David’s webinar Monday on long term cycles was timely as I have been working on a number of the same issues using different spectral analysis techniques. Sentient Trader is great for short term trading but I needed additional tools that allowed for analysis of long data sets and systematic backtesting if possible (more on this later).

One advanced spectral approach that is excellent for looking at financial data is empirical mode decomposition (specifically ensemble EMD). EMD can handle non-stationary, nonlinear financial data better than any other spectral analysis method because it is entirely empirically-based (no functional form assumption of sine waves like FFT) and it uses local fitting to decompose a time series into its primary frequencies (intrinsic mode functions or IMFs). I won’t get into the weeds too much here because there has been a lot written on EMD over the last few years. One word of caution, EMD does an excellent job identifying cycles in-sample but is basically worthless for backtesting and trading out-of-sample because of serious repainting issues (also know as the end-point effect).

My partner and I analyzed the DJIA monthly since 1790 and used EMD to decompose the price time series into the following cycles.

3 months

6 months

9 months

18 months

42 months

104 months

210 months

426 months

Not bad, from a Hurst perspective.

We then created composites by combining multiple IMFs (frequencies). The results are shown below. Visually, this approach not only smooths the data but adds some structure and context to the raw price chart.

When I first look at a chart I always start with the eyeball test. What struck me in the above analysis was the fractal similarities between the 1835-1860 and 1929-1950 time frames. I then overlaid the 18 year and 42 month IMFs on the price chart from 1850 to present (Bloomberg does not allow dates prior to 1850) to see if this would help me phase these long cycles. This is shown below.

What is interesting is the near perfect phasing the 18 yr IMF produces from 1861 to 1932. After 1932, the measurement of the 18 yr cycle breaks down. Given how EMD measures cycle periods, the average cycle length over the entire time period is not significantly impacted by the 18 yr cycle disappearing for an extended period. (I added what I think is the correct 18 yr cycle length of 212 months at the bottom of the chart). To use William’s words, the 9 and 18 year cycles lack “cohesiveness”, which creates a challenge when doing this type of long term analysis. However, the 42 month cycle keeps time like a Swiss watch. In fact, when these two cycles are in sync from 1861 to 1932, there are exactly five turns of the 42 month cycle for every one of the 18 year cycle. William has also stated a number of times that Hurst made simplifying assumptions regarding cycle synchronicity. This analysis proves it’s close but not perfect. Many of you who have traded are likely nodding your head in agreement.

You are probably thinking “So what? I care about the right edge of the chart and not all the way back into the 1800’s”. I actually think this type of analysis can be helpful if carried forward to the current day. Because you have very good harmonics and agreement between these two cycles earlier in the data set, you can use this to phase the early periods and simply count five turns of the 42 month cycle to phase the more recent 18 year lows. This approach, and the fact I used more data than David, produces a slightly different analysis than what he came up with in his webinar. For example, our EMD analysis shows the lows in 1932 and 2003 are both 18 year lows. BTW, these results are consistent with the long term phasings in both Profit Magic and Christopher Grafton’s book.

The real punch line to all this is the next chart. It pieces together five 18 yr (212 month) cycles into a monster 88.37 year cycle (1060 months). Since there isn’t enough data to prove it with spectrum (227 years of data gives only 2.5 turns of the 88 year cycle), you have to look at this chart and ask yourself, “Can the 88 year cycle be dominant?” Before answering, I suggest you drag a 1060 month cycle ellipse around the chart and see for yourself. My answer is yes, with several caveats. I do not expect a 90% drop in stock prices and a repeat of the Great Depression over the next three years. However, I could envision a very severe drop in stocks over this time period. In addition, shorter cycles, which are not considered in this analysis, could also have a significant impact on the direction and magnitude of upcoming price moves. The good news is we won’t have to wait long to find out. We are exactly 1060 months from the August, 1929 high. Gulp. Even if you don’t believe any of this, we are approaching an 18 year high as David mentioned in the webinar. The last 18 year high produced a 50% drop in the S&P over a comparable time frame (2000-2003). No need to stock up on beef jerky quite yet, but it probably pays to be a little cautious over the next several months.

For those of you who are curious, Google the following:

- 1921 depression (also known as the drive-by depression). 1921+88 years=2009.
- Lunatic Trader 88 year cycle
- Gleissberg cycle. It’s real and it’s been around a very long time.
- Stanley Druckenmiller and the Kitchin cycle.

Curt