import numpy as np
import pandas as pd


def generate_synthetic_sku(
    n_periods: int = 52,
    base_price: float = 10.0,
    base_demand: float = 120.0,
    elasticity: float = -1.5,
    noise_std: float = 0.1,
    seed: int = 42,
) -> pd.DataFrame:
    """
    Generate a single-SKU synthetic price–demand time series.
    Elasticity is constant and known (ground truth).
    """
    rng = np.random.default_rng(seed)

    # price variation around base price
    prices = base_price * (1 + rng.normal(0, 0.15, size=n_periods))
    prices = np.clip(prices, base_price * 0.6, base_price * 1.4)

    # demand model: q = A * p^elasticity * noise
    noise = np.exp(rng.normal(0, noise_std, size=n_periods))
    demand = base_demand * (prices ** elasticity) * noise

    df = pd.DataFrame(
        {
            "t": np.arange(n_periods),
            "price": prices,
            "qty": demand,
        }
    )

    return df