Trend analysis for the S&P 500 and NASDAQ 100 in February 2020

Trend following in stock and index prices has a long and well-established history. I reviewed some of the background in a past article on this topic. For additional examples see this article. As explained in these pieces, trend following is all about separating the low-frequency persistent part of price variability from the high-frequency part, which may be thought of as the ‘noise’ of transient effects. Moving averages are one type of trend-following model. Another approach, which I favor, is Fourier analysis. Fourier methods involve the decomposition of a data series (prices, in this case) into a series of periodic terms (waves). I calculate the trend using the strongest / most significant time scales in the Fourier analysis. This does not mean that there are, in fact, periodic elements in price series. The Fourier analysis simply allows an estimation of the robustness of different times scales.

Fourier trend analysis and 10-month moving average for QQQ (NASDAQ 100)
Fourier trend analysis and 10-month moving average for SPY (S&P 500)

Both the S&P 500 (SPY) and the NASDAQ 100 (QQQ) have had major run-ups in recent months. For both of these, the Fourier model suggests that the upward trend is weakening but remains positive. While the differences in the vertical scales makes it difficult to see, the upward trend for QQQ is stronger than that for SPY. The trend in QQQ is also slightly more statistically significant than that in SPY.

It is notable that recent short-term price declines (moves below the Fourier trend) are larger than price gains above the trend, and this is true for both indexes. In other words, the markets have been disproportionately overreacting to bad news during a prolonged period of gains. This effect is particularly evident at the end of 2018, when the markets had a bit of a panic attack, and to a lesser extent in May 2019. Academic research suggests that this is a common dynamic.

In summary, then, the Fourier trend analysis suggests that there will be more gains in the S&P 500 and NASDAQ 100 indexes in the near term, although the upward trends in both are less robust than a couple of months ago. It will be interesting to see whether the trends continue to weaken, persist at their lower rate, or recover.