A stationary time series is a set of data derived from a single underlying process. A simple example of a stationary time series would be the distribution of values from the rolling of fair dice. Any given roll is not predictable, but the distribution of values over time would be stable.
Suppose, however, that we used weighted dice and then changed the dice at random intervals. Now each roll would not be predictable, but the distribution of values would also be random. The distribution would no longer be stationary, as it's generated from multiple processes (dice).
The stock market--and, indeed, financial markets in general--does not yield stationary time series. This has been evident in recent markets. If we compare the market from the past couple of months with the market from, say, the same months in 2019, we see very different patterns of trend/price change and volatility. Correlations among stocks and sectors vary from time period to time period, as well.
What this means is that markets are ever-changing. This shouldn't be surprising. Simply observing the differences in volume across various market periods tells us that the participants in the marketplace are not constant.
The ever-changing nature of markets has a couple of important implications:
1) Simply looking for patterns across various historical periods is apt to yield weak results. Similarly, trading volatile bear markets with the same methods and "setups" as were used in range markets or low volatility bull markets is not likely to be useful. A more intelligent process would be to identify a few key regime variables, study markets in those regimes, and identify trading patterns specific to particular market conditions. A very simple analogy would be a football team that has to play different opponents and play in very different field and weather conditions. The successful team will adapt to each set of circumstances with unique game strategies. The successful team will not adopt the same strategy for all opponents and field conditions.
2) Psychological disruptions often reflect poor trading processes. It is commonplace to hear coaches and gurus insist that trading is a mental game and that the right mindset will yield consistent, profitable results. If you understand point number one above, you'll recognize that the idea that poor trading comes from poor psychology is a limited perspective at best. What commonly occurs is that we adopt one set of trading practices and strategies adapted to a particular environment, only to find that environment changing. When the trading strategies that used to work no longer produce consistent profits, we become frustrated, fearful, etc. The problem is not the emotions attached to trading: those are the consequences of the more fundamental problem of not identifying and adapting to changed market conditions.
It is a commonplace observation that successful traders follow a disciplined "process". If trading were like manufacturing widgets, that would be all that traders would need. In an ever-changing environment, however, a successful trading process would need to include an assessment of the current environment and the opportunity set specific to that environment. The successful trader is much more like the entrepreneur than the manufacturer of widgets. Identifying and adapting to changing markets is central to success.
The changing nature of markets impacts active traders as well as investors. The markets behave differently at different hours of the day, as we see different volume/participation and different event/catalysts across times of day and time zones. Similarly, would we invest in the markets of the 1970s the way we invested during the 1990s?
And might it be the case that some market periods are simply not tradeable, if they change more rapidly than we can adapt our strategies?
An important source of trading psychology woes is holding positions across non-stationary market periods. Key to successful trading is knowing when to hold 'em and when to fold 'em.
Further Reading:
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