# ** 6 ARIMA Analysis** 통계를 활용한 시계열 데이터 분석
ARIMA 시계열 분석을 활용한 주가예측¶
1 시계열 데이터의 AR, MA 특성 찾기¶
- AR(자기회귀)의 특성 : 고유한 값을 기준으로 이동
- MA(이동평균)의 특성 : 이동평균
In [1]:
# from pandas_datareader import get_data_yahoo
# start_date = '2013-01-01'
# codes = ['KO', 'MS', '005930.KS', '000660.KS']
# result = {}
# for code in codes:
# result[code] = get_data_yahoo(code, start_date).Close
# import pandas as pd
# prices = pd.DataFrame(result)
# prices = prices.fillna(method='ffill')
# prices = prices.dropna()
# prices.to_csv('./data/stocks.csv', encoding="ms949")
# prices.tail(3)
In [2]:
# 저장된 CSV 파일을 사용한다
import pandas as pd
prices = pd.read_csv('./data/stocks.csv')
prices = prices.set_index('Date')
prices.index = pd.DatetimeIndex(prices.index)
prices.info()
<class 'pandas.core.frame.DataFrame'> DatetimeIndex: 1410 entries, 2013-01-02 to 2018-06-11 Data columns (total 4 columns): KO 1410 non-null float64 MS 1410 non-null float64 005930.KS 1410 non-null float64 000660.KS 1410 non-null float64 dtypes: float64(4) memory usage: 55.1 KB
In [3]:
price = prices.MS
price = price['2016-07-01': '2016-12-31']
price.tail()
Out[3]:
Date 2016-12-26 43.060001 2016-12-27 43.119999 2016-12-28 42.619999 2016-12-29 42.150002 2016-12-30 42.250000 Name: MS, dtype: float64
### ** 01-1. ACF & PACF Plots** 1. AR이 크면 ACF는 천천히 감소, **PACF는 급격**하게 감소 1. MA가 크면 **ACF는 급격**히 감소, PACF는 천천히 감소
pip install statsmodels==0.8.0
In [4]:
%matplotlib inline
import warnings
warnings.filterwarnings("ignore")
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
import matplotlib.pyplot as plt
plot_acf(price)
plt.show()
In [5]:
plot_pacf(price)
plt.show()
### ** 01-2. ACF & PACF Plots 2**
In [6]:
diff_1 = price.diff(periods=1).dropna()
plot_acf(diff_1)
plt.show()
In [7]:
plot_pacf(diff_1)
plt.show()
## ** 2 모형을 만들고 통계적 검정** statemodels
### **01 선형회귀모델의 생성 및 통계적해석** **OLS**
In [8]:
from sklearn.datasets import load_iris
data = load_iris()
import pandas as pd
df = pd.DataFrame(data.data)
df.columns = ['sepal_length', 'sepal_width', 'petal_length', 'petal_width']
df['class'] = [data.target_names[no] for no in data.target]
df.head(3)
Out[8]:
| sepal_length | sepal_width | petal_length | petal_width | class | |
|---|---|---|---|---|---|
| 0 | 5.1 | 3.5 | 1.4 | 0.2 | setosa |
| 1 | 4.9 | 3.0 | 1.4 | 0.2 | setosa |
| 2 | 4.7 | 3.2 | 1.3 | 0.2 | setosa |
In [9]:
# 'sepal_width', 'sepal_length'
%matplotlib inline
import matplotlib.pyplot as plt
fig, ax = plt.subplots(figsize=(4,4))
ax.scatter(df['sepal_width'][:50], df['sepal_length'][:50])
ax.set_ylabel('Sepal Length')
ax.set_xlabel('Sepal Width')
Out[9]:
Text(0.5,0,'Sepal Width')
In [10]:
import statsmodels.api as sm
y = df['sepal_length'][:50]
x = df['sepal_width'][:50]
X = sm.add_constant(x)
results = sm.OLS(y, X).fit()
print(results.summary())
OLS Regression Results
==============================================================================
Dep. Variable: sepal_length R-squared: 0.558
Model: OLS Adj. R-squared: 0.548
Method: Least Squares F-statistic: 60.52
Date: Mon, 11 Jun 2018 Prob (F-statistic): 4.75e-10
Time: 16:37:15 Log-Likelihood: 2.0879
No. Observations: 50 AIC: -0.1759
Df Residuals: 48 BIC: 3.648
Df Model: 1
Covariance Type: nonrobust
===============================================================================
coef std err t P>|t| [0.025 0.975]
-------------------------------------------------------------------------------
const 2.6447 0.305 8.660 0.000 2.031 3.259
sepal_width 0.6909 0.089 7.779 0.000 0.512 0.869
==============================================================================
Omnibus: 0.252 Durbin-Watson: 2.517
Prob(Omnibus): 0.882 Jarque-Bera (JB): 0.436
Skew: -0.110 Prob(JB): 0.804
Kurtosis: 2.599 Cond. No. 34.0
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
In [11]:
fig, ax = plt.subplots(figsize=(4,4))
ax.plot(x, results.fittedvalues, label='regression line')
ax.scatter(x, y, label='data point', color='r')
ax.set_ylabel('Sepal Length')
ax.set_xlabel('Sepal Width')
ax.legend()
Out[11]:
<matplotlib.legend.Legend at 0x7f4c1f956b70>
### **02 ARMA 모델의 생성 및 통계적해석** **ARMA**
In [12]:
price.plot()
Out[12]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f4c1f9a7278>
In [13]:
import statsmodels.tsa.api as tsa
ARMA = tsa.ARMA(price, order =(2, 1))
ARMA
Out[13]:
<statsmodels.tsa.arima_model.ARMA at 0x7f4c1f89e1d0>
In [14]:
ARMA_results= ARMA.fit()
ARMA_results.summary2()
Out[14]:
| Model: | ARMA | BIC: | 208.9308 |
| Dependent Variable: | MS | Log-Likelihood: | -92.277 |
| Date: | 2018-06-11 16:37 | Scale: | 1.0000 |
| No. Observations: | 131 | Method: | css-mle |
| Df Model: | 4 | Sample: | 07-01-2016 |
| Df Residuals: | 127 | 12-30-2016 | |
| Converged: | 1.0000 | S.D. of innovations: | 0.476 |
| AIC: | 194.5548 | HQIC: | 200.396 |
| Coef. | Std.Err. | t | P>|t| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| const | 39.8576 | 640.9964 | 0.0622 | 0.9505 | -1216.4722 | 1296.1874 |
| ar.L1.MS | 1.9731 | 0.0033 | 590.2741 | 0.0000 | 1.9665 | 1.9796 |
| ar.L2.MS | -0.9733 | 0.0122 | -80.0569 | 0.0000 | -0.9971 | -0.9494 |
| ma.L1.MS | -0.9087 | 0.6227 | -1.4593 | 0.1470 | -2.1292 | 0.3118 |
| Real | Imaginary | Modulus | Frequency | |
|---|---|---|---|---|
| AR.1 | 1.0136 | -0.0024 | 1.0136 | -0.0004 |
| AR.2 | 1.0136 | 0.0024 | 1.0136 | 0.0004 |
| MA.1 | 1.1005 | 0.0000 | 1.1005 | 0.0000 |
03 ARIMA 모델의 생성 및 통계적해석¶
ARIMA
In [15]:
from statsmodels.tsa.arima_model import ARIMA
model = ARIMA (price, order = (0, 0, 3))
model_fit = model.fit()
print(model_fit.summary())
ARMA Model Results
==============================================================================
Dep. Variable: MS No. Observations: 131
Model: ARMA(0, 3) Log Likelihood -225.805
Method: css-mle S.D. of innovations 1.308
Date: Mon, 11 Jun 2018 AIC 461.609
Time: 16:37:16 BIC 475.985
Sample: 07-01-2016 HQIC 467.451
- 12-30-2016
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const 33.8328 0.553 61.165 0.000 32.749 34.917
ma.L1.MS 1.4846 0.037 40.541 0.000 1.413 1.556
ma.L2.MS 1.5323 0.057 26.796 0.000 1.420 1.644
ma.L3.MS 0.8765 0.046 18.851 0.000 0.785 0.968
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
MA.1 -0.3040 -0.9530j 1.0003 -0.2991
MA.2 -0.3040 +0.9530j 1.0003 0.2991
MA.3 -1.1402 -0.0000j 1.1402 -0.5000
-----------------------------------------------------------------------------
/home/markbaum/Python/python/lib/python3.6/site-packages/statsmodels/base/model.py:496: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals "Check mle_retvals", ConvergenceWarning)
In [16]:
model = ARIMA(price, order = (0,0,3))
model_fit = model.fit(trend = 'c', full_output = True, disp = 1)
print(model_fit.summary())
ARMA Model Results
==============================================================================
Dep. Variable: MS No. Observations: 131
Model: ARMA(0, 3) Log Likelihood -225.805
Method: css-mle S.D. of innovations 1.308
Date: Mon, 11 Jun 2018 AIC 461.609
Time: 16:37:16 BIC 475.985
Sample: 07-01-2016 HQIC 467.451
- 12-30-2016
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const 33.8328 0.553 61.165 0.000 32.749 34.917
ma.L1.MS 1.4846 0.037 40.541 0.000 1.413 1.556
ma.L2.MS 1.5323 0.057 26.796 0.000 1.420 1.644
ma.L3.MS 0.8765 0.046 18.851 0.000 0.785 0.968
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
MA.1 -0.3040 -0.9530j 1.0003 -0.2991
MA.2 -0.3040 +0.9530j 1.0003 0.2991
MA.3 -1.1402 -0.0000j 1.1402 -0.5000
-----------------------------------------------------------------------------
/home/markbaum/Python/python/lib/python3.6/site-packages/statsmodels/base/model.py:496: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals "Check mle_retvals", ConvergenceWarning)
In [17]:
model_fit.plot_predict()
plt.grid()
plt.show()
04 ARIMA 모델로 데이터 예측하기¶
ARIMA Forcast
In [18]:
fore = model_fit.forecast(steps = 10)
len(fore)
Out[18]:
3
In [19]:
fore[0]
Out[19]:
array([40.08894159, 37.48880583, 35.21725227, 33.83283769, 33.83283769,
33.83283769, 33.83283769, 33.83283769, 33.83283769, 33.83283769])
In [20]:
fore[1]
Out[20]:
array([1.30815564, 2.34162078, 3.08240795, 3.28875563, 3.28875563,
3.28875563, 3.28875563, 3.28875563, 3.28875563, 3.28875563])
In [21]:
fore[2].shape
Out[21]:
(10, 2)
In [22]:
print('예측주가 : {} \nstderr : {} \nupper bound : {} \nlower bound : {}'.format(
fore[0],
fore[1][0],
fore[2][0][0],
fore[2][0][1]))
pd.Series(fore[0]).plot(figsize=(16,2), grid=True)
예측주가 : [40.08894159 37.48880583 35.21725227 33.83283769 33.83283769 33.83283769 33.83283769 33.83283769 33.83283769 33.83283769] stderr : 1.3081556360989681 upper bound : 37.52500365641113 lower bound : 42.65287952226525
Out[22]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f4c21e399b0>
