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In [1]:

    
print("Linear Regression Model")









    



Linear Regression Model



In [2]:

    
#Needed Libraries
%matplotlib inline
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import pandas as pd
from pandas import Series, DataFrame
from pandas import merge



In [3]:

    
#Input Variables
oilDataPath = 'https://raw.githubusercontent.com/Sree-vathsan/CSE591-Data-Science-Project/master/regressionModel/data/CRUDE_OIL_WTI_US_ENERGY_Daily_1994-10-03_2014-09-30.csv'
sp500DataPath = 'https://raw.githubusercontent.com/Sree-vathsan/CSE591-Data-Science-Project/master/regressionModel/data/YAHOO_SP500_INDEX_DAILY_1994-10-03_2014-09-30.csv'
nyseDataPath = 'https://raw.githubusercontent.com/Sree-vathsan/CSE591-Data-Science-Project/master/regressionModel/data/YAHOO_NYSE_INDEX_DAILY_1994-10-03_2014-09-30.csv'
usdIndexDataPath = 'https://raw.githubusercontent.com/Sree-vathsan/CSE591-Data-Science-Project/master/regressionModel/data/USD_Index_Daily_1994-10-03_2014-09-30.csv'
trainingRatio = 0.6
pRuns = 10 
pThreshold = 0.4



In [4]:

    
#Source Data Loading

dfOil = pd.read_csv(oilDataPath)
dfSP500 = pd.read_csv(sp500DataPath)
dfNyse = pd.read_csv(nyseDataPath)
dfUsInd = pd.read_csv(usdIndexDataPath)



In [5]:

    
dfOil.head()



In [6]:

    
dfSP500.head()









    Out[6]:






  
    
      
      Date
      SP500_Value
    
  
  
    
      0
       9/30/2014
       1972.29
    
    
      1
       9/29/2014
       1977.80
    
    
      2
       9/26/2014
       1982.85
    
    
      3
       9/25/2014
       1965.99
    
    
      4
       9/24/2014
       1998.30



In [7]:

    
dfNyse.head()



In [8]:

    
dfUsInd.head()



In [9]:

    
dfMaster = merge(dfOil,dfSP500,on='Date',how='inner')
dfMaster = merge(dfMaster,dfNyse,on='Date',how='inner')
dfMaster = merge(dfMaster,dfUsInd,on='Date',how='inner')



In [10]:

    
dfMaster.head()









    Out[10]:






  
    
      
      Date
      Oil_Value
      SP500_Value
      NYSE_Value
      USD_Value
    
  
  
    
      0
       9/30/2014
       91.17
       1972.29
       10702.93
       81.3001
    
    
      1
       9/29/2014
       94.53
       1977.80
       10749.05
       80.9136
    
    
      2
       9/26/2014
       95.55
       1982.85
       10798.88
       80.9983
    
    
      3
       9/25/2014
       93.59
       1965.99
       10722.21
       80.5957
    
    
      4
       9/24/2014
       93.60
       1998.30
       10885.60
       80.4465



In [11]:

    
#Corelation Heat Matrix

def computeDataTableCorr(datatable, columnNames):
    corrCandidates =  datatable[candidatesList]
    return corrCandidates.corr()

# Plotting correlation heat graph
def displayCorrHeatGraph(cTable, title):
    #_ = pd.scatter_matrix(corrTable, diagonal='kde', figsize=(10, 10))
    plt.imshow(cTable, cmap='hot', interpolation='none')
    plt.colorbar()
    plt.xticks(range(len(cTable)), cTable.columns, rotation=90)
    plt.yticks(range(len(cTable)), cTable.columns)
    plt.title(title)
    
candidatesList = ['Oil_Value',	'SP500_Value',	'NYSE_Value',	'USD_Value']
corrTable = computeDataTableCorr(dfMaster,candidatesList)
displayCorrHeatGraph(corrTable,'Correlation Heat Matrix (Oil_Value,SP500_Value,NYSE_Value,USD_Value)')



In [12]:

    
dfCorrOil = corrTable[:1]
dfCorrOil









    Out[12]:






  
    
      
      Oil_Value
      SP500_Value
      NYSE_Value
      USD_Value
    
  
  
    
      Oil_Value
       1
       0.626521
       0.789685
      -0.804935

More the p-Value, lesser the significance



In [16]:

    
#pValue Test
def shuffleAndCorr(df, orgCorr, runs=10, threshold=0.3, axis=0):     
    df_sh = df.copy(deep=True)
    success_count = 0
    for _ in range(runs):
        df_sh.apply(np.random.shuffle, axis=axis)
        newCor = df_sh['Col1'].corr(df_sh['Col2'])
        if (orgCorr < 0): orgCorr = orgCorr * -1
        if (newCor < 0): newCor = newCor * -1
        #print(newCor)
        diff = abs(newCor - orgCorr)
        #print(diff)
        if (diff < threshold): success_count = success_count + 1
    p = success_count / runs
    return p

dfpValue = pd.DataFrame(data=None,columns=candidatesList)
pValue = []
pValue.append(0)

for i in range(1,len(candidatesList),1):
    orgCorr = dfCorrOil[candidatesList[i]]
    #print(orgCorr)
    temp_df = pd.DataFrame({'Col1':dfMaster[candidatesList[0]], \
                                'Col2':dfMaster[candidatesList[i]]})
    pValue.append(shuffleAndCorr(temp_df,np.float(orgCorr),pRuns,pThreshold))

dfpValue.loc[0] = pValue
dfpValue









    Out[16]:






  
    
      
      Oil_Value
      SP500_Value
      NYSE_Value
      USD_Value
    
  
  
    
      0
       0
       0
       0
       0

As the pValues are all zeros, The factors does not correlates by chance.

Model 1.0: Multivariate Linear Regression



In [251]:

    
import statsmodels.api as sm



In [252]:

    
#Inputs, Train and Test Data preparation
trainSize = np.floor(len(dfMaster['Date']) * trainingRatio) #60:40 ratio
dfMasterTrain = dfMaster[len(dfMaster)-np.int(trainSize):len(dfMaster)]
dfMasterTest = dfMaster[0:np.int(trainSize)]



In [253]:

    
xArrTrain = [ \
         #np.array(dfMasterTrain[candidatesList[0]]), \
         np.array(dfMasterTrain[candidatesList[1]]), \
         np.array(dfMasterTrain[candidatesList[2]]), \
         np.array(dfMasterTrain[candidatesList[3]]), \
         ]
xArrTrain = np.array(xArrTrain)
xArrTest = [ \
         #np.array(dfMasterTest[candidatesList[0]]), \
         np.array(dfMasterTest[candidatesList[1]]), \
         np.array(dfMasterTest[candidatesList[2]]), \
         np.array(dfMasterTest[candidatesList[3]]), \
         ]
xArrTest = np.array(xArrTest)

yArrTrain = np.array(dfMasterTrain[candidatesList[0]])
yArrTest = np.array(dfMasterTest[candidatesList[0]])



In [254]:

    
def mvRegress(y, x):
    ones = np.ones(len(x[0]))
    X = sm.add_constant(np.column_stack((x[0], ones)))
    for ele in x[1:]:
        X = sm.add_constant(np.column_stack((ele, X)))
    results = sm.OLS(y, X).fit()
    return results

def mvPredict(x,res):
    ones = np.ones(len(x[0]))
    X = sm.add_constant(np.column_stack((x[0], ones)))
    for ele in x[1:]:
        X = sm.add_constant(np.column_stack((ele, X)))
    return res.predict(X)



In [255]:

    
res = mvRegress(yArrTrain, xArrTrain)



In [256]:

    
res.summary()









    Out[256]:





OLS Regression Results

  Dep. Variable:             y           R-squared:             0.817 


  Model:                    OLS          Adj. R-squared:        0.816 


  Method:              Least Squares     F-statistic:           4422. 


  Date:              Mon, 27 Oct 2014    Prob (F-statistic):     0.00  


  Time:                  06:03:32        Log-Likelihood:      -9853.8 


  No. Observations:         2985         AIC:                1.972e+04


  Df Residuals:             2981         BIC:                1.974e+04


  Df Model:                    3                                      




           coef      std err       t       P>|t|  [95.0% Conf. Int.] 


  x1        -0.4984      0.017    -28.652   0.000     -0.532    -0.464


  x2         0.0182      0.000     66.455   0.000      0.018     0.019


  x3        -0.0625      0.002    -40.188   0.000     -0.066    -0.059


  const     36.9946      1.580     23.417   0.000     33.897    40.092




  Omnibus:        19.455    Durbin-Watson:         0.017


  Prob(Omnibus):   0.000    Jarque-Bera (JB):     19.647


  Skew:           -0.190    Prob(JB):           5.42e-05


  Kurtosis:        2.887    Cond. No.           7.93e+04



In [257]:

    
#res.params
# estY = res.params[3] + (res.params[2] * xArrTest[0]) + (res.params[1] * xArrTest[1]) + (res.params[0] * xArrTest[2])
yPred0 = mvPredict(xArrTest,res)
yPred0









    Out[257]:





array([ 68.12932771,  68.81741134,  69.36694532, ...,  17.65250357,
        18.59926649,  18.22854643])



In [258]:

    
yArrTest









    Out[258]:





array([ 91.17,  94.53,  95.55, ...,  29.31,  29.56,  29.65])



In [259]:

    
def futurePredictMLR(res,sp500,nyse,usdi):
    return (res.params[3] + (res.params[2] * sp500) + (res.params[1] * nyse) + (res.params[0] * usdi))

Future Oil Price (By Model 1.0 - Multivariate Linear Regression)

OP(i) = (3.69945988e+01) + ( (-6.24695329e-02) * sp500(i) ) + ( (1.82062382e-02) * nyse(i) ) + ( (-4.98367518e-01) * usdi(i) )

Model 1.1: Polynomial Fit Regression

Time Series Analysis - Auto Regression Models

Model 1.2: Univariate Autogressive Processes (AR)

Model 1.3: Autogressive Moving-Average Processes (ARMA) and Kalman Filter

Model 1.4: Vector Autogressive Processes (VAR)

Error Metrics



In [260]:

    
from sklearn.metrics import mean_squared_error



In [261]:

    
errVar_y0 = 100 * (np.absolute(yPred0 - yArrTest) / yArrTest)
errRMS_y0 = sqrt(mean_squared_error(yArrTest,yPred0))
errABS_y0= np.absolute(yPred0-yArrTest)



In [262]:

    
dfErr = pd.DataFrame(data=None, columns=['Model','Minimum % Error','Maximum % Error', 'RMSE Error', 'Mean Absolute Error','Mean Percentage Error'])
dfErr['Model'] = ('Model 1.0','Model 1.1 (Polynomial Fit)')
dfErr['Minimum % Error'] = (min(errVar_y0),0)
dfErr['Maximum % Error'] = (max(errVar_y0),0)
dfErr['RMSE Error'] = (errRMS_y0,0)
dfErr['Mean Absolute Error'] = (np.mean(errABS_y0),0)
dfErr['Mean Percentage Error'] = (np.mean(errVar_y0),0)



In [263]:

    
dfErr









    Out[263]:






  
    
      
      Model
      Minimum % Error
      Maximum % Error
      RMSE Error
      Mean Absolute Error
      Mean Percentage Error
    
  
  
    
      0
                        Model 1.0
       0.005307
       47.564602
       21.85895
       17.587581
       21.750334
    
    
      1
       Model 1.1 (Polynomial Fit)
       0.000000
        0.000000
        0.00000
        0.000000
        0.000000



In [263]:

	Date	Oil_Value
0	9/30/2014	91.17
1	9/29/2014	94.53
2	9/26/2014	95.55
3	9/25/2014	93.59
4	9/24/2014	93.60

	Date	SP500_Value
0	9/30/2014	1972.29
1	9/29/2014	1977.80
2	9/26/2014	1982.85
3	9/25/2014	1965.99
4	9/24/2014	1998.30

	Date	NYSE_Value
0	9/30/2014	10702.93
1	9/29/2014	10749.05
2	9/26/2014	10798.88
3	9/25/2014	10722.21
4	9/24/2014	10885.60

	Date	USD_Value
0	9/30/2014	81.3001
1	9/29/2014	80.9136
2	9/26/2014	80.9983
3	9/25/2014	80.5957
4	9/24/2014	80.4465

Dep. Variable:	y	R-squared:	0.817
Model:	OLS	Adj. R-squared:	0.816
Method:	Least Squares	F-statistic:	4422.
Date:	Mon, 27 Oct 2014	Prob (F-statistic):	0.00
Time:	06:03:32	Log-Likelihood:	-9853.8
No. Observations:	2985	AIC:	1.972e+04
Df Residuals:	2981	BIC:	1.974e+04
Df Model:	3

	coef	std err	t	P>\|t\|	[95.0% Conf. Int.]
x1	-0.4984	0.017	-28.652	0.000	-0.532 -0.464
x2	0.0182	0.000	66.455	0.000	0.018 0.019
x3	-0.0625	0.002	-40.188	0.000	-0.066 -0.059
const	36.9946	1.580	23.417	0.000	33.897 40.092

Omnibus:	19.455	Durbin-Watson:	0.017
Prob(Omnibus):	0.000	Jarque-Bera (JB):	19.647
Skew:	-0.190	Prob(JB):	5.42e-05
Kurtosis:	2.887	Cond. No.	7.93e+04

	Model	Minimum % Error	Maximum % Error	RMSE Error	Mean Absolute Error	Mean Percentage Error
0	Model 1.0	0.005307	47.564602	21.85895	17.587581	21.750334
1	Model 1.1 (Polynomial Fit)	0.000000	0.000000	0.00000	0.000000	0.000000