使用 pandas 的擴展視窗函式

Manipulating Time Series Data in Python

Stefan Jansen

Founder & Lead Data Scientist at Applied Artificial Intelligence

pandas 的擴展視窗

從滾動視窗到擴展視窗
計算截至當日的期間指標
新的時間序列涵蓋所有歷史值
用於累積報酬、累積最小/最大
在 pandas 有兩種作法：
- .expanding() —— 類似 .rolling()
- .cumsum()、.cumprod()、cummin()/max()

基本概念

df = pd.DataFrame({'data': range(5)})

df['expanding sum'] = df.data.expanding().sum()

df['cumulative sum'] = df.data.cumsum()

df

   data  expanding sum  cumulative sum
0     0            0.0               0
1     1            1.0               1
2     2            3.0               3
3     3            6.0               6
4     4           10.0              10

取得 S&P 500 資料

data = pd.read_csv('sp500.csv', parse_dates=['date'], index_col='date')

DatetimeIndex: 2519 entries, 2007-05-24 to 2017-05-24
Data columns (total 1 columns):
SP500    2519 non-null float64

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如何計算累積報酬

單期報酬 $r_t$：現價除以上期價格再減 1：

$$r_t = \frac{P_t}{P_{t-1}} - 1$$
- 多期報酬：所有期間的 $(1 + r_t)$ 連乘，再減 1：
$$R_T = (1 + r_1)(1 + r_2)...(1 + r_T) - 1$$
- 計算單期報酬：.pct_change()
- 基本運算：.add()、.sub()、.mul()、.div()
- 累積乘積：.cumprod()

累積報酬：實作

pr = data.SP500.pct_change() # period return

pr_plus_one = pr.add(1)

cumulative_return = pr_plus_one.cumprod().sub(1)

cumulative_return.mul(100).plot()

ch3_2_v2 - Expanding Window Functions with Pandas.021.png

取得累積最小與最大值

data['running_min'] = data.SP500.expanding().min()

data['running_max'] = data.SP500.expanding().max()

data.plot()

ch3_2_v2 - Expanding Window Functions with Pandas.023.png

滾動年度報酬率

def multi_period_return(period_returns):
    return np.prod(period_returns + 1) - 1

pr = data.SP500.pct_change() # period return

r = pr.rolling('360D').apply(multi_period_return)

data['Rolling 1yr Return'] = r.mul(100)

data.plot(subplots=True)

滾動年度報酬率

data['Rolling 1yr Return'] = r.mul(100)

data.plot(subplots=True)

ch3_2_v2 - Expanding Window Functions with Pandas.027.png

一起來練習吧！

Manipulating Time Series Data in Python