5、時期及其算數運算
時期（period）表示的是時間區間，比如數日、數月、數季、數年等。Period類所表示的就是這種數據類型，其構造函數需要用到一個字符串或整數，以及頻率。
#-*- coding:utf-8 -*- import numpy as np import pandas as pd import matplotlib.pyplot as plt import datetime as dt from pandas import Series,DataFrame from datetime import datetime from dateutil.parser import parse import time from pandas.tseries.offsets import Hour,Minute,Day,MonthEnd import pytz #下面的'A-DEC'是年第12月底最后一個日歷日 p = pd.Period('2016',freq = 'A-DEC') #Period可以直接加減 print p + 5 #相同頻率的Period可以進行加減,不同頻率是不能加減的 rng = pd.Period('2015',freq = 'A-DEC') - p print rng rng = pd.period_range('1/1/2000','6/30/2000',freq = 'M') #類型是<class 'pandas.tseries.period.PeriodIndex'>，形式上是一個array數組 #注意下面的形式已經不是書上的形式，而是float類型，但是做索引時，還是日期形式 print rng print type(rng) print Series(np.random.randn(6),index = rng),'\n' #PeriodIndex類的構造函數還允許直接使用一組字符串 values = ['2001Q3','2002Q2','2003Q1'] index = pd.PeriodIndex(values,freq = 'Q-DEC') #下面index的 print index
>>>
2021
-1
array([360, 361, 362, 363, 364, 365], dtype=int64)
<class 'pandas.tseries.period.PeriodIndex'>
2000-01 -0.504031
2000-02 1.345024
2000-03 0.074367
2000-04 -1.152187
2000-05 -0.460272
2000-06 0.486135
Freq: M
array([126, 129, 132], dtype=int64)
[Finished in 1.4s]
-
時期的頻率轉換
Period和PeriodIndex對象都可以通過其asfreq方法轉換為別的頻率。
#-*- coding:utf-8 -*- import numpy as np import pandas as pd import matplotlib.pyplot as plt import datetime as dt from pandas import Series,DataFrame from datetime import datetime from dateutil.parser import parse import time from pandas.tseries.offsets import Hour,Minute,Day,MonthEnd import pytz #下面這條語句實際上是一個被划分為多個月度時期的時間段中的游標 p = pd.Period('2007',freq = 'A-DEC') print p print p.asfreq('M',how = 'start') print p.asfreq('M',how = 'end') #高頻率轉換為低頻率時，超時期是由子時期所屬位置決定的,例如在A-JUN頻率中，月份“2007年8月”實際上屬於“2008年” p = pd.Period('2007-08','M') print p.asfreq('A-JUN'),'\n' #PeriodIndex或TimeSeries的頻率轉換方式也是如此： rng = pd.period_range('2006','2009',freq = 'A-DEC') ts = Series(np.random.randn(len(rng)),index = rng) print ts print ts.asfreq('M',how = 'start') print ts.asfreq('B',how = 'end'),'\n'
>>>
2007
2007-01
2007-12
2008
2006 0.001601
2007 0.285760
2008 -0.458762
2009 0.076204
Freq: A-DEC
2006-01 0.001601
2007-01 0.285760
2008-01 -0.458762
2009-01 0.076204
Freq: M
2006-12-29 0.001601
2007-12-31 0.285760
2008-12-31 -0.458762
2009-12-31 0.076204
Freq: B
[Finished in 1.4s]
Period頻率轉換示意圖：
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按季度計算的時期頻率
季度型數據在會計、金融等領域中很常見。許多季度型數據都會涉及“財年末”的概念，通常是一年12個月中某月的最后一個日歷日或工作日。就這一點來說，“2012Q4”根據財年末的會有不同含義。pandas支持12種可能的季度頻率，即Q-JAN、Q-DEC。
#-*- coding:utf-8 -*- import numpy as np import pandas as pd import matplotlib.pyplot as plt import datetime as dt from pandas import Series,DataFrame from datetime import datetime from dateutil.parser import parse import time from pandas.tseries.offsets import Hour,Minute,Day,MonthEnd import pytz p = pd.Period('2012Q4',freq = 'Q-JAN') print p #在以1月結束的財年中，2012Q4是從11月到1月 print p.asfreq('D','start') print p.asfreq('D','end'),'\n' #因此，Period之間的運算會非常簡單，例如，要獲取該季度倒數第二個工作日下午4點的時間戳 p4pm = (p.asfreq('B','e') - 1).asfreq('T','s') + 16 * 60 print p4pm print p4pm.to_timestamp(),'\n' #period_range還可以用於生產季度型范圍，季度型范圍的算數運算也跟上面是一樣的： #要非常小心的是Q-JAN是什么意思 rng = pd.period_range('2011Q3','2012Q4',freq = 'Q-JAN') print rng.to_timestamp() ts = Series(np.arange(len(rng)),index = rng) print ts,'\n' new_rng = (rng.asfreq('B','e') - 1).asfreq('T','s') + 16 * 60 ts.index = new_rng.to_timestamp() print ts,'\n' >>> 2012Q4 2011-11-01 2012-01-31 2012-01-30 16:00 2012-01-30 16:00:00 <class 'pandas.tseries.index.DatetimeIndex'> [2010-10-31 00:00:00, ..., 2012-01-31 00:00:00] Length: 6, Freq: Q-OCT, Timezone: None 2011Q3 0 2011Q4 1 2012Q1 2 2012Q2 3 2012Q3 4 2012Q4 5 Freq: Q-JAN 2010-10-28 16:00:00 0 2011-01-28 16:00:00 1 2011-04-28 16:00:00 2 2011-07-28 16:00:00 3 2011-10-28 16:00:00 4 2012-01-30 16:00:00 5 [Finished in 3.3s]
下面是一個示意圖，很直觀：
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將Timestamp轉換為Period
通過to_period方法，可以將由時間戳索引的Series和DataFrame對象轉換為以時期為索引的對象。
#-*- coding:utf-8 -*- import numpy as np import pandas as pd import matplotlib.pyplot as plt import datetime as dt from pandas import Series,DataFrame from datetime import datetime from dateutil.parser import parse import time from pandas.tseries.offsets import Hour,Minute,Day,MonthEnd import pytz rng = pd.date_range('1/1/2015',periods = 3,freq = 'M') ts = Series(np.random.randn(3),index = rng) print ts pts = ts.to_period() print pts,'\n' #由於時期指的是非重疊時間區間，因此對於給定的頻率，一個時間戳只能屬於一個時期。 #新PeriodIndex的頻率默認是從時間戳推斷而來的，當然可以自己指定頻率，當然會有重復時期存在 rng = pd.date_range('1/29/2000',periods = 6,freq = 'D') ts2 = Series(np.random.randn(6),index = rng) print ts2 print ts2.to_period('M') #要想轉換為時間戳，使用to_timestamp即可 print pts.to_timestamp(how = 'end') >>> 2015-01-31 -1.085886 2015-02-28 -0.919741 2015-03-31 0.656477 Freq: M 2015-01 -1.085886 2015-02 -0.919741 2015-03 0.656477 Freq: M 2000-01-29 -0.394812 2000-01-30 0.669354 2000-01-31 0.197537 2000-02-01 -1.374942 2000-02-02 0.451683 2000-02-03 1.542144 Freq: D 2000-01 -0.394812 2000-01 0.669354 2000-01 0.197537 2000-02 -1.374942 2000-02 0.451683 2000-02 1.542144 Freq: M 2015-01-31 -1.085886 2015-02-28 -0.919741 2015-03-31 0.656477 Freq: M [Finished in 1.8s]
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通過數組創建PeriodIndex
固定頻率的數據集通常會將時間信息分開存放在多個列中。例如下面的這個宏觀經濟數據集中，年度和季度就分別存放在不同的列中。
#-*- coding:utf-8 -*- import numpy as np import pandas as pd import matplotlib.pyplot as plt import datetime as dt from pandas import Series,DataFrame from datetime import datetime from dateutil.parser import parse import time from pandas.tseries.offsets import Hour,Minute,Day,MonthEnd import pytz data = pd.read_csv('E:\\macrodata.csv') print data.year print data.quarter,'\n' index = pd.PeriodIndex(year = data.year,quarter = data.quarter,freq = 'Q-DEC') #index是以整數數組的形式存儲的，當顯示某一個是才會有年份-季度的展示 print index print index[0],'\n' data.index = index #下面的結果證明，infl的index已經變為了年份-季度形式 print data.infl >>> 0 1959 1 1959 2 1959 3 1959 4 1960 5 1960 6 1960 7 1960 8 1961 9 1961 10 1961 11 1961 12 1962 13 1962 14 1962 ... 188 2006 189 2006 190 2006 191 2006 192 2007 193 2007 194 2007 195 2007 196 2008 197 2008 198 2008 199 2008 200 2009 201 2009 202 2009 Name: year, Length: 203 0 1 1 2 2 3 3 4 4 1 5 2 6 3 7 4 8 1 9 2 10 3 11 4 12 1 13 2 14 3 ... 188 1 189 2 190 3 191 4 192 1 193 2 194 3 195 4 196 1 197 2 198 3 199 4 200 1 201 2 202 3 Name: quarter, Length: 203 array([-44, -43, -42, -41, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158], dtype=int64) 1959Q1 1959Q1 0.00 1959Q2 2.34 1959Q3 2.74 1959Q4 0.27 1960Q1 2.31 1960Q2 0.14 1960Q3 2.70 1960Q4 1.21 1961Q1 -0.40 1961Q2 1.47 1961Q3 0.80 1961Q4 0.80 1962Q1 2.26 1962Q2 0.13 1962Q3 2.11 ... 2006Q1 2.60 2006Q2 3.97 2006Q3 -1.58 2006Q4 3.30 2007Q1 4.58 2007Q2 2.75 2007Q3 3.45 2007Q4 6.38 2008Q1 2.82 2008Q2 8.53 2008Q3 -3.16 2008Q4 -8.79 2009Q1 0.94 2009Q2 3.37 2009Q3 3.56 Freq: Q-DEC, Name: infl, Length: 203 [Finished in 1.8s]
6、重采樣及頻率轉換
重采樣（resampling）指的是將時間序列從一個頻率轉換到另一個頻率的過程。將高頻率數據聚合到低頻率成為降采樣（downsampling），而將低頻率數據轉換到高頻率成為升采樣（uosampling）。並不是所有的重采樣都能被划分到這兩類中，比如將W-WED轉換為W-FRI既不是降采樣也不是升采樣。
pandas中的resample方法，它是各種頻率轉換工作的主力函數。
#-*- coding:utf-8 -*- import numpy as np import pandas as pd import matplotlib.pyplot as plt import datetime as dt from pandas import Series,DataFrame from datetime import datetime from dateutil.parser import parse import time from pandas.tseries.offsets import Hour,Minute,Day,MonthEnd import pytz rng = pd.date_range('1/1/2000',periods = 100,freq = 'D') ts = Series(np.random.randn(100),index = rng) #print ts #注意下面的結果中有4個月的值，因為ts已經到了四月份 print ts.resample('M',how = 'mean') print ts.resample('M',how = 'mean',kind = 'period') >>> 2000-01-31 0.015620 2000-02-29 0.002502 2000-03-31 -0.029775 2000-04-30 -0.618537 Freq: M 2000-01 0.015620 2000-02 0.002502 2000-03 -0.029775 2000-04 -0.618537 Freq: M [Finished in 0.7s]
下面是resample的參數：
-
降采樣
將數據的頻率降低稱為降采樣，也就是將數據進行聚合。一個數據點只能屬於一個聚合時間段，所有時間段的並集組成整個時間幀。在進行降采樣時，應該考慮如下：
-
各區間那便是閉合的
-
如何標記各個聚合面元，用區間的開頭還是結尾
#-*- coding:utf-8 -*- import numpy as np import pandas as pd import matplotlib.pyplot as plt import datetime as dt from pandas import Series,DataFrame from datetime import datetime from dateutil.parser import parse import time from pandas.tseries.offsets import Hour,Minute,Day,MonthEnd import pytz #下面生成1分鍾線 rng = pd.date_range('1/1/2000',periods = 12,freq = 'T') ts = Series(range(0,12),index = rng) print ts,'\n' #下面聚合到5min線 print ts.resample('5min',how = 'sum') #傳入的頻率將會以“5min”的增量定義面元。默認情況下，面元的有邊界是包含右邊屆的，即00:00到00:05是包含00:05的 #傳入closed = 'left'會讓左邊的區間閉合 print ts.resample('5min',how = 'sum',closed = 'left') #最終的時間序列默認是用右側的邊界標記，但是傳入label = 'left'可以轉換為左邊標記 print ts.resample('5min',how = 'sum',closed = 'left',label = 'left'),'\n' #最后，你可能需要對結果索引做一些位移，比如將右邊界減去一秒更容易明白到底是屬於哪一個區間 #通過loffset設置一個字符串或者日期偏移量即可實現此目的,書上作者沒有加left是矛盾的，當然也可以調用shift來進行時間偏移 print ts.resample('5min',how = 'sum',closed = 'left',loffset = '-1s') >>> 2000-01-01 00:00:00 0 2000-01-01 00:01:00 1 2000-01-01 00:02:00 2 2000-01-01 00:03:00 3 2000-01-01 00:04:00 4 2000-01-01 00:05:00 5 2000-01-01 00:06:00 6 2000-01-01 00:07:00 7 2000-01-01 00:08:00 8 2000-01-01 00:09:00 9 2000-01-01 00:10:00 10 2000-01-01 00:11:00 11 Freq: T 2000-01-01 00:00:00 0 2000-01-01 00:05:00 15 2000-01-01 00:10:00 40 2000-01-01 00:15:00 11 Freq: 5T 2000-01-01 00:05:00 10 2000-01-01 00:10:00 35 2000-01-01 00:15:00 21 Freq: 5T 2000-01-01 00:00:00 10 2000-01-01 00:05:00 35 2000-01-01 00:10:00 21 Freq: 5T 2000-01-01 00:04:59 10 2000-01-01 00:09:59 35 2000-01-01 00:14:59 21 Freq: 5T [Finished in 0.6s]
下面是個下采樣的一個直觀展示：
a、OHLC重采樣
金融領域中有一種無所不在的時間序列聚合方式，及計算四個面元值：open、close、hign、close。傳入how = ‘ohlc’即可得到一個含有這四種聚合值的DataFrame。這個過程很高效！（順便：真的很實用啊！）只需一次掃描即可計算出結果：
#-*- coding:utf-8 -*- import numpy as np import pandas as pd import matplotlib.pyplot as plt import datetime as dt from pandas import Series,DataFrame from datetime import datetime from dateutil.parser import parse import time from pandas.tseries.offsets import Hour,Minute,Day,MonthEnd import pytz rng = pd.date_range('1/1/2000',periods = 12,freq = 'T') ts = Series(np.random.randn(12),index = rng) print ts,'\n' print ts.resample('5min',how = 'ohlc')
>>>
open high low close
2000-01-01 00:00:00 1.239881 1.239881 1.239881 1.239881
2000-01-01 00:05:00 0.035189 0.371294 -1.764463 -1.764463
2000-01-01 00:10:00 -0.959353 1.441732 -0.959353 0.019104
2000-01-01 00:15:00 1.169352 1.169352 1.169352 1.169352
[Finished in 0.7s]
b、通過groupby進行重采樣
另一種方法是使用pandas的groupby功能。例如，你打算根據月份或者周幾進行分組，只需傳入一個能夠訪問時間序列的索引上的這些字段的函數即可：
#-*- coding:utf-8 -*- import numpy as np import pandas as pd import matplotlib.pyplot as plt import datetime as dt from pandas import Series,DataFrame from datetime import datetime from dateutil.parser import parse import time from pandas.tseries.offsets import Hour,Minute,Day,MonthEnd import pytz rng = pd.date_range('1/1/2000',periods = 100,freq = 'D') ts = Series(np.arange(100),index = rng) print ts.groupby(lambda x:x.month).mean() #作真是越寫越省事了…… print ts.groupby(lambda x:x.weekday).mean() >>> 1 15 2 45 3 75 4 95 0 47.5 1 48.5 2 49.5 3 50.5 4 51.5 5 49.0 6 50.0 [Finished in 0.6s]
- 升采樣和差值
將數據從低頻率轉換到高頻率是，就不需要聚合了。看一下下面的例子：
#-*- coding:utf-8 -*- import numpy as np import pandas as pd import matplotlib.pyplot as plt import datetime as dt from pandas import Series,DataFrame from datetime import datetime from dateutil.parser import parse import time from pandas.tseries.offsets import Hour,Minute,Day,MonthEnd import pytz frame = DataFrame(np.random.randn(2,4),index = pd.date_range('1/1/2000',periods = 2,freq = 'W-WED'), columns = ['Colorado','Texas','New York','Ohio']) print frame,'\n' #將其重采樣到日頻率，默認會引入缺省值 df_daily = frame.resample('D') print df_daily,'\n' #可以跟fillna和reindex一樣，將上面的數值用resampling進行填充 print frame.resample('D',fill_method = 'ffill'),'\n' #同樣，這里可以只填充指定的時期數（目的是限制前面的觀測值的持續使用距離） print frame.resample('D',fill_method = 'ffill',limit = 2) #注意，新的日期索引完全沒必要跟舊的相交,注意這個例子展現了數據日期可以延長 print frame.resample('W-THU',fill_method = 'ffill') >>> Colorado Texas New York Ohio 2000-01-05 0.093695 1.382325 -0.146193 1.206698 2000-01-12 -1.873184 0.603526 -1.407574 1.452790 Colorado Texas New York Ohio 2000-01-05 0.093695 1.382325 -0.146193 1.206698 2000-01-06 NaN NaN NaN NaN 2000-01-07 NaN NaN NaN NaN 2000-01-08 NaN NaN NaN NaN 2000-01-09 NaN NaN NaN NaN 2000-01-10 NaN NaN NaN NaN 2000-01-11 NaN NaN NaN NaN 2000-01-12 -1.873184 0.603526 -1.407574 1.452790 Colorado Texas New York Ohio 2000-01-05 0.093695 1.382325 -0.146193 1.206698 2000-01-06 0.093695 1.382325 -0.146193 1.206698 2000-01-07 0.093695 1.382325 -0.146193 1.206698 2000-01-08 0.093695 1.382325 -0.146193 1.206698 2000-01-09 0.093695 1.382325 -0.146193 1.206698 2000-01-10 0.093695 1.382325 -0.146193 1.206698 2000-01-11 0.093695 1.382325 -0.146193 1.206698 2000-01-12 -1.873184 0.603526 -1.407574 1.452790 Colorado Texas New York Ohio 2000-01-05 0.093695 1.382325 -0.146193 1.206698 2000-01-06 0.093695 1.382325 -0.146193 1.206698 2000-01-07 0.093695 1.382325 -0.146193 1.206698 2000-01-08 NaN NaN NaN NaN 2000-01-09 NaN NaN NaN NaN 2000-01-10 NaN NaN NaN NaN 2000-01-11 NaN NaN NaN NaN 2000-01-12 -1.873184 0.603526 -1.407574 1.452790 Colorado Texas New York Ohio 2000-01-06 0.093695 1.382325 -0.146193 1.206698 2000-01-13 -1.873184 0.603526 -1.407574 1.452790 [Finished in 0.7s]
- 通過日期進行重采樣
對那些使用時期索引的數據進行重采樣是一件非常簡單的事情。
#-*- coding:utf-8 -*- import numpy as np import pandas as pd import matplotlib.pyplot as plt import datetime as dt from pandas import Series,DataFrame from datetime import datetime from dateutil.parser import parse import time from pandas.tseries.offsets import Hour,Minute,Day,MonthEnd import pytz frame = DataFrame(np.random.randn(24,4),index = pd.period_range('1-2000','12-2001',freq = 'M'), columns = ['Colorado','Texas','New York','Ohio']) print frame,'\n' annual_frame = frame.resample('A-DEC',how = 'mean') print annual_frame,'\n' #升采樣要稍微麻煩些，因為你必須決定在新的頻率中各區間的哪端用於放置原來的值，就像asfreq方法一樣，convention默認為'end',可設置為'start' #Q-DEC：季度型（每年以12月結束） print annual_frame.resample('Q-DEC',fill_method = 'ffill') print annual_frame.resample('Q-DEC',fill_method = 'ffill',convention = 'start'),'\n' #由於時期指的是時間區間，所以升采樣和降采樣的規則就比較嚴格 #在降采樣中，目標頻率必須是原頻率的子時期 #在升采樣中，目標頻率必須是原頻率的超時期 #如果不滿足這些條件，就會引發異常，主要影響的是按季、年、周計算的頻率。 #例如，由Q-MAR定義的時間區間只能升采樣為A-MAR、A-JUN等 print annual_frame.resample('Q-MAR',fill_method = 'ffill') #實話說，上面的幾個例子需要在實戰中去理解 >>> Colorado Texas New York Ohio 2000-01 0.531119 0.514660 -1.051243 1.900872 2000-02 0.937613 -0.301391 1.034113 -0.015524 2000-03 0.368118 -1.236412 0.455100 1.648863 2000-04 -0.728873 0.250044 1.523354 0.230613 2000-05 -0.188811 1.418581 -1.285510 1.051915 2000-06 2.059990 -0.703682 1.293203 -0.792534 2000-07 0.911168 -0.362981 -1.873637 1.033383 2000-08 0.817223 1.512153 -0.365323 -1.325069 2000-09 -0.087511 0.238656 -2.078260 1.415511 2000-10 0.185765 0.223584 1.242821 -0.654831 2000-11 -0.725814 0.723152 -0.250924 -2.110532 2000-12 -0.153382 1.535816 1.455040 0.700309 2001-01 -0.146100 -1.036274 -0.954112 -0.212434 2001-02 0.283262 1.868316 2.128798 -0.857980 2001-03 -0.793054 -1.858595 -1.243900 0.952001 2001-04 0.878166 -0.846098 1.161008 1.060023 2001-05 0.071310 -0.705115 0.489365 0.187680 2001-06 -0.622563 -1.070024 -1.044217 0.119744 2001-07 1.086923 -1.142216 1.015157 0.804685 2001-08 -2.642336 -0.758853 -0.248052 -0.024919 2001-09 -0.335489 -1.354160 0.171963 -0.993819 2001-10 -0.715587 -0.833531 0.797166 0.127754 2001-11 -0.265285 -2.005336 1.271591 0.016298 2001-12 0.971353 -0.150070 -1.170043 1.067736 Colorado Texas New York Ohio 2000 0.327217 0.317682 0.008228 0.256915 2001 -0.185783 -0.824330 0.197894 0.187231 Colorado Texas New York Ohio 2000Q4 0.327217 0.317682 0.008228 0.256915 2001Q1 0.327217 0.317682 0.008228 0.256915 2001Q2 0.327217 0.317682 0.008228 0.256915 2001Q3 0.327217 0.317682 0.008228 0.256915 2001Q4 -0.185783 -0.824330 0.197894 0.187231 Colorado Texas New York Ohio 2000Q1 0.327217 0.317682 0.008228 0.256915 2000Q2 0.327217 0.317682 0.008228 0.256915 2000Q3 0.327217 0.317682 0.008228 0.256915 2000Q4 0.327217 0.317682 0.008228 0.256915 2001Q1 -0.185783 -0.824330 0.197894 0.187231 Colorado Texas New York Ohio 2001Q3 0.327217 0.317682 0.008228 0.256915 2001Q4 0.327217 0.317682 0.008228 0.256915 2002Q1 0.327217 0.317682 0.008228 0.256915 2002Q2 0.327217 0.317682 0.008228 0.256915 2002Q3 -0.185783 -0.824330 0.197894 0.187231 [Finished in 0.8s]