我想出来了！我需要在我的百分比更改列表前加上原始值的期间量，以回到原始值。

# Get percent difference
df["ema_10_diff"] = df["mid_price"].pct_change(10 * 60) + 1

# Prepend data with original values of length: period
x = (
        df["mid_price"][: 10 * 60]
        .append(df["ema_10_diff"], ignore_index=True)
    )

# Function to get the cumulative product with period in between.
def cumprod_period(series: pd.Series, period=1) -> pd.Series:
    output = list(series[:period])
    series_length = len(series)
    for i in range(period, series_length):
        current_item = series[i]
        previous_item = output[-period]
        prod = current_item * previous_item

        output.append(prod)

    return pd.Series(output)

# Result is same as df['mid_price']
df["reconstructed_mid_price"] = cumprod_period(x, 10 * 60)

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下面是我写的单元测试，以检查它是否有效：

def test_cumprod_period():
    """Tests if the function works"""
    input = [10, 20, 80, 20, 20, 10]

    period = 2

    # Prepended the first 2 values of the original list to the percentage 
    changed.
    pct_change = pd.Series([10, 20, 8.0, 1.0, 0.25, 0.5])

    output = cumprod_period(pct_change, period)

    assert list(output) == input, f"{list(output)} != {input}"

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