The discontinuity phenomenon is the chaotic system that arises after the formation of an original price pattern or trend in the markets. All financial time series depict this. That is, they jump from one pattern to the next and in doing so, the current period of market order comes to an abrupt end.
In “Exploiting stock market cycles” (March 2009), we presented a condensed methodological introduction to algorithms that could be applied to selected financial time series. We defined a universal pattern that emerges and can be detected through the use of an optimized algorithm. We also showed how many economic time series demonstrate this innate property, making so-called random behavior random in name only. The discontinuity phenomenon is an extension of these studies; one of its goals is to identify inverse, sequential patterns to the current market state that render the current pattern obsolete.
If we consider the formation of a pattern as a state of market order, the discontinuity that follows can be viewed best as the chaos and order sequence that links all financial times series. According to Maria Lorca in “The Euro in the 21st Century” (Ashgate, 2011), this continuous jump from one pattern across sequential environments is a “singularity,” which she defines as a spontaneous phenomenon in the economy completely independent of human intervention.
Using traditional technical analysis tools in unique ways, we can uncover these moments of key shifts in the markets. First, however, we need to understand better the market environments that contain these shifts.
The first step to debunking the discontinuity phenomenon is identifying the singularities. To detect these patterns, and the consequent discontinuity, we need to utilize continuous sequential analysis with the least number of gaps or jumps. Time series can be defined in many ways, such as tick or time compression. We will want to use the method that results in the smoothest data series. In our examples here, we use time-based charts.
The second requirement is the use of a specialized index. This can be done through the combination of positively correlated time series; this often yields more robust forecasting power than individual time series alone. The use of isolated time series makes the predictive forecasting less reliable. Part of the reason is while we may have the right tools to detect the pattern, we have no control over when, where and how it emerges. A complex series includes more information and, therefore, more clues to discovering the pattern.
The third rule is that while the discontinuity phenomenon may be a complex problem difficult to solve, we know that it begins and ends with the formation of similar but inverse patterns in sequential time frames.
Detection of these patterns is difficult because it’s rare that both can be defined in constant numerical terms across time series; this is why we see them as self-similarities. One tool for detection is a pattern-recognition scan, such as the technology used in database searches, facial recognition, DNA sequencing, etc. Another method applies coinciding statistical tools to the complex index across time frames. If the condition is met across the time frames, it automatically grants the pattern a higher statistical degree of reliability.
The latter approach will be used here. The techniques themselves do not have to be exceptionally sophisticated. For instance, a moving average crossover in different sequential time frames automatically makes the patterns similar and concurrently makes the forecasting relationship much stronger. This is the case with the charts included in “Cross-time signals” (below) where two exponential moving averages are applied in four sequential time frames on the Volatility Index (VIX).
Analyzing the VIX
There are several expert systems in the industry that use a wide variety of statistical and fundamental tools; however, we can search for the discontinuity phenomenon using a simplified model of a 10- and 24-period exponential moving average crossover. We will apply it to the VIX, considered a so-called contrarian indicator, meaning it moves opposite of market prices. (Other contrarian indexes also are good candidates for this analysis.) We will use multiple time frames to increase the reliability of the forecast.
As seen in “Cross-time signals,” the highlighted ellipses on the six-day, one-day, four-hour and 30-minute charts identify key concepts. In the six-day chart, the moving average crossover pattern gives way to a sustained and aggressive rally of the VIX, which is concurrent with the fall in late July 2011 of the major equity indexes. At the same time, we see some important activity on the one-day chart. There are two highlighted areas, the first coinciding with the bullish pattern in the six-day chart. This implies a double convergence and, thus, a stronger reinforcement of the original bullish forecast.
On the other hand, the second and more recent ellipse in the one-day chart reveals a sell crossover signal that is complemented further in the four-hour and 30-minute charts. This triple convergence in different time frames is a powerful indication of the robustness of the sell signal. It also is significant because it constitutes the first discontinuity in the original trend and could have enough momentum to overcome the earlier signal in the six- and one-day charts.
The 30-minute chart shows a second ellipse that occurred two days prior and constituted a buy crossover signal, which preceded a significant rally in the VIX and a plummeting of equity indexes the subsequent two days.
Despite this price action, however, the VIX subsequently showed a strong bearish correction through three coinciding patterns, which explains the stock market rally since Oct. 4. The more recent spike in the VIX, as shown in the 30-minute chart, clearly marked the discontinuation of the trend of the previous one-day, four-hour and 30-minute patterns, at least in the short term. What remained to be seen was whether the development had enough momentum to serve as a follow-up pattern of the six-day chart, which had its original trend intact.
In this example, price trends, two confirmed cases of discontinuity and a triple convergence in a single time series (but in different sequential environments) helped increase the robustness of our market forecast. It’s also through this process that we develop a scientific set of routines that can be applied to other markets to detect the same directional price movement.
A key element of discontinuity analysis is the role of news. When the market jumps from one pattern to the next, the pressure on the financial press to explain the move is immense. In practice, market forces demonstrate we should be cautious when analyzing common causal relationships between market direction and events.
On any given day, financial news can be spun to accommodate how the markets are behaving. However, when intraday reversals take place, fundamental analysts often play catch up when what was described as the driver behind a given market move suddenly becomes obsolete.
Another issue to consider in event trading is how to weigh economic and financial news. The high degree of subjectivity associated with this analysis, again and again, reinforces the argument for a coherent, thorough and scientific analysis of financial time series. One case in point is how the European debt crisis has clouded the global macroeconomic environment. Given this news, it’s difficult to justify fundamentally how the Dow had its biggest monthly point gain since 1987 while the S&P 500 had its biggest monthly gain since 1974.
Francisco J. Lorca-Susino, Ph.D., CMT, is senior analyst at Banco Santander in Boston, Mass., and the economic and foreign exchange editor for PinHawk LLC. E-mail him at firstname.lastname@example.org.