"A stationary price series is one that is generated by a single process. If cards are drawn at random from a deck in a game of blackjack, the distribution of cards selected will show evidence of stationarity; that is, they will follow a stable, predictable distribution over time.
If, however, the dealer at the casino shifts from using a single deck of cards to using a shoe of several decks, the distribution of cards selected will change. The distribution will now show evidence of nonstationarity--there will be significant differences in the frequency of cards coming up using many decks versus one.
Stationarity is important to traders because every so often the markets switch the number of decks from which they're dealing. The market will meander in a given direction with low volatility for a while and then suddenly zoom off on high volatility. If you look at the statistical distribution of price changes, you can see evidence of nonstationarity...
One of the greatest weaknesses of the methods utilized by many traders I have interviewed is the failure to assess stationarity and factor that into decisions. Instead of identifying the type of market they are in and trading methods specific to that kind of market, they adopt mechanical signals and uniform chart or oscillator patterns to apply to all markets. As long as the market works from the same number of decks, their methods may produce profits. Once the changing cycles described by Niederhoffer change the decks, however, the formerly useful methodologies will produce substandard results.
Any single set of trading rules or methods is vulnerable to breakdown if repeatedly traded across nonstationary periods."
From The Psychology of Trading; p. 86-7.