def analytics_kernel(econ, logistics, energy, sentiment, lag):
    projected_price = (
        econ["price_index"]
        * (1 + (1 - sentiment["market_confidence"]) * 0.1)
    )

    return {
        "lag_days": lag,
        "projected_price": round(projected_price, 2),
        "volatility": round(0.02 * lag, 3)
    }