!pip install numpy pandas matplotlib seaborn scipy yfinance --quiet

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats, optimize
import warnings

warnings.filterwarnings('ignore')
%matplotlib inline
plt.rcParams['figure.figsize'] = (14, 5)
plt.rcParams['axes.spines.top'] = False
plt.rcParams['axes.spines.right'] = False
print('Imports ready.')

# ── Data Source Toggle ─────────────────────────────
USE_LIVE_DATA = False
TICKERS       = ['BTC-USD','ETH-USD','SOL-USD','BNB-USD']
START_DATE    = '2020-01-01'
END_DATE      = '2024-12-31'
# ──────────────────────────────────────────────────
ASSETS          = ['BTC','ETH','SOL','BNB']
SIGNAL_LOOKBACK = 7    # days of past return used as signal
MAX_HORIZON     = 30   # maximum forward horizon to test
MIN_OBS         = 50   # minimum observations to compute IC
print('Config ready.')

if USE_LIVE_DATA:
    import yfinance as yf
    prices = yf.download(TICKERS, start=START_DATE, end=END_DATE)['Close']
    prices.columns = ASSETS
    prices.dropna(inplace=True)
    returns = prices.pct_change().dropna()
    print(f'Live data: {len(returns)} days')
else:
    rng  = np.random.default_rng(42)
    n    = 1200
    vols = np.array([0.65, 0.75, 1.20, 0.70]) / np.sqrt(252)
    # AR(1) process per asset to create decaying autocorrelation
    ar_coef = np.array([0.12, 0.10, 0.08, 0.11])
    data = np.zeros((n, 4))
    for t in range(1, n):
        data[t] = ar_coef * data[t-1] + rng.standard_normal(4) * vols
    idx = pd.date_range('2020-01-01', periods=n, freq='B')
    returns = pd.DataFrame(data, columns=ASSETS, index=idx)
    print(f'Synthetic AR(1) data: {n} days, AR coef = {ar_coef}')

def compute_ic_at_horizon(returns: pd.DataFrame, signal_lookback: int, horizon: int) -> float:
    """
    Compute the mean cross-sectional Spearman IC between signal and h-day forward return.

    Parameters
    ----------
    returns        : pd.DataFrame  Daily returns for each asset.
    signal_lookback: int           Lookback window for the signal.
    horizon        : int           Forward horizon in days.

    Returns
    -------
    float  Mean rank IC across assets.
    """
    signal  = returns.rolling(signal_lookback).mean()  # avg past return as signal
    forward = returns.rolling(horizon).mean().shift(-horizon)
    daily_ics = []
    for date in returns.index[signal_lookback + horizon:-horizon]:
        s = signal.loc[date]
        f = forward.loc[date]
        valid = s.notna() & f.notna()
        if valid.sum() >= 2:
            ic, _ = stats.spearmanr(s[valid], f[valid])
            daily_ics.append(ic)
    return np.nanmean(daily_ics) if daily_ics else 0.0


horizons = list(range(1, MAX_HORIZON + 1))
ic_values = [compute_ic_at_horizon(returns, SIGNAL_LOOKBACK, h) for h in horizons]
decay_df = pd.DataFrame({'horizon': horizons, 'ic': ic_values})
print(decay_df.to_string(index=False))

def exp_decay(h, ic0, lam):
    """Exponential decay: IC(h) = IC_0 * exp(-lambda * h)."""
    return ic0 * np.exp(-lam * h)


try:
    popt, pcov = optimize.curve_fit(exp_decay, horizons, ic_values,
                                     p0=[ic_values[0], 0.1], maxfev=5000)
    ic0_fit, lam_fit = popt
    half_life = np.log(2) / lam_fit
    ic_fitted = [exp_decay(h, ic0_fit, lam_fit) for h in horizons]
    print(f'Exponential fit: IC_0 = {ic0_fit:.4f}, λ = {lam_fit:.4f}')
    print(f'Signal half-life: {half_life:.1f} days')
    print(f'Optimal holding period (IC > 0.02): ~{next((h for h,ic in zip(horizons,ic_fitted) if abs(ic)<0.02), MAX_HORIZON)} days')
except Exception as e:
    ic_fitted = [0] * len(horizons)
    print(f'Fit failed: {e}')

fig, axes = plt.subplots(1, 2, figsize=(14, 5))
fig.suptitle('Signal Decay Analysis', fontsize=13, fontweight='bold')

ax1 = axes[0]
ax1.bar(horizons, ic_values, color='#1976d2', alpha=0.6, label='Observed IC')
ax1.plot(horizons, ic_fitted, color='#e53935', lw=2,
          label=f'Exp fit (half-life={half_life:.1f}d)' if max(ic_fitted) > 0 else 'Fit')
ax1.axhline(0, color='black', lw=0.8, ls='--')
ax1.axhline(0.02, color='green', lw=0.8, ls=':', label='IC = 0.02 threshold')
ax1.set_xlabel('Forward Horizon (days)')
ax1.set_ylabel('Rank IC (Spearman)')
ax1.legend(fontsize=8)
ax1.set_title(f'Signal Decay Curve (lookback={SIGNAL_LOOKBACK}d)')

ax2 = axes[1]
cumulative_ic = np.cumsum(ic_values)
ax2.plot(horizons, cumulative_ic, color='#43a047', lw=2)
ax2.fill_between(horizons, cumulative_ic, alpha=0.15, color='#43a047')
ax2.set_xlabel('Forward Horizon (days)')
ax2.set_ylabel('Cumulative IC')
ax2.set_title('Cumulative Predictive Power vs Holding Period')

plt.tight_layout(); plt.show()

decay_df['ic_fitted'] = ic_fitted
decay_df.to_csv('signal_decay_analysis.csv', index=False)
print('Saved: signal_decay_analysis.csv')