A reader commented and asked: “Ned Davis Research calculates a time cycle composite. How good is an equal weighting of the annual seasonal cycle, the Presidential term cycle and the decennial cycle at predicting the direction of the market?” To check, we forecast return for a given month by averaging: (1) the average return for the calendar month up through the previous year; (2) the average monthly return for the Presidential term year up through the previous Presidential term; and, (3) the average monthly return for the year of a decade up through the previous decade. Using monthly levels of the Dow Jones Industrial Average (DJIA) since October 1928, the S&P 500 Index since January 1950 and Shiller’s S&P Composite Index since January 1871, all through December 2016, we find that:
The following charts summarize average return by calendar month, average monthly return by Presidential term year and average monthly return by year of the decade for all three datasets. Results across the three samples for calendar year and decade decompositions are not remarkably alike, undermining belief in recurring cycles at annual and decade frequencies. Note that:
- Average monthly returns for the entire samples are 0.55%, 0.70% and 0.44% respectively for the DJIA, the S&P 500 Index and the S&P Composite Index, indicating that market returns may vary considerably over long periods.
- Samples are small for inferring a Presidential term cycle, consisting of only 22, 17 and 36 Presidential terms. The underlying political process offers some non-empirical basis for belief in this cycle.
- Samples are extremely small for inferring a decennial cycle, consisting of only about 9, 7 and 14 decades. Given the variability in the data, these samples are too small to support reliable inference.
Assuming nevertheless that annual seasonal, Presidential term and decennial cycles exist, we proceed using DJIA data as a compromise between sample length and modernity, keeping in mind that an investor operating in real time could know only averages to date. In other words, data used for forecasting should not include any future actual returns.
To test 3-cycle predictive power, we apply the forecasting method specified above to predict DJIA returns by month for January 2001 through December 2016 (192 forecasted months based on at least 867 months of historical data). Forecast granularity must be monthly to exploit an annual seasonal (calendar month) input. For example, to forecast the return for January 2001, we take an average of: (1) average return for January through 2000; (2) average monthly return for Presidential term year one up through 1997; and, (3) average monthly return for the first year of a decade up through 1991. For subsequent months and years, we extend historical data to incorporate additional actual returns as realized.
The next chart shows the three DJIA forecast inputs to be averaged for January 2001 through December 2016. Peaks (Valleys) in calendar month inputs are for December-January (September). Peaks in Presidential term year inputs are for year three. Peaks by year of decade are for xxx5. Next, we average the three inputs to calculate a 3-cycle monthly forecast.
The next chart compares the monthly 3-cycle DJIA forecasted returns for January 2001 through December 2016 to actual DJIA returns. The average forecasted and actual monthly returns are 0.58% and 0.40%, respectively (the 2000s have an historically very low average monthly return). The usefulness of relative highs and lows of the forecast series is not clear from visual inspection.
Unsurprisingly, actual returns are far more volatile than forecasts calculated with averages (respective standard deviations 4.09% and 0.38%). The 3-cycle forecasted return is negative for 14 of 192 months. During those 14 months, the actual return is positive seven times and negative seven times. The 3-cycle forecasted return is positive for 178 of 192 months. During those 178 months, the actual return is positive 107 times and negative 71 times.
For precision in measuring forecasting power, we recast the data as a scatter plot.
The following scatter plot relates actual to forecasted DJIA monthly returns for January 2001 through December 2012. The Pearson correlation for the relationship is 0.03 and the R-squared statistic 0.001, indicating that forecasts explain practically none of the variation in actual results. In other words, the 3-cycle combination is not usefully predictive since the beginning of 2001.
How does accuracy of the 3-cycle forecast compare with those of average monthly return to date and the separate cycle inputs?
The final chart summarizes average monthly forecast errors and standard deviations of monthly forecast errors for five monthly DJIA return forecasting methods:
- Average monthly return to date (all past months).
- Average monthly return to date for the given calendar month (3-cycle input one).
- Average monthly return to date for the given Presidential term year (3-cycle input two).
- Average monthly return to date for the given year of the decade (3-cycle input three).
- Average 3-cycle monthly forecasted return as specified above.
Results indicate that the average monthly return to date is as good as or better than all individual cycle forecasts and the 3-cycle forecast. R-squared statistics for regressions of actual returns versus the five forecast series are, in order, 0.008, 0.005, 0.000, 0.001 and (as above) 0.001. In other words, none of the methods appear to have useful predictive power out-of-sample.
In summary, evidence from simple tests of a forecast that straightforwardly combines calendar month, Presidential term and decennial cycles in stock market behavior does not support belief that these inputs usefully predict stock market returns.
Cautions regarding findings include:
- Other datasets or other methods of combining the three inputs may produce different results.
- As noted, samples are small for analysis of the Presidential term and (especially) decennial cycles.
- The Shiller data uses the average daily close during a month rather than monthly close, thereby introducing some differences in cycle indications (likely dampening monthly differences).
Frequently Asked Questions
What is a 3-cycle stock market forecast combining seasonal, Presidential term and decennial patterns?
A 3-cycle stock market forecast averages three historical return patterns: the average return for the calendar month, for the Presidential term year, and for the year of the decade. Each input uses only data available up to the forecast date. The approach assumes recurring annual, four-year political and ten-year cycles influence market returns, similar in concept to time cycle composites used by some research firms.
Does combining seasonal, Presidential and decennial cycles predict stock market returns?
A 3-cycle forecast combining seasonal, Presidential term and decennial cycles did not usefully predict Dow Jones Industrial Average monthly returns. For 192 forecasted months from January 2001 through December 2016, the correlation between forecast and actual returns was 0.03 and the R-squared was 0.001. The forecasts explained practically none of the variation in actual results.
How do you test whether a 3-cycle forecast predicts monthly stock returns out-of-sample?
The test forecasts each month's DJIA return as the average of three historical averages: the same calendar month, the same Presidential term year, and the same year of the decade, using only data available before that month. Forecasts covered January 2001 through December 2016 (192 months, each based on at least 867 months of history), with the history expanding as actual returns were realized. Forecasts were then compared to actual returns via correlation and R-squared, and against simpler methods such as the average monthly return to date.
Is a 3-cycle forecast better than just using the average historical monthly stock return?
A 3-cycle forecast was not better than simply using the average monthly return to date for the DJIA. The average return to date was as good as or better than each individual cycle forecast and the combined forecast. R-squared values were 0.008 for the average to date, 0.005 for calendar month, 0.000 for Presidential term year, 0.001 for year of decade and 0.001 for the 3-cycle forecast, so none showed useful out-of-sample predictive power.
What are the limitations of testing stock market cycles like the Presidential term and decennial cycle?
Samples for these cycles are small: only 22, 17 and 36 Presidential terms and about 9, 7 and 14 decades across the DJIA, S&P 500 and Shiller datasets, which is too few for reliable inference. Other datasets or other ways of combining the three inputs might produce different results. The Shiller data uses average daily closes within a month rather than monthly closes, which likely dampens monthly differences in cycle indications.