import pandas as pd
import random
import numpy as np
n_rows=5
n_cols=2
df = pd.DataFrame(np.random.randn(n_rows, n_cols),
index = pd.date_range('1/1/2000', periods=n_rows),
columns = ['A','B'])
df=df.apply(lambda x:[int(xx*10) for xx in x],axis=0)
df

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A B
2000-01-01 -18 3
2000-01-02 5 -4
2000-01-03 -2 8
2000-01-04 0 1
2000-01-05 -18 3

pct_change

## pct_change() to compute the percent change over a given number of periods
df.pct_change(periods=1) # b{t}=(a{t}-a{t-1})/a{t-1}

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A B
2000-01-01 NaN NaN
2000-01-02 -1.277778 -2.333333
2000-01-03 -1.400000 -3.000000
2000-01-04 -1.000000 -0.875000
2000-01-05 -inf 2.000000
df.pct_change(periods=2)  # b{t}=(a{t}-a{t-2})/a{t-2}

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A B
2000-01-01 NaN NaN
2000-01-02 NaN NaN
2000-01-03 -0.888889 1.666667
2000-01-04 -1.000000 -1.250000
2000-01-05 8.000000 -0.625000

Covariance

df.cov()

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A B
A 114.80 -17.85
B -17.85 18.70
df.A.cov(df.B)
-17.849999999999998

Correlation

df.corr()

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A B
A 1.000000 -0.385253
B -0.385253 1.000000

Data ranking

df.rank()

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A B
2000-01-01 1.5 3.5
2000-01-02 5.0 1.0
2000-01-03 3.0 5.0
2000-01-04 4.0 2.0
2000-01-05 1.5 3.5
df.rank(axis=1)

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A B
2000-01-01 1.0 2.0
2000-01-02 2.0 1.0
2000-01-03 1.0 2.0
2000-01-04 1.0 2.0
2000-01-05 1.0 2.0
method parameter:
average : average rank of tied group
min : lowest rank in the group
max : highest rank in the group
first : ranks assigned in the order they appear in the array

Window Functions

cumsum

df

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A B
2000-01-01 -18 3
2000-01-02 5 -4
2000-01-03 -2 8
2000-01-04 0 1
2000-01-05 -18 3
df.cumsum()

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A B
2000-01-01 -18 3
2000-01-02 -13 -1
2000-01-03 -15 7
2000-01-04 -15 8
2000-01-05 -33 11

rolling

df

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A B
2000-01-01 -18 3
2000-01-02 5 -4
2000-01-03 -2 8
2000-01-04 0 1
2000-01-05 -18 3
r=df.rolling(window=2)
r.mean()

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A B
2000-01-01 NaN NaN
2000-01-02 -6.5 -0.5
2000-01-03 1.5 2.0
2000-01-04 -1.0 4.5
2000-01-05 -9.0 2.0
r.count()

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A B
2000-01-01 1.0 1.0
2000-01-02 2.0 2.0
2000-01-03 2.0 2.0
2000-01-04 2.0 2.0
2000-01-05 2.0 2.0
r.max()

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A B
2000-01-01 NaN NaN
2000-01-02 5.0 3.0
2000-01-03 5.0 8.0
2000-01-04 0.0 8.0
2000-01-05 0.0 3.0
Method Description
count() Number of non-null observations
sum() Sum of values
mean() Mean of values
median() Arithmetic median of values
min() Minimum
max() Maximum
std() Bessel-corrected sample standard deviation
var() Unbiased variance
skew() Sample skewness (3rd moment)
kurt() Sample kurtosis (4th moment)
quantile() Sample quantile (value at %)
apply() Generic apply
cov() Unbiased covariance (binary)
corr() Correlation (binary)

win_type can specify distribution function.

parameter 'on' to specify a column (rather than the default of the index) in a DataFrame.

df

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A B
2000-01-01 -18 3
2000-01-02 5 -4
2000-01-03 -2 8
2000-01-04 0 1
2000-01-05 -18 3
df.rolling(window='3d',min_periods=3).sum()   ## 最近三天

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A B
2000-01-01 NaN NaN
2000-01-02 NaN NaN
2000-01-03 -15.0 7.0
2000-01-04 3.0 5.0
2000-01-05 -20.0 12.0

expanding

df

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A B
2000-01-01 -18 3
2000-01-02 5 -4
2000-01-03 -2 8
2000-01-04 0 1
2000-01-05 -18 3
df.expanding().mean()  ## statistic with all data up to a point in time

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A B
2000-01-01 -18.00 3.000000
2000-01-02 -6.50 -0.500000
2000-01-03 -5.00 2.333333
2000-01-04 -3.75 2.000000
2000-01-05 -6.60 2.200000

Exponentially Weighted Windows(ewm)

df

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A B
2000-01-01 -18 3
2000-01-02 5 -4
2000-01-03 -2 8
2000-01-04 0 1
2000-01-05 -18 3
df.ewm(alpha=0.9).mean()

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A B
2000-01-01 -18.000000 3.000000
2000-01-02 2.909091 -3.363636
2000-01-03 -1.513514 6.873874
2000-01-04 -0.151215 1.586859
2000-01-05 -16.215282 2.858699

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