CAD and Oil Regression Analysis

Code quant-trading

Summary

This notebook explores relationships among the Canadian dollar, crude oil benchmarks, and other currencies or commodities. It compares normalized series and fits separate ordinary least squares regressions of CAD against candidate variables, using R-squared to summarize in-sample association. It then applies K-means clustering to CAD, Western Canadian Select prices, and a time index, choosing cluster counts with elbow and silhouette diagnostics.

The notebook treats the two clusters as before and after periods, compares CAD–WCS regression fit across them, and plots fitted values with residual-based one- and two-standard-deviation bands. These are descriptive analyses, not a demonstrated trading strategy or causal test. The source data and resulting figures are not included, and the code does not report out-of-sample trading performance; clustering and regression fit alone cannot establish predictive value.

Key ideas

The notebook compares CAD with oil prices and other assets using normalized charts and univariate regressions.
It uses elbow and silhouette diagnostics to guide K-means clustering of CAD, WCS, and time.
Separate regressions and residual bands describe the relationship across the resulting time clusters.
The analysis is descriptive and supplies no evidence of causal effects or profitable trading performance.

Tags

Forex Commodities Statistics Machine learning

Full text

# Oil Money CAD.py


```py

# coding: utf-8

# In[1]:


import pandas as pd
import os
import matplotlib.pyplot as plt
import copy
import matplotlib.patches as mpatches
from mpl_toolkits import mplot3d
import matplotlib.cm as cm
import statsmodels.api as sm
import numpy as np
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score,silhouette_samples
from sklearn.model_selection import train_test_split
os.chdir('d:/')


# In[2]:

#plot two curves on same x axis, different y axis
def dual_axis_plot(xaxis,data1,data2,fst_color='r',
                    sec_color='b',fig_size=(10,5),
                   x_label='',y_label1='',y_label2='',
                   legend1='',legend2='',grid=False,title=''):
    
    fig=plt.figure(figsize=fig_size)
    ax=fig.add_subplot(111)
    

    ax.set_xlabel(x_label)
    ax.set_ylabel(y_label1, color=fst_color)
    ax.plot(xaxis, data1, color=fst_color,label=legend1)
    ax.tick_params(axis='y',labelcolor=fst_color)
    ax.yaxis.labelpad=15

    plt.legend(loc=3)
    ax2=ax.twinx()

    ax2.set_ylabel(y_label2, color=sec_color,rotation=270)
    ax2.plot(xaxis, data2, color=sec_color,label=legend2)
    ax2.tick_params(axis='y',labelcolor=sec_color)
    ax2.yaxis.labelpad=15

    fig.tight_layout()
    plt.legend(loc=4)
    plt.grid(grid)
    plt.title(title)
    plt.show()

#get distance between a point and a line
def get_distance(x,y,a,b):
    
    temp1=y-x*a-b
    temp2=(a**2+1)**0.5
    
    return np.abs(temp1/temp2)

#create line equation from two points
def get_line_params(x1,y1,x2,y2):
    
    a=(y1-y2)/(x1-x2)
    b=y1-a*x1
    
    return a,b


# In[3]:


df=pd.read_csv('wcs crude cadaud.csv',encoding='utf-8')
df.set_index('date',inplace=True)


# In[4]:


df.index=pd.to_datetime(df.index,format='%m/%d/%Y')


# In[5]:


df=df.reindex(columns=
['cny',
 'gbp',
 'usd',
 'eur',
 'krw',
 'mxn',
 'gas',
 'wcs',
 'edmonton',
 'wti',
 'gold',
 'jpy',
 'cad'])


# In[6]:

#create r squared bar charts

var=locals()

for i in df.columns:
    if i!='cad':
            x=sm.add_constant(df[i])
            y=df['cad']
            m=sm.OLS(y,x).fit()
            var[str(i)]=m.rsquared
     
ax=plt.figure(figsize=(10,5)).add_subplot(111)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

width=0.7
colorlist=['#9499a6','#9499a6','#9499a6','#9499a6',
           '#9499a6','#9499a6','#9499a6','#582a20',
           '#be7052','#f2c083','#9499a6','#9499a6']

temp=list(df.columns)
for i in temp:
    if i!='cad':
        plt.bar(temp.index(i)+width,            
            var[str(i)],width=width,label=i,
               color=colorlist[temp.index(i)])
 
plt.title('Regressions on Loonie')
plt.ylabel('R Squared\n')
plt.xlabel('\nRegressors')
plt.xticks(np.arange(len(temp))+width,
           ['Yuan', 'Sterling', 'Dollar', 'Euro', 'KRW',
             'MXN', 'Gas', 'WCS', 'Edmonton',
             'WTI', 'Gold', 'Yen'],fontsize=10)
plt.show()


# In[7]:

#normalized value of loonie,yuan and sterling

ax=plt.figure(figsize=(10,5)).add_subplot(111)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

(df['cny']/df['cny'].iloc[0]).plot(c='#77c9d4',label='Yuan')
(df['gbp']/df['gbp'].iloc[0]).plot(c='#57bc90',label='Sterling')
(df['cad']/df['cad'].iloc[0]).plot(c='#015249',label='Loonie')

plt.legend(loc=0)
plt.xlabel('Date')
plt.ylabel('Normalized Value by 100')
plt.title('Loonie vs Yuan vs Sterling')
plt.show()


# In[8]:

#normalized value of wti,wcs and edmonton

ax=plt.figure(figsize=(10,5)).add_subplot(111)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

(df['wti']/df['wti'].iloc[0]).plot(c='#2a78b2',
                                   label='WTI',alpha=0.5)
(df['wcs']/df['wcs'].iloc[0]).plot(c='#7b68ee',
                                   label='WCS',alpha=0.5)
(df['edmonton']/df['edmonton'].iloc[0]).plot(c='#110b3c',
                                             label='Edmonton',alpha=0.5)
plt.legend(loc=0)
plt.xlabel('Date')
plt.ylabel('Normalized Value by 100')
plt.title('Crude Oil Blends')
plt.show()


# In[9]:


dual_axis_plot(df.index,df['cad'],df['wcs'],
               x_label='Date',y_label1='Canadian Dollar',
               y_label2='Western Canadian Select',
               legend1='Loonie',
               legend2='WCS',
               title='Loonie VS WCS in AUD',
               fst_color='#a5a77f',sec_color='#d8dc2c')

dual_axis_plot(df.index,
               np.divide(df['cad'],df['usd']),
               np.divide(df['wcs'],df['usd']),
               x_label='Date',y_label1='Canadian Dollar',
               y_label2='Western Canadian Select',
               legend1='Loonie',
               legend2='WCS',
               title='Loonie VS WCS in USD',
               fst_color='#eb712f',sec_color='#91371b')


# In[10]:

#using elbow method to find optimal number of clusters

df['date']=[i for i in range(len(df.index))]

x=df[['cad','wcs','date']].reset_index(drop=True)

sse=[]
for i in range(1, 8):
    kmeans = KMeans(n_clusters = i)
    kmeans.fit(x)
    sse.append(kmeans.inertia_/10000)

a,b=get_line_params(0,sse[0],len(sse)-1,sse[-1])

distance=[]
for i in range(len(sse)):    
    distance.append(get_distance(i,sse[i],a,b))

dual_axis_plot(np.arange(1,len(distance)+1),sse,distance,
               x_label='Numbers of Cluster',y_label1='Sum of Squared Error',
               y_label2='Perpendicular Distance',legend1='SSE',legend2='Distance',
               title='Elbow Method for K Means',fst_color='#116466',sec_color='#e85a4f')
  
  
  
# In[11]:

#using silhouette score to find optimal number of clusters

sil=[]
for n in range(2,8):
    
    clf=KMeans(n).fit(x)
    projection=clf.predict(x)
        
    sil.append(silhouette_score(x,projection))
    
ax=plt.figure(figsize=(10,5)).add_subplot(111)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

ax.plot(np.arange(2,len(sil)+2),sil,
       label='Silhouette',c='#5c0811',
       drawstyle='steps-mid')
ax.plot(sil.index(max(sil))+2,max(sil),
        marker='*',markersize=20,lw=0,
       label='Max Score',c='#d94330')

plt.ylabel('Silhouette Score')
plt.xlabel('Numbers of Cluster')
plt.title('Silhouette Analysis for K Means')
plt.legend(loc=0)
plt.show()


# In[12]:

#k means

clf=KMeans(n_clusters=2).fit(x)
df['class']=clf.predict(x)
threshold=df[df['class']==0].index[-1]


# In[13]:

#plot clusters in 3d figure

ax=plt.figure(figsize=(10,7)).add_subplot(111, projection='3d')


xdata=df['wcs']
ydata=df['cad']
zdata=df['date']
ax.scatter3D(xdata[df['class']==0],ydata[df['class']==0],
             zdata[df['class']==0],c='#faed26',s=10,alpha=0.5,
             label='Before {}'.format(threshold.strftime('%Y-%m-%d')))
ax.scatter3D(xdata[df['class']==1],ydata[df['class']==1],
             zdata[df['class']==1],c='#46344e',s=10,alpha=0.5,
             label='After {}'.format(threshold.strftime('%Y-%m-%d')))
ax.grid(False)
for i in ax.w_xaxis, ax.w_yaxis, ax.w_zaxis:
    i.pane.set_visible(False)  
    
ax.set_xlabel('WCS')
ax.set_ylabel('Loonie')
ax.set_zlabel('Date')
ax.set_title('K Means on Loonie')
ax.legend(loc=6,bbox_to_anchor=(0.12, -0.1), ncol=4)

plt.show()

#to generate gif, u can use the following code
#it generates 3d figures from different angles
#use imageio to concatenate 
"""
for ii in range(0,360,10):
    ax.view_init(elev=10., azim=ii)
    plt.savefig("cad kmeans%d.png" % (ii))

import imageio

filenames=["movie%d.png" % (ii) for ii in range(0,360,10)] 

images=list(map(lambda filename:imageio.imread(filename),
                filenames))

imageio.mimsave('cad kmeans.gif',images,duration = 0.2)
"""

# In[14]:

#create before/after regression comparison
#the threshold is based upon the finding of k means

m=sm.OLS(df['cad'][df['class']==0],sm.add_constant(df['wcs'][df['class']==0])).fit()
before=m.rsquared
m=sm.OLS(df['cad'][df['class']==1],sm.add_constant(df['wcs'][df['class']==1])).fit()
after=m.rsquared

ax=plt.figure(figsize=(10,5)).add_subplot(111)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
plt.bar(['Before {}'.format(threshold.strftime('%Y-%m-%d')),
         'After {}'.format(threshold.strftime('%Y-%m-%d'))],
        [before,after],color=['#f172a1','#a1c3d1'])
plt.ylabel('R Squared')
plt.title('Cluster + Regression')
plt.show()



# In[15]:

#create 1 std, 2 std band

for i in range(2):
    
    x_train,x_test,y_train,y_test=train_test_split(
        sm.add_constant(df['wcs'][df['class']==i]),
        df['cad'][df['class']==i],test_size=0.5,shuffle=False)
    
    m=sm.OLS(y_test,x_test).fit()
    
    forecast=m.predict(x_test)
    
    ax=plt.figure(figsize=(10,5)).add_subplot(111)
    ax.spines['top'].set_visible(False)
    ax.spines['right'].set_visible(False)
    forecast.plot(label='Fitted',c='#ab987a')
    y_test.plot(label='Actual',c='#ff533d')
    ax.fill_between(y_test.index,
                    forecast+np.std(m.resid),
                    forecast-np.std(m.resid),
                    color='#0f1626', \
                    alpha=0.6, \
                    label='1 Sigma')
    
    ax.fill_between(y_test.index,
                    forecast+2*np.std(m.resid),
                    forecast-2*np.std(m.resid),
                    color='#0f1626', \
                    alpha=0.8, \
                    label='2 Sigma')
    
    plt.legend(loc=0)
    title='Before '+threshold.strftime('%Y-%m-%d') if i==0 else 'After '+threshold.strftime('%Y-%m-%d')
    plt.title(f'{title}\nCanadian Dollar Positions\nR Squared {round(m.rsquared*100,2)}%\n')
    plt.xlabel('\nDate')
    plt.ylabel('CADAUD')
    plt.show()





```

Shown in full with attribution under the source's licence. Licence: Apache-2.0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.

Analyzing CAD and Oil Relationships with Regression and Clustering

Summary

Key ideas

Tags