From a259a6abd336d5958686298abab372091ce825ee Mon Sep 17 00:00:00 2001 From: jackfrued Date: Tue, 11 Jan 2022 17:12:41 +0800 Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0=E4=BA=86=E6=97=A5=E5=BF=97?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ...\347\232\204\345\272\224\347\224\250-5.md" | 433 ++++++++++++++++++ res/ABF827024EA535099DC0E6A66A336C51.png | Bin 0 -> 1585662 bytes ...64\346\226\260\346\227\245\345\277\227.md" | 6 + 3 files changed, 439 insertions(+) create mode 100644 "Day66-80/09.Pandas\347\232\204\345\272\224\347\224\250-5.md" create mode 100644 res/ABF827024EA535099DC0E6A66A336C51.png diff --git "a/Day66-80/09.Pandas\347\232\204\345\272\224\347\224\250-5.md" "b/Day66-80/09.Pandas\347\232\204\345\272\224\347\224\250-5.md" new file mode 100644 index 0000000..3864ed7 --- /dev/null +++ "b/Day66-80/09.Pandas\347\232\204\345\272\224\347\224\250-5.md" @@ -0,0 +1,433 @@ +## Pandas的应用-5 + +### DataFrame的应用 + +#### 窗口计算 + +`DataFrame`对象的`rolling`方法允许我们将数据置于窗口中,然后就可以使用函数对窗口中的数据进行运算和处理。例如,我们获取了某只股票近期的数据,想制作5日均线和10日均线,那么就需要先设置窗口再进行运算。我们可以使用三方库`pandas-datareader`来获取指定的股票在某个时间段内的数据,具体的操作如下所示。 + +安装`pandas-datareader`三方库。 + +```Bash +pip install pandas-datareader +``` + +通过`pandas-datareader` 提供的`get_data_stooq`从 Stooq 网站获取百度(股票代码:BIDU)近期股票数据。 + +```Python +import pandas_datareader as pdr + +baidu_df = pdr.get_data_stooq('BIDU', start='2021-11-22', end='2021-12-7') +baidu_df.sort_index(inplace=True) +baidu_df +``` + +输出: + + + +上面的`DataFrame`有`Open`、`High`、`Low`、`Close`、`Volume`五个列,分别代表股票的开盘价、最高价、最低价、收盘价和成交量,接下来我们对百度的股票数据进行窗口计算。 + +```Python +baidu_df.rolling(5).mean() +``` + +输出: + + + +上面的`Close` 列的数据就是我们需要的5日均线,当然,我们也可以用下面的方法,直接在`Close`列对应的`Series`对象上计算5日均线。 + +```Python +baidu_df.Close.rolling(5).mean() +``` + +输出: + +``` +Date +2021-11-22 NaN +2021-11-23 NaN +2021-11-24 NaN +2021-11-26 NaN +2021-11-29 150.608 +2021-11-30 151.014 +2021-12-01 150.682 +2021-12-02 150.196 +2021-12-03 147.062 +2021-12-06 146.534 +2021-12-07 146.544 +Name: Close, dtype: float64 +``` + +#### 相关性判定 + +在统计学中,我们通常使用协方差(covariance)来衡量两个随机变量的联合变化程度。如果变量 $X$ 的较大值主要与另一个变量 $Y$ 的较大值相对应,而两者较小值也相对应,那么两个变量倾向于表现出相似的行为,协方差为正。如果一个变量的较大值主要对应于另一个变量的较小值,则两个变量倾向于表现出相反的行为,协方差为负。简单的说,协方差的正负号显示着两个变量的相关性。方差是协方差的一种特殊情况,即变量与自身的协方差。 + +$$ +cov(X,Y) = E((X - \mu)(Y - \upsilon)) = E(X \cdot Y) - \mu\upsilon +$$ + +如果 $X$ 和 $Y$ 是统计独立的,那么二者的协方差为0,这是因为在 $X$ 和 $Y$ 独立的情况下: + +$$ +E(X \cdot Y) = E(X) \cdot E(Y) = \mu\upsilon +$$ + +协方差的数值大小取决于变量的大小,通常是不容易解释的,但是正态形式的协方差可以显示两变量线性关系的强弱。在统计学中,皮尔逊积矩相关系数就是正态形式的协方差,它用于度量两个变量 $X$ 和 $Y$ 之间的相关程度(线性相关),其值介于`-1`到`1`之间。 + +$$ +\rho{X,Y} = \frac {cov(X, Y)} {\sigma_{X}\sigma_{Y}} +$$ + +估算样本的协方差和标准差,可以得到样本皮尔逊系数,通常用希腊字母 $\rho$ 表示。 + +$$ +\rho = \frac {\sum_{i=1}^{n}(X_i - \bar{X})(Y_i - \bar{Y})} {\sqrt{\sum_{i=1}^{n}(X_i - \bar{X})^2} \sqrt{\sum_{i=1}^{n}(Y_i - \bar{Y})^2}} +$$ + +我们用 $\rho$ 值判断指标的相关性时遵循以下两个步骤。 + +1. 判断指标间是正相关、负相关,还是不相关。 + - 当 $ \rho \gt 0 $,认为变量之间是正相关,也就是两者的趋势一致。 + - 当 $ \rho \lt 0 $,认为变量之间是负相关,也就是两者的趋势相反。 + - 当 $ \rho = 0 $,认为变量之间是不相关的,但并不代表两个指标是统计独立的。 +2. 判断指标间的相关程度。 + - 当 $ \rho $ 的绝对值在 $ [0.6,1] $ 之间,认为变量之间是强相关的。 + - 当 $ \rho $ 的绝对值在 $ [0.1,0.6) $ 之间,认为变量之间是弱相关的。 + - 当 $ \rho $ 的绝对值在 $ [0,0.1) $ 之间,认为变量之间没有相关性。 + +皮尔逊相关系数适用于: + + 1. 两个变量之间是线性关系,都是连续数据。 + 2. 两个变量的总体是正态分布,或接近正态的单峰分布。 + 3. 两个变量的观测值是成对的,每对观测值之间相互独立。 + +`DataFrame`对象的`cov`方法和`corr`方法分别用于计算协方差和相关系数,`corr`方法的第一个参数`method`的默认值是`pearson`,表示计算皮尔逊相关系数;除此之外,还可以指定`kendall`或`spearman`来获得肯德尔系数或斯皮尔曼等级相关系数。 + +接下来,我们从名为`boston_house_price.csv`的文件中获取著名的[波士顿房价数据集](https://www.heywhale.com/mw/dataset/590bd595812ede32b73f55f2)来创建一个`DataFrame`,我们通过`corr`方法计算可能影响房价的`13`个因素中,哪些跟房价是正相关或负相关的,代码如下所示。 + +```Python +boston_df = pd.read_csv('data/csv/boston_house_price.csv') +boston_df.corr() +``` + +> **说明**:如果需要上面例子中的 CSV 文件,可以通过下面的百度云盘地址进行获取,数据在《从零开始学数据分析》目录中。链接:,提取码:e7b4。 + +输出: + + + +斯皮尔曼相关系数对数据条件的要求没有皮尔逊相关系数严格,只要两个变量的观测值是成对的等级评定资料,或者是由连续变量观测资料转化得到的等级资料,不论两个变量的总体分布形态、样本容量的大小如何,都可以用斯皮尔曼等级相关系数来进行研究。我们通过下面的方式来计算斯皮尔曼相关系数。 + +```Python +boston_df.corr('spearman') +``` + + 输出: + + + +在 Notebook 或 JupyterLab 中,我们可以为`PRICE`列添加渐变色,用颜色直观的展示出跟房价负相关、正相关、不相关的列,`DataFrame`对象`style`属性的`background_gradient`方法可以完成这个操作,代码如下所示。 + +```Python +boston_df.corr('spearman').style.background_gradient('RdYlBu', subset=['PRICE']) +``` + + + +上面代码中的`RdYlBu`代表的颜色如下所示,相关系数的数据值越接近`1`,颜色越接近红色;数据值越接近`1`,颜色越接近蓝色;数据值在`0`附件则是黄色。 + +```Python +plt.get_cmap('RdYlBu') +``` + + + +### Index的应用 + +我们再来看看`Index`类型,它为`Series`和`DataFrame`对象提供了索引服务,常用的`Index`有以下几种,我们直接上代码。 + +1. 范围索引(`RangeIndex`) + +代码: + +```Python +sales_data = np.random.randint(400, 1000, 12) +month_index = pd.RangeIndex(1, 13, name='月份') +ser = pd.Series(data=sales_data, index=month_index) +ser +``` + +输出: + +``` +月份 +1 703 +2 705 +3 557 +4 943 +5 961 +6 615 +7 788 +8 985 +9 921 +10 951 +11 874 +12 609 +dtype: int64 +``` + +2. 分类索引(`CategoricalIndex`) + +代码: + +```Python +cate_index = pd.CategoricalIndex( + ['苹果', '香蕉', '苹果', '苹果', '桃子', '香蕉'], + ordered=True, + categories=['苹果', '香蕉', '桃子'] +) +ser = pd.Series(data=amount, index=cate_index) +ser +``` + +输出: + +``` +苹果 6 +香蕉 6 +苹果 7 +苹果 6 +桃子 8 +香蕉 6 +dtype: int64 +``` + +基于索引分组数据,然后使用`sum`进行求和。 + +```Python +ser.groupby(level=0).sum() +``` + +输出: + +``` +苹果 19 +香蕉 12 +桃子 8 +dtype: int64 +``` + +3. 多级索引(`MultiIndex`) + +代码: + +```Python +ids = np.arange(1001, 1006) +sms = ['期中', '期末'] +index = pd.MultiIndex.from_product((ids, sms), names=['学号', '学期']) +courses = ['语文', '数学', '英语'] +scores = np.random.randint(60, 101, (10, 3)) +df = pd.DataFrame(data=scores, columns=courses, index=index) +df +``` + +> **说明**:上面的代码使用了`MultiIndex`的类方法`from_product`,该方法通过`ids`和`sms`两组数据的笛卡尔积构造了多级索引。 + +输出: + +``` + 语文 数学 英语 +学号 学期 +1001 期中 93 77 60 + 期末 93 98 84 +1002 期中 64 78 71 + 期末 70 71 97 +1003 期中 72 88 97 + 期末 99 100 63 +1004 期中 80 71 61 + 期末 91 62 72 +1005 期中 82 95 67 + 期末 84 78 86 +``` + +根据第一级索引分组数据,按照期中成绩占`25%`,期末成绩占`75%` 的方式计算每个学生每门课的成绩。 + +```Python +# 计算每个学生的成绩,期中占25%,期末占75% +df.groupby(level=0).agg(lambda x: x.values[0] * 0.25 + x.values[1] * 0.75) +``` + +输出: + +``` + 语文 数学 英语 +学号 +1001 93.00 92.75 78.00 +1002 68.50 72.75 90.50 +1003 92.25 97.00 71.50 +1004 88.25 64.25 69.25 +1005 83.50 82.25 81.25 +``` + +4. 日期时间索引(`DatetimeIndex`) + +通过`date_range()`函数,我们可以创建日期时间索引,代码如下所示。 + +代码: + +```Python +pd.date_range('2021-1-1', '2021-6-1', periods=10) +``` + +输出: + +``` +DatetimeIndex(['2021-01-01 00:00:00', '2021-01-17 18:40:00', + '2021-02-03 13:20:00', '2021-02-20 08:00:00', + '2021-03-09 02:40:00', '2021-03-25 21:20:00', + '2021-04-11 16:00:00', '2021-04-28 10:40:00', + '2021-05-15 05:20:00', '2021-06-01 00:00:00'], + dtype='datetime64[ns]', freq=None) +``` + +代码: + +```Python +pd.date_range('2021-1-1', '2021-6-1', freq='W') +``` + +输出: + +``` +DatetimeIndex(['2021-01-03', '2021-01-10', '2021-01-17', '2021-01-24', + '2021-01-31', '2021-02-07', '2021-02-14', '2021-02-21', + '2021-02-28', '2021-03-07', '2021-03-14', '2021-03-21', + '2021-03-28', '2021-04-04', '2021-04-11', '2021-04-18', + '2021-04-25', '2021-05-02', '2021-05-09', '2021-05-16', + '2021-05-23', '2021-05-30'], + dtype='datetime64[ns]', freq='W-SUN') +``` + +通过`DateOffset`类型,我们可以设置时间差并和`DatetimeIndex`进行运算,具体的操作如下所示。 + +代码: + +```Python +index = pd.date_range('2021-1-1', '2021-6-1', freq='W') +index - pd.DateOffset(days=2) +``` + +输出: + +``` +DatetimeIndex(['2021-01-01', '2021-01-08', '2021-01-15', '2021-01-22', + '2021-01-29', '2021-02-05', '2021-02-12', '2021-02-19', + '2021-02-26', '2021-03-05', '2021-03-12', '2021-03-19', + '2021-03-26', '2021-04-02', '2021-04-09', '2021-04-16', + '2021-04-23', '2021-04-30', '2021-05-07', '2021-05-14', + '2021-05-21', '2021-05-28'], + dtype='datetime64[ns]', freq=None) +``` + +代码: + +```Python +index + pd.DateOffset(days=2) +``` + +输出: + +``` +DatetimeIndex(['2021-01-05', '2021-01-12', '2021-01-19', '2021-01-26', + '2021-02-02', '2021-02-09', '2021-02-16', '2021-02-23', + '2021-03-02', '2021-03-09', '2021-03-16', '2021-03-23', + '2021-03-30', '2021-04-06', '2021-04-13', '2021-04-20', + '2021-04-27', '2021-05-04', '2021-05-11', '2021-05-18', + '2021-05-25', '2021-06-01'], + dtype='datetime64[ns]', freq=None) +``` + +可以使用`DatatimeIndex`类型的相关方法来处理数据,例如`shift()`方法可以通过时间前移或后移数据。我们仍然以上面百度股票数据为例,来演示`shift()`方法的使用,代码如下所示。 + +代码: + +```Python +baidu_df.shift(3, fill_value=0) +``` + +输出: + + + +代码: + +```Python +baidu_df.shift(-1, fill_value=0) +``` + +输出: + + + +通过`asfreq()`方法,我们可以指定一个时间频率抽取对应的数据,代码如下所示。 + +代码: + +```Python +baidu_df.asfreq('5D') +``` + +输出: + + + +代码: + +```Python +baidu_df.asfreq('5D', method='ffill') +``` + +输出: + + + +通过`resample()`方法,我们可以基于时间对数据进行重采样,相当于根据时间周期对数据进行了分组操作,代码如下所示。 + +代码: + +```Python +baidu_df.resample('1M').mean() +``` + +输出: + + + +> **说明**:上面的代码中,`W`表示一周,`5D`表示`5`天,`1M`表示`1`个月。 + +如果要实现日期时间的时区转换,我们首先用`tz_localize()`方法将日期时间本地化,代码如下所示。 + +代码: + +```Python +baidu_df = baidu_df.tz_localize('Asia/Chongqing') +baidu_df +``` + +输出: + + + +在对时间本地化以后,我们使用`tz_convert()`方法就可以实现转换时区,代码如下所示。 + +代码: + +```Python +baidu_df.tz_convert('America/New_York') +``` + +输出: + + diff --git a/res/ABF827024EA535099DC0E6A66A336C51.png b/res/ABF827024EA535099DC0E6A66A336C51.png new file mode 100644 index 0000000000000000000000000000000000000000..b2b446c21193dae35f206bd2db72f8012ac78054 GIT binary patch literal 1585662 zcmbTdcR*81*EhOTAc+E@NHstpQB;sB8X$BHAW{?+r7Iu;(m_HGMUdV^j!09QsDLO% zI-w(nj-a5Bg3?41r9_PQ<(#M9?|uKc_pXq=S7z4Co;A$Op7mR6e!u%o0r<}nOb7r7 z1OUdI5Ad4`@jgRzzX1SdX23B30N?;ONDzQt@Hsiv%{b`k*iGXMa_ zk$`eCRWcy|stu%<0sS|BF@yhao+AgknIZ6R-Zw+=-#jrB^pAQ#UO_`mP^R)!`foO;4!^)Hxs-|&&u43jkpxD?>3e?eCB# z+dAbJq{yz%*Bk4bd2-lolZ@J$H{Ev{~&1>Fnu4h7A&vBCf zDX74C+CS3&CI3G%EPVn3gZ%&ZLgqdJuK%OJUo{!tbmz49Zw3DI2s59cz?=Ug^&&^~ zuOk1<;OJ}MdMzk0#_;_iGc(A7oX+52Cjf7PsS@(=0%s@A~Y-R))| zN6&!&O0>Fp&EMDczuRPS%jJI*z2NE+zcFYf0gGn$@rSL%Pm*`f3->9*Vp`- 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