
1. Leading and lagging indicators
Indicators transform past price, volume, or time into summaries. A leading indicator attempts to flag momentum change before trend confirmation, which makes it responsive but prone to false signals. A lagging indicator confirms price action after it occurs, which is slower but often smoother. Classification depends on use: SMA, EMA, and MACD are commonly trend-following; RSI and Stochastic are commonly leading oscillators; Bollinger Bands and ATR describe volatility; Fibonacci is a swing-projection tool rather than a continuously calculated indicator.
2. SMA — lagging
SMAₜ=(Pₜ+…+Pₜ₋ₙ₊₁)÷n. For closes 100, 102, 101, 104, 108, SMA(5)=103. On a new close of 110, discard 100 and obtain 105. Use slope and price location as a trend filter; expect whipsaws in ranges.
3. EMA — lagging but faster than SMA
EMAₜ=αPₜ+(1−α)EMAₜ₋₁, where α=2÷(n+1). For EMA(5), α=.333; prior EMA 103 and close 110 produce about 105.33. Fast/slow crossovers confirm movement after it happens and can repeatedly whipsaw.
4. MACD — lagging momentum/trend
MACD=fast EMA−slow EMA; Signal is an EMA of MACD; Histogram=MACD−Signal. Standard settings commonly use 12, 26, and 9. MACD and EMA crossovers are not independent evidence because they reuse EMA-derived price data.
5. RSI — commonly used as a leading oscillator
RS=average gain÷average loss; RSI=100−100÷(1+RS). If gain=1.2 and loss=.8, RSI=60. Levels 70/30 do not force reversal; trends can remain extreme. Divergence is a warning, not an entry.
6. Stochastic — commonly used as a leading oscillator
%K=100×(Close−Lowest Low)÷(Highest High−Lowest Low); %D smooths %K. With low 90, high 110 and close 106, %K=80. It measures close location within a range, not cheapness or expensiveness.
7. Bollinger Bands — descriptive volatility
Middle=SMA(n); Upper=SMA+kσ; Lower=SMA−kσ. If SMA=100, σ=2 and k=2, bands are 104 and 96. Band touches are not automatic reversal signals; trends can walk a band.
8. ATR — lagging/descriptive volatility
TR=max(H−L, |H−previous close|, |L−previous close|); ATR smooths TR. For H=105, L=100 and previous close=98, TR=7. ATR measures movement size, not direction, and can help normalize buffers or risk.
9. Fibonacci Retracement — projection tool
For an upswing L to H, a retracement level is H−r(H−L). With L=100 and H=120, 38.2%=112.36, 50%=110 and 61.8%=107.64. Fix anchor rules beforehand; a touch is not an entry.
10. Selection workflow
Choose by question: trend, momentum, volatility, or projection. Use one representative per job, specify symbol, timeframe, source, period, closed-bar rule, invalidation, size, and costs, then evaluate out of sample.

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