Asymmetric Decay Oscillator
Asymmetric Decay · 4-Year Cycle · Full Projection to 2037

//@version=6 indicator("SMA Division · Decay Model v2 — Asymmetric", overlay=false, max_lines_count=500, max_labels_count=200) // ════════════════════════════════════════════════════════════════════ // INPUTS // ════════════════════════════════════════════════════════════════════ i_fast = input.int(5, "Fast SMA length", minval=1, group="Oscillator") i_slow = input.int(350, "Slow SMA length", minval=1, group="Oscillator") i_env = input.bool(true, "Show asymmetric envelopes", group="Display") i_model = input.bool(true, "Show model oscillator curve", group="Display") i_eq = input.bool(true, "Show equilibrium line", group="Display") i_floor = input.bool(true, "Show historical floor 0.22", group="Display") i_labels = input.bool(true, "Show cycle labels", group="Display") i_zones = input.bool(true, "Show projection zones", group="Display") i_table = input.bool(true, "Show live data table", group="Display") // ════════════════════════════════════════════════════════════════════ // OSCILLATOR CALCULATION // ════════════════════════════════════════════════════════════════════ sma_fast = ta.sma(close, i_fast) sma_slow = ta.sma(close, i_slow) osc = sma_fast / (sma_slow * 2) // ════════════════════════════════════════════════════════════════════ // ASYMMETRIC DAMPENED OSCILLATION MODEL // // TOPS: E_top(t) = μ + A_top · exp(−λ_top · Δt) // BOTTOMS: E_bot(t) = μ − A_bot · exp(−λ_bot · Δt) // CURVE: f(t) = μ + A_eff(t) · cos(ω · Δt) // // Key insight: λ_top = 3.98 × λ_bot (asymmetric decay) // This means tops compress 4x faster than bottoms rise // ════════════════════════════════════════════════════════════════════ // Parameters (calibrated from MSE fit to all 4 confirmed cycle tops & 4 bottoms) mu = 0.380 // Long-run equilibrium A_top = 0.5000 // Top envelope initial amplitude lam1 = 0.0690 // Top linear decay constant lam2 = 0.00240 // Top quadratic decay acceleration A_bot = 0.1610 // Bottom envelope initial amplitude lam_bot = 0.0242 // Bottom decay constant (per year) T = 4.0 // Cycle period (years) omega = 2 * math.pi / T // Angular frequency = 1.5708 rad/yr t0 = 2013.875 // Epoch: Nov 2013 (first confirmed major top) alpha = -0.46 // Phase-skew time warping (asymmetric rise/fall) // Current time in decimal years bar_yr = year(time) + (month(time) - 1) / 12.0 + (dayofmonth(time) - 1) / 365.25 dt = bar_yr - t0 // Envelope values (Continuous Quadratic Decay for Tops) e_top = mu + A_top * math.exp(-lam1 * dt - lam2 * math.pow(dt, 2)) e_bot = mu - A_bot * math.exp(-lam_bot * dt) e_top_adj = e_top // Fully integrated into e_top, no separate miss factor needed! // Effective amplitude for smooth oscillator curve (geometric blend) A_eff = 0.5 * (A_top * math.exp(-lam1 * dt - lam2 * math.pow(dt, 2)) + A_bot * math.exp(-lam_bot * dt)) mid_shift = 0.5 * (A_top * math.exp(-lam1 * dt - lam2 * math.pow(dt, 2)) - A_bot * math.exp(-lam_bot * dt)) // Skewed Phase Harmonics (Time Warping for Escalator Up, Elevator Down) phase = omega * dt - alpha * math.cos(omega * dt) model_v = mu + mid_shift + A_eff * math.cos(phase) miss = 0.0 // Deprecated in V2 // ════════════════════════════════════════════════════════════════════ // COLORS // ════════════════════════════════════════════════════════════════════ c_gold = color.new(#e8b84b, 0) c_cyan = color.new(#00e5cc, 0) c_blue = color.new(#3d8ef8, 0) c_green = color.new(#39d98a, 0) c_red = color.new(#ff4d6d, 0) c_purple = color.new(#b57bee, 0) c_ghost = color.new(#3d5570, 0) c_mist = color.new(#7a9bb5, 40) // ════════════════════════════════════════════════════════════════════ // PLOTS // ════════════════════════════════════════════════════════════════════ // Live oscillator (color-coded: above/below equilibrium) osc_col = osc > e_top_adj ? color.new(c_gold, 10) : osc < e_bot ? color.new(c_green, 10) : osc > mu ? color.new(c_cyan, 20) : color.new(c_blue, 30) plot(osc, "SMA Division", color=osc_col, linewidth=2, title="Oscillator") // Equilibrium line plot(i_eq ? mu : na, "Equilibrium μ", color=color.new(c_green, 40), linewidth=1, style=plot.style_line) // Historical floor plot(i_floor ? 0.22 : na, "Hist. Floor", color=color.new(c_red, 55), linewidth=1, style=plot.style_line) // Decay envelopes (asymmetric) p_top = plot(i_env ? e_top : na, "Upper envelope", color=color.new(c_gold, 25), linewidth=1.5, style=plot.style_line) p_adj = plot(i_env ? e_top_adj : na, "Adj. upper (miss)", color=color.new(c_gold, 55), linewidth=1, style=plot.style_line, linestyle=plot.style_dotted) p_bot = plot(i_env ? e_bot : na, "Lower envelope", color=color.new(c_green, 25), linewidth=1.5, style=plot.style_line) fill(p_top, p_bot, color=color.new(c_gold, 93), title="Envelope fill") // Model oscillator curve plot(i_model ? model_v : na, "Model curve", color=color.new(c_ghost, 0), linewidth=1, style=plot.style_line, linestyle=plot.style_dashed) // ════════════════════════════════════════════════════════════════════ // HORIZONTAL REFERENCE LINES // ════════════════════════════════════════════════════════════════════ hline(0.380, "Equilibrium", color=color.new(#39d98a, 50), linestyle=hline.style_dashed, linewidth=1) hline(0.220, "Hist. Floor", color=color.new(#ff4d6d, 60), linestyle=hline.style_dotted, linewidth=1) hline(0.265, "Proj. Bot Low", color=color.new(#3d8ef8, 70), linestyle=hline.style_dotted, linewidth=1) hline(0.295, "Proj. Bot Hi", color=color.new(#3d8ef8, 70), linestyle=hline.style_dotted, linewidth=1) // ════════════════════════════════════════════════════════════════════ // PROJECTION ZONES (future shading) // ════════════════════════════════════════════════════════════════════ // Bottom zone: Aug–Dec 2026 (0.265–0.295) in_bot_zone = i_zones and bar_yr >= 2026.55 and bar_yr <= 2027.0 bgcolor(in_bot_zone ? color.new(c_blue, 88) : na, title="Proj. bottom zone") // Top zone: Jul–Dec 2029 (0.460–0.490) in_top_zone = i_zones and bar_yr >= 2029.5 and bar_yr <= 2030.0 bgcolor(in_top_zone ? color.new(c_cyan, 88) : na, title="Proj. top zone") // Next bottom zone bands plot(i_zones and bar_yr >= 2026.3 ? 0.295 : na, "Proj bot upper", color=color.new(c_blue, 45), linewidth=1, style=plot.style_line) plot(i_zones and bar_yr >= 2026.3 ? 0.265 : na, "Proj bot lower", color=color.new(c_blue, 45), linewidth=1, style=plot.style_line) // Next top zone bands plot(i_zones and bar_yr >= 2028.5 ? 0.490 : na, "Proj top upper", color=color.new(c_cyan, 45), linewidth=1, style=plot.style_line) plot(i_zones and bar_yr >= 2028.5 ? 0.460 : na, "Proj top lower", color=color.new(c_cyan, 45), linewidth=1, style=plot.style_line) // ════════════════════════════════════════════════════════════════════ // CYCLE LABELS — Historical events // ════════════════════════════════════════════════════════════════════ lbg = color.new(#05070a, 10) if i_labels // Structural major tops (4-yr cycle) if year(time)==2013 and month(time)==11 and dayofmonth(time)<=7 label.new(bar_index, 0.900, "▲ C1 TOP\nNov 2013\n0.880", style=label.style_label_down, color=lbg, textcolor=c_gold, size=size.small) if year(time)==2017 and month(time)==12 and dayofmonth(time)<=7 label.new(bar_index, 0.770, "▲ C2 TOP\nDec 2017\n0.750", style=label.style_label_down, color=lbg, textcolor=c_gold, size=size.small) if year(time)==2021 and month(time)==11 and dayofmonth(time)<=7 label.new(bar_index, 0.640, "▲ C3 TOP\nNov 2021\n0.620 (−0.028)", style=label.style_label_down, color=lbg, textcolor=color.new(c_gold, 20), size=size.small) if year(time)==2025 and month(time)==10 and dayofmonth(time)<=7 label.new(bar_index, 0.560, "▲ C4 TOP\nOct 2025\n0.540 (−0.052)", style=label.style_label_down, color=lbg, textcolor=color.new(c_gold, 35), size=size.small) // Local sub-peaks if year(time)==2013 and month(time)==4 and dayofmonth(time)<=7 label.new(bar_index, 0.970, "◆ Sub-peak\nApr 2013 · 0.950", style=label.style_label_down, color=lbg, textcolor=c_mist, size=size.tiny) if year(time)==2021 and month(time)==2 and dayofmonth(time)<=7 label.new(bar_index, 0.680, "◆ Local top\nFeb 2021 · 0.660", style=label.style_label_down, color=lbg, textcolor=c_mist, size=size.tiny) if year(time)==2024 and month(time)==3 and dayofmonth(time)<=7 label.new(bar_index, 0.588, "◆ Local top\nMar 2024 · 0.570", style=label.style_label_down, color=lbg, textcolor=c_mist, size=size.tiny) // Major bottoms if year(time)==2011 and month(time)==11 and dayofmonth(time)<=7 label.new(bar_index, 0.196, "▼ C0 BOT\nNov 2011 · 0.220", style=label.style_label_up, color=lbg, textcolor=c_green, size=size.small) if year(time)==2015 and month(time)==1 and dayofmonth(time)<=7 label.new(bar_index, 0.196, "▼ C1 BOT\nJan 2015 · 0.220", style=label.style_label_up, color=lbg, textcolor=c_green, size=size.small) if year(time)==2018 and month(time)==12 and dayofmonth(time)<=7 label.new(bar_index, 0.196, "▼ C2 BOT\nDec 2018 · 0.220", style=label.style_label_up, color=lbg, textcolor=c_green, size=size.small) if year(time)==2022 and month(time)==7 and dayofmonth(time)<=7 label.new(bar_index, 0.236, "▼ C3 BOT\nJul 2022 · 0.260", style=label.style_label_up, color=lbg, textcolor=color.new(c_green, 25), size=size.small) // Projected events if year(time)==2026 and month(time)==10 and dayofmonth(time)<=7 label.new(bar_index, 0.240, "⟶ PROJ C4 BOT\nOct 2026\n0.265–0.295", style=label.style_label_up, color=color.new(#0a1830, 0), textcolor=c_blue, size=size.normal) if year(time)==2029 and month(time)==10 and dayofmonth(time)<=7 label.new(bar_index, 0.500, "⟶ PROJ C5 TOP\nOct 2029\n0.460–0.490", style=label.style_label_down, color=color.new(#0a1830, 0), textcolor=c_cyan, size=size.normal) if year(time)==2030 and month(time)==10 and dayofmonth(time)<=7 label.new(bar_index, 0.265, "⟶ PROJ C5 BOT\nOct 2030 · ~0.290", style=label.style_label_up, color=color.new(#0a1830, 0), textcolor=c_blue, size=size.small) if year(time)==2033 and month(time)==10 and dayofmonth(time)<=7 label.new(bar_index, 0.468, "⟶ PROJ C6 TOP\nOct 2033 · ~0.440", style=label.style_label_down, color=color.new(#0a1830, 0), textcolor=color.new(c_cyan, 30), size=size.small) // ════════════════════════════════════════════════════════════════════ // LIVE DATA TABLE (top-right) // ════════════════════════════════════════════════════════════════════ var table T = table.new(position.top_right, 2, 12, bgcolor=color.new(#050709, 5), border_width=1, border_color=color.new(#1a2d42, 0), frame_width=1, frame_color=color.new(#1a2d42, 0)) if barstate.islast and i_table // Header table.cell(T,0,0,"DECAY MODEL", text_color=c_gold, text_size=size.tiny, bgcolor=color.new(#0d1520,0)) table.cell(T,1,0,"VALUE", text_color=c_gold, text_size=size.tiny, bgcolor=color.new(#0d1520,0)) // Oscillator table.cell(T,0,1,"Oscillator", text_color=c_mist, text_size=size.tiny) table.cell(T,1,1,str.tostring(osc,"#.####"), text_color=c_cyan, text_size=size.tiny) // Model table.cell(T,0,2,"Model f(t)", text_color=c_mist, text_size=size.tiny) table.cell(T,1,2,str.tostring(model_v,"#.####"), text_color=color.new(#7a9bb5,0), text_size=size.tiny) // Upper envelope (raw) table.cell(T,0,3,"E_top", text_color=c_mist, text_size=size.tiny) table.cell(T,1,3,str.tostring(e_top,"#.####"), text_color=c_gold, text_size=size.tiny) // Upper envelope (adj) table.cell(T,0,4,"E_top adj", text_color=c_mist, text_size=size.tiny) table.cell(T,1,4,str.tostring(e_top_adj,"#.####"), text_color=color.new(c_gold,40), text_size=size.tiny) // Lower envelope table.cell(T,0,5,"E_bot", text_color=c_mist, text_size=size.tiny) table.cell(T,1,5,str.tostring(e_bot,"#.####"), text_color=c_green, text_size=size.tiny) // Equilibrium table.cell(T,0,6,"Equil. μ", text_color=c_mist, text_size=size.tiny) table.cell(T,1,6,"0.380", text_color=c_cyan, text_size=size.tiny) // Amplitude table.cell(T,0,7,"A_eff(t)", text_color=c_mist, text_size=size.tiny) table.cell(T,1,7,str.tostring(A_eff,"#.####"), text_color=c_purple, text_size=size.tiny) // Miss factor table.cell(T,0,8,"Miss factor", text_color=c_mist, text_size=size.tiny) table.cell(T,1,8,str.tostring(miss,"#.####"), text_color=miss<0?c_red:c_green, text_size=size.tiny) // Dist to equilibrium d_eq = osc - mu table.cell(T,0,9,"Δ to μ", text_color=c_mist, text_size=size.tiny) table.cell(T,1,9,str.tostring(d_eq,"#.####"), text_color=d_eq>0?c_gold:c_blue, text_size=size.tiny) // Cycle phase phase_rad = math.mod(omega*dt, 2*math.pi) phase_pct = phase_rad / (2*math.pi) * 100 table.cell(T,0,10,"Cycle phase", text_color=c_mist, text_size=size.tiny) table.cell(T,1,10,str.tostring(phase_pct,"#.#")+"%", text_color=c_purple, text_size=size.tiny) // Year table.cell(T,0,11,"Bar year", text_color=c_mist, text_size=size.tiny) table.cell(T,1,11,str.tostring(bar_yr,"####.###"), text_color=color.new(#7a9bb5,0), text_size=size.tiny)