Double Moving Average

Formula

$$\begin{array}{rl}{S}_{1,t}& =\text{SMA of }X\\ S_{2,t}& =\text{SMA of }{S}_1\\ F_{t+h}& =A_t+h{B}_t\\ A_t& =2S_{1,t}-S_{2,t}\\ B_t& =\frac{2}{m-1}(S_{1,t}-S_{2,t})\end{array}$$

from dataclasses import dataclass
 
 
@dataclass
class DMAResult:
    t: int
    A: float
    B: float
    forecast: float
 
 
def _sma(x: list[float], m: int) -> list[float]:
    return [sum(x[i:i+m]) / m for i in range(len(x) - m + 1)]
 
 
def double_moving_average(x: list[float], m: int, h: int) -> list[DMAResult]:
    S1 = _sma(x, m)
    S2 = _sma(S1, m)
 
    offset_S1 = m - 1
    offset_S2 = 2 * m - 2
 
    results: list[DMAResult] = []
    for t in range(offset_S2, len(x)):
        s1 = S1[t - offset_S1]
        s2 = S2[t - offset_S2]
        A = 2 * s1 - s2
        B = (2 / (m - 1)) * (s1 - s2)
        results.append(DMAResult(t=t, A=A, B=B, forecast=A + h * B))
 
    return results

Tip

SMA process performed twice. Suitable for data with trends.