.
Consider a simple example. A small urn filled with different colored marbles (100 white, 50 blue, 50 red, 25 black). You shake the urn, remove 1 marble, write down the color and put it back in the urn. Repeat at least one hundred times. The series of colors you will have generated is "stationary".
Now we do that again, but without our knowing, someone has come in to the room and removed 50 white marbles. So we go through the process again. In this instance we do not have a stationary series, because the relative distribution of colors has changed. This is called a "non-stationary" time series.
This is how the market works. As you watch the prices move up and down, YOU have no clue as to whether the series is stationary or not. In order to find out you have to submit the series to specific tests.
As I have said before, go buy the book
"Mathematics of Technical Analysis" by Clifford Sherry
Read it, do the exercises. Learn something worthwhile.
Steve