Information Discreteness [TradingView] [PineScript]

Information Discreteness.pine

// Based on Da, Gurun and Warachka's 2014 paper:
// "Frog in the Pan: Continuous Information and Momentum"
// PDF: https://www3.nd.edu/~zda/Frog.pdf

//@version=5
indicator("Information Discreteness", overlay=false, precision=1, timeframe="D")

LENGTH = input.int(title="Window Length", defval=365, minval=7)
SKIP_RECENT = input.int(title="Skip most recent", defval=30, minval=0)
MA_LENGTH = input.int(title="Average returns over", defval=7, minval=1)

POSITIVE_ID_COLOR = input.color(title="Discrete", defval=#ff0000, group="Colors")
NEGATIVE_ID_COLOR = input.color(title="Continuous", defval=#00ff00, group="Colors")

priceAt(daysAgo) => ta.sma(close[daysAgo], MA_LENGTH)
float recentPrice = priceAt(SKIP_RECENT)
float ancientPrice = priceAt(LENGTH)
float PRET = recentPrice / ancientPrice

int upDays = 0
int downDays = 0
for i = 1 to LENGTH
    delta = close[i-1] - close[i]
    if delta > 0
        upDays += 1
    if delta < 0
        downDays += 1

upDaysPercent = upDays / (upDays + downDays)
downDaysPercent = downDays / (upDays + downDays)

ID = math.sign(PRET) * (downDaysPercent - upDaysPercent)
// -1: continuous
// ...
// +1: discrete

plot(ID, "ID", color=ID > 0 ? POSITIVE_ID_COLOR : NEGATIVE_ID_COLOR, style=plot.style_area)