《利用python进行数据分析》读书笔记--第十章 时间序列(二)
5、時(shí)期及其算數(shù)運(yùn)算
時(shí)期(period)表示的是時(shí)間區(qū)間,比如數(shù)日、數(shù)月、數(shù)季、數(shù)年等。Period類(lèi)所表示的就是這種數(shù)據(jù)類(lèi)型,其構(gòu)造函數(shù)需要用到一個(gè)字符串或整數(shù),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(gè)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(jìn)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(lèi)型是<class 'pandas.tseries.period.PeriodIndex'>,形式上是一個(gè)array數(shù)組 #注意下面的形式已經(jīng)不是書(shū)上的形式,而是float類(lèi)型,但是做索引時(shí),還是日期形式 print rng print type(rng) print Series(np.random.randn(6),index = rng),'\n' #PeriodIndex類(lèi)的構(gòu)造函數(shù)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)
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- 時(shí)期的頻率轉(zhuǎn)換
Period和PeriodIndex對(duì)象都可以通過(guò)其asfreq方法轉(zhuǎn)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(yǔ)句實(shí)際上是一個(gè)被劃分為多個(gè)月度時(shí)期的時(shí)間段中的游標(biāo) 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(zhuǎn)換為低頻率時(shí),超時(shí)期是由子時(shí)期所屬位置決定的,例如在A-JUN頻率中,月份“2007年8月”實(shí)際上屬于“2008年” p = pd.Period('2007-08','M') print p.asfreq('A-JUN'),'\n' #PeriodIndex或TimeSeries的頻率轉(zhuǎn)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
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Period頻率轉(zhuǎn)換示意圖:
- 按季度計(jì)算的時(shí)期頻率
季度型數(shù)據(jù)在會(huì)計(jì)、金融等領(lǐng)域中很常見(jiàn)。許多季度型數(shù)據(jù)都會(huì)涉及“財(cái)年末”的概念,通常是一年12個(gè)月中某月的最后一個(gè)日歷日或工作日。就這一點(diǎn)來(lái)說(shuō),“2012Q4”根據(jù)財(cái)年末的會(huì)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 pytzp = pd.Period('2012Q4',freq = 'Q-JAN') print p #在以1月結(jié)束的財(cái)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(yùn)算會(huì)非常簡(jiǎn)單,例如,要獲取該季度倒數(shù)第二個(gè)工作日下午4點(diǎn)的時(shí)間戳 p4pm = (p.asfreq('B','e') - 1).asfreq('T','s') + 16 * 60 print p4pm print p4pm.to_timestamp(),'\n' #period_range還可以用于生產(chǎn)季度型范圍,季度型范圍的算數(shù)運(yùn)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(gè)示意圖,很直觀:
- 將Timestamp轉(zhuǎn)換為Period
通過(guò)to_period方法,可以將由時(shí)間戳索引的Series和DataFrame對(duì)象轉(zhuǎn)換為以時(shí)期為索引的對(duì)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 pytzrng = 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' #由于時(shí)期指的是非重疊時(shí)間區(qū)間,因此對(duì)于給定的頻率,一個(gè)時(shí)間戳只能屬于一個(gè)時(shí)期。 #新PeriodIndex的頻率默認(rèn)是從時(shí)間戳推斷而來(lái)的,當(dāng)然可以自己指定頻率,當(dāng)然會(huì)有重復(fù)時(shí)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(zhuǎn)換為時(shí)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]- 通過(guò)數(shù)組創(chuàng)建PeriodIndex
固定頻率的數(shù)據(jù)集通常會(huì)將時(shí)間信息分開(kāi)存放在多個(gè)列中。例如下面的這個(gè)宏觀經(jīng)濟(jì)數(shù)據(jù)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 pytzdata = 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(shù)數(shù)組的形式存儲(chǔ)的,當(dāng)顯示某一個(gè)是才會(huì)有年份-季度的展示 print index print index[0],'\n' data.index = index #下面的結(jié)果證明,infl的index已經(jīng)變?yōu)榱四攴?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(zhuǎn)換
重采樣(resampling)指的是將時(shí)間序列從一個(gè)頻率轉(zhuǎn)換到另一個(gè)頻率的過(guò)程。將高頻率數(shù)據(jù)聚合到低頻率成為降采樣(downsampling),而將低頻率數(shù)據(jù)轉(zhuǎn)換到高頻率成為升采樣(uosampling)。并不是所有的重采樣都能被劃分到這兩類(lèi)中,比如將W-WED轉(zhuǎn)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(zhuǎn)換工作的主力函數(shù)。
#-*- 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 pytzrng = 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(jié)果中有4個(gè)月的值,因?yàn)閠s已經(jīng)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(shù):
- 降采樣
將數(shù)據(jù)的頻率降低稱為降采樣,也就是將數(shù)據(jù)進(jìn)行聚合。一個(gè)數(shù)據(jù)點(diǎn)只能屬于一個(gè)聚合時(shí)間段,所有時(shí)間段的并集組成整個(gè)時(shí)間幀。在進(jìn)行降采樣時(shí),應(yīng)該考慮如下:
下面是個(gè)下采樣的一個(gè)直觀展示:
a、OHLC重采樣
金融領(lǐng)域中有一種無(wú)所不在的時(shí)間序列聚合方式,及計(jì)算四個(gè)面元值:open、close、hign、close。傳入how = ‘ohlc’即可得到一個(gè)含有這四種聚合值的DataFrame。這個(gè)過(guò)程很高效!(順便:真的很實(shí)用啊!)只需一次掃描即可計(jì)算出結(jié)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 pytzrng = 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???? close2000-01-01 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
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b、通過(guò)groupby進(jìn)行重采樣
另一種方法是使用pandas的groupby功能。例如,你打算根據(jù)月份或者周幾進(jìn)行分組,只需傳入一個(gè)能夠訪問(wèn)時(shí)間序列的索引上的這些字段的函數(shù)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 pytzrng = 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(xiě)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(shù)據(jù)從低頻率轉(zhuǎn)換到高頻率是,就不需要聚合了??匆幌孪旅娴睦?#xff1a;
#-*- 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 pytzframe = 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(rèn)會(huì)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(shù)值用resampling進(jìn)行填充 print frame.resample('D',fill_method = 'ffill'),'\n' #同樣,這里可以只填充指定的時(shí)期數(shù)(目的是限制前面的觀測(cè)值的持續(xù)使用距離) print frame.resample('D',fill_method = 'ffill',limit = 2) #注意,新的日期索引完全沒(méi)必要跟舊的相交,注意這個(gè)例子展現(xiàn)了數(shù)據(jù)日期可以延長(zhǎng) 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 1.452790Colorado 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(guò)日期進(jìn)行重采樣
對(duì)那些使用時(shí)期索引的數(shù)據(jù)進(jìn)行重采樣是一件非常簡(jiǎn)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 pytzframe = 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?yàn)槟惚仨殯Q定在新的頻率中各區(qū)間的哪端用于放置原來(lái)的值,就像asfreq方法一樣,convention默認(rèn)為'end',可設(shè)置為'start' #Q-DEC:季度型(每年以12月結(jié)束) print annual_frame.resample('Q-DEC',fill_method = 'ffill') print annual_frame.resample('Q-DEC',fill_method = 'ffill',convention = 'start'),'\n' #由于時(shí)期指的是時(shí)間區(qū)間,所以升采樣和降采樣的規(guī)則就比較嚴(yán)格 #在降采樣中,目標(biāo)頻率必須是原頻率的子時(shí)期 #在升采樣中,目標(biāo)頻率必須是原頻率的超時(shí)期 #如果不滿足這些條件,就會(huì)引發(fā)異常,主要影響的是按季、年、周計(jì)算的頻率。 #例如,由Q-MAR定義的時(shí)間區(qū)間只能升采樣為A-MAR、A-JUN等 print annual_frame.resample('Q-MAR',fill_method = 'ffill') #實(shí)話說(shuō),上面的幾個(gè)例子需要在實(shí)戰(zhàn)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 0.187231Colorado 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]?
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