Trend-Spotting In The Markets by Rick Martinelli
Identifying the beginning and end of trends is a challenge that many traders face. This technique will help you determine when a trend begins and when it ends.
Most stock market data can be thought of as combinations of trends of various lengths and directions, and cycles of various frequencies and durations. As a result, many techniques have been developed to discern when a particular stock is trending or cycling. Let me describe a simple approach to trend-spotting that is based on the idea that correlations in price differences translate into trends in prices.
TRENDS AND CYCLES
Consider exactly what constitutes a trend at the smallest level. If we assume the minimum number of consecutive prices required to spot a trend is three, there are four possible arrangements of three prices, as shown in Figure 1. In case A, prices show two successive increases and are in a short uptrend, a microtrend upward. Case B shows two successive decreases, so it is a downward microtrend. Cases C and D show no trend, but instead are interpreted as small portions of cycles, or microcycles.
If values P1, P2, and P3 are assigned to the three consecutive prices, then in the first case, P2 > P1 and P3 > P2, while in the third case P2 > P1 but P3 < P2.
Similarly, the other two cases may be characterized by their corresponding price inequalities. But all of this information may be summarized instead by considering the price increments D1 = P2–P1 and D2 = P3–P2. Then for the first two trend cases, we see the product as D1*D2 > 0, while for the cycle cases D1*D2 < 0 — that is, the product of increments is positive for a trend! In addition, the value of the product gives a rough indication of the amount of price movement in the three points, the intensity of the microtrend.
TRENDS AND CORRELATIONS
Now consider a series of daily stock prices represented by x(k) for k = 1 to N, where N is the total number of days. Its series of price changes, known as its increment series, is
z(k) = x(k) – x(k-1)
Next, define a new series a(k) as the product of consecutive increments — that is,
a(k) = z(k) z(k-1)