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Timing and Volatility

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Timing and Volatility Models

Princeton Economics utilizes 5 separate models to identify turning points and periods of changing volatility. They are:

  • Composite Timing Models
  • Empirical Timing Models
  • Trading Timing Models
  • Bifurcation Models
  • Volatility Models

Composite Timing Models

There are numerous types of cyclical activity within economies and markets. Some cyclical trends expand and contract with no definitive fixed duration. One wave might be 50 days, the next 62 days followed by another of 48 days. This type of cyclical activity is addressed by “Composite” Timing Models for they are the result of a harmonic mix of many other timing elements. Composite frequencies form not only from cyclical frequencies within the same market but also from external influences from other markets around the globe. Cyclical analysis conducted on any individual market without correlation to the global market structure will ALWAYS produce inconsistent results.

empir 1Empirical Timing Models

Fixed length timing frequencies also exist. On lessor levels of price activity, such as weekly, a fixed length cycle of 8 weeks may produce a high and low precisely every 8 weeks for a brief period in time. This cycle may suddenly disappear as it becomes overpowered by a longer timing frequency from monthly, quarterly or even yearly levels of activity within the same market. After a few apparent failures, this 8-week cycle will suddenly reappear exactly on target as if nothing had happened. This is a fixed length cycle that never changes in duration. When it stops working it is only because a frequency of greater importance is taking control. This greater force may be from within the same market or the result of global interrelationships. We have provided an illustration of this effect using a weekly chart of gold upon which is overlaid an 8-week cycle. A number of arrows point to targets when gold produced a high or low on an intraday or closing basis. Some of the successful targets were minor 1 week reactions while others produced the major high or low for the move. Empirical turning points are just that—turning points irrespective of its significance relative to a major high or low. Whenever a frequency is of a fixed length, we refer to it as our “Empirical” models.

18 Year Cycle:

  • 1902 (Directional Change)
  • 1920 (Lowest Close)
  • 1938 (Low)
  • 1956 (High)
  • 1974 (Major Low)
  • 1992
  • 2010

Table #1


One of the primary Empirical Timing Models in the Dow Jones Industrials Index is the 18- year cycle. The targets produced by this one cycle during the 20th century have been quite impressive on an annual basis (Table #1, Figure #1). While 1902 did not provide the intraday low, it did mark the beginning of a decline known as the “Rich Man’s Panic” that led to the final low in 1903. The next target of 1920 produced the majority of the decline for this panic which followed the end of World War I. While new intraday lows were formed in early 1921, the market closed higher and began its long ascent into the famous 1929 high. 1938 produced the first major low following the 1937 high, producing a mini-panic at the time and raising fears of a renewed depression which failed to materialize. The next target of 1956 produced a temporary high at 524.4 on the Dow. This was the first temporary high followed by a sharp 20% correction the following year. The last target was the major low established in 1974 at 570.0 which ended a 46% correction from the high of 1973 (1067.2).

The 18-year cycle has one more curious trait worth mentioning. Major highs also formed in 1901, 1919, 1937 and 1973, one year prior to each turning point. The only exception was 1956 where a major low formed to the right side in time (1957). This means that the extremes of the price movements from high to low were all contained within a 2-year period.

Empirical models are very important timing elements. Just because a particular timing frequency may appear to be successful on a few occasions DOES NOT guarantee its validity. Each timing frequency employed in our Empirical models has been historically tested as far back as possible and under all conditions. The 18-year Empirical frequency in the US stock market has been tested back into the early 19th century. The 8-week frequency in gold has been tested back to 1970 in the US market. One CANNOT ascertain the validity of any timing frequency unless it is successful in both bull and bear markets. For example, a frequency in gold is ONLY valid if it is as consistent during the bull market prior to 1980 as that in the post 1980 bear market. The majority of mistakes made by analysts are caused by the use of timing models that have not been tested in both bull and bear market climates.

Trading Timing Models

Our Trading Timing Models are concerned strictly with the nominal durational differences between bull and bear markets. Our turning points generated by this model reflect the statistical differences between these opposing trends without consideration of various timing frequencies or intermarket relationships. This model specifically states what the expected event should be (high or low) at a particular time interval. Unlike Composite or Empirical models, our Trading Timing Models offer a union of time and direction and thus enable the end-user to qualify the forecast. Thus, our Trading Timing Models can offer a completely independent view as to what should be expected. Because trends become much clearer during violent price action, this tool performs best during panics in either direction. The periods when this tool provides a lower degree of accuracy is during quiet non-trading periods. These are periods when both forces are about equal and tend to cancel each other out.

Bifurcation Models and the Science of Chaos

Chaos has become a hot topic in science. Bifurcation analysis is the art of attempting to find a specific point in time and price that acts as a “strange attractor” in market or economic movement. The theory is that at certain intervals in time, a given market is compelled to move to a point of maximum trend, be it overbought or oversold. This type of analysis takes the form of what we refer to as a “logistics map” which involves a contango of price and time.

The Princeton Bifurcation Analysis is designed to produce a listing of timing targets completely independent from cyclical based models. We use the results of this form of analysis to further filter our findings derived through different model systems. Our Bifurcation Analysis is accomplished by first establishing a Primary Time Interval between two major points of an opposite trend (high and low) which is then projected forward in time on an equal basis. A box is then drawn with its width equal in time while the height is defined by the full distance in price between the extremes of high and low. This box is then referred to as the “Time & Price Window.” A proprietary formula is then introduced to create what we call the “Parabolic of Time & Price” which is then plotted within our Time & Price Window. A diagonal is then drawn from the lower left corner to the upper right corner. Once this framework is established, the Bifurcation plot begins.

bifor 3

bifor 2

The starting point for our Bifurcation plot is also determined by a proprietary model measured from the lower left corner of the Time & Price Window. Our plot begins on the upper-side of the diagonal and continues vertically until it encounters the parabolic, where it then turns 90 degrees to the right. Plotting continues until it once again reaches the diagonal where it turns 90 degrees proceeding vertically once again. The Bifurcation plot continues in this fashion making a 90 degree turn each time it encounters either the parabolic or the diagonal.

Each time the Bifurcation plot turns vertically we obtain a time projection. All horizontal plots offer a price projection. Extremely well behaved markets will contain this plot between the diagonal and the parabolic. Occasionally, a strong strange attractor will appear around the juncture of the diagonal and the parabolic which will be evident by the plot forming a box around this area. Very chaotic markets will show the plot suddenly breaking out of the confining area between the parabolic and the diagonal. The time and price targets that are derived from a Bifurcation plot will often line up with targets derived by cyclical and technical models, even though there is no similarity between these methodologies. At other times, the targets highlighted through our Bifurcation plots cannot be determined by any other form of analysis.

The purpose of our Bifurcation model is to determine whether or not there will be any major strange attractors in the future. This can be very helpful in warning about dramatic changes in trend such as the 1987 stock market crash.

We provide the results of this model to our clients mainly as a confirming tool rather than an exclusive tool by itself. However, we do interface this model with that of our timing models to help filter out which timing targets will be stronger than others.

Again, it is not always possible to determine if a particular target will produce a high or low well in advance. Nonetheless, this tool can be used to determine when a particular trend will change direction and what the next event should be relative to a high or low formation.

Volatility Models

In addition to our timing models, we also want to know how a market moves. This is accomplished by models designed to identify periods of high and low volatility. The results from this type of model are helpful for short-term traders looking to take advantage of volatile days and option traders seeking to trade volatility rather than market direction.

The volatility forecasts are given in the same format as the timing models. Each target is a time reference identifying when periods of higher levels of volatility or lower levels of consolidation will develop.

There are two distinct types of volatility in economic and market behavior. The first is the volatility that takes place overnight between the opening level and the previous trading session close. The second type of volatility is that of intraday. This is measured by expressing the difference between the high and low of the day as a percent of the high.

Our volatility models are run on all levels of price activity from intraday to yearly. This again allows us to pinpoint volatile years, quarters, months, weeks and days. Intraday models can bring the forecasts down to a specific 10 minute period.