// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Chande Forecast Oscillator (CFO)", "CFO", overlay=false)

//@function Chande Forecast Oscillator - measures percentage difference between price and forecasted price
//@param source Price data to analyze
//@param period Number of bars for linear regression calculation
//@returns Oscillator value showing forecast error percentage
//@optimized O(1) complexity using incremental sumXY maintenance
cfo(series float source, simple int period) =>
    if period <= 0
        runtime.error("Period must be greater than 0")
    if period > 5000
        runtime.error("Period exceeds maximum of 5000")
    
    var int count = 0
    var int head = 0
    var float sumY = 0.0
    var float sumXY = 0.0
    var array<float> buffer = array.new_float(period, na)
    
    if na(source)
        na
    else
        float oldest = array.get(buffer, head)
        if not na(oldest)
            sumY -= oldest
            sumXY -= sumY
            sumXY += (period - 1) * source
        else
            sumXY += count * source
            count += 1
        
        sumY += source
        array.set(buffer, head, source)
        head := (head + 1) % period
        
        if count < period
            na
        else
            float sumX = period * (period - 1) / 2
            float sumX2 = period * (period - 1) * (2 * period - 1) / 6
            float denomX = period * sumX2 - sumX * sumX
            
            float slope = (period * sumXY - sumX * sumY) / denomX
            float intercept = (sumY - slope * sumX) / period
            float tsf = intercept + slope * (period - 1)
            
            float result = source == 0.0 ? na : 100.0 * (source - tsf) / source
            result

// ---------- Main loop ----------

i_period = input.int(14, "Period", minval=1, maxval=5000)
i_source = input.source(close, "Source")

result = cfo(i_source, i_period)

plot(result, "CFO", color=color.yellow, linewidth=2)
hline(0, "Zero Line", color=color.gray, linestyle=hline.style_dotted)