Year-by-Year OLS Analysis of Ruble Exchange Rate Regressors
Code quant-trading
Summary
This notebook explores how several market series relate to the Russian ruble exchange rate against the Australian dollar. It fits separate ordinary least squares regressions for each candidate regressor within each year, then repeats the analysis cumulatively through successive years. It plots the resulting R-squared values to compare how explanatory fit changes over time. Additional charts compare observed and fitted exchange rates using Urals crude alone for 2017–2018 and Urals crude plus the euro through 2016.
For a simple annual forecasting exercise, the notebook fits a crude-only model on the first third of each year and predicts the remaining observations, displaying residual-based one- and two-standard-deviation bands. These plots illustrate changing relationships and basic regression diagnostics, but the notebook gives no reported numerical conclusions or trading results. R-squared is not evidence of predictive or causal value, and the approach does not address serial dependence, model selection bias, transaction costs, or robust out-of-sample validation. The code also relies on a local data file and fixed chart labels.
Key ideas
- The notebook compares each regressor’s annual and cumulative in-sample R-squared for the ruble exchange rate.
- Separate fitted charts examine crude oil and euro relationships in different historical periods.
- A yearly split fits on the earlier third of observations and forecasts the remaining portion.
- Residual standard deviations are used to draw simple forecast bands.
- The analysis does not establish causation or demonstrate a profitable trading strategy.
Tags
Full text
# Oil Money RUB.py
```py
# coding: utf-8
# In[1]:
import os
import pandas as pd
import numpy as np
import statsmodels.api as sm
import matplotlib.pyplot as plt
import re
os.chdir('d:/')
df=pd.read_csv('urals crude rubaud.csv')
# In[2]:
df.set_index('date',inplace=True)
df.index=pd.to_datetime(df.index)
df.dropna(inplace=True)
# In[3]:
#this is the part to create r squared of different regressors
#in different years for stepwise regression
#we can use locals to create lists for different currency
#each list contains r squared of different years
year=df.index.year.drop_duplicates().tolist()
var=locals()
for i in df.columns:
if i!='rub':
var[i]=[]
for j in year:
x=sm.add_constant(df[i][str(j):str(j)])
y=df['rub'][str(j):str(j)]
m=sm.OLS(y,x).fit()
var[i].append(m.rsquared)
ax=plt.figure(figsize=(10,5)).add_subplot(111)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
#to save you from the hassle
#just use these codes to generate the bar chart
width=0.3
colorlist=['#c0334d','#d6618f','#f3d4a0','#f1931b']
bar=locals()
for j in range(len(year)):
bar[j]=[var[i][j] for i in df.columns if i!='rub']
plt.bar(np.arange(1,len([i for i in df.columns if i!='rub'])*2+1,2)+j*width,
bar[j],width=width,label=year[j],color=colorlist[j])
plt.legend(loc=0)
plt.title('Stepwise Regression Year by Year')
plt.ylabel('R Squared')
plt.xlabel('Regressors')
plt.xticks(np.arange(1,len([i for i in df.columns if i!='rub'])*2+1,2)+(len(year)-1)*width/2,
['Urals Crude', 'Japanese\nYen',
'Euro', 'Henry Hub', 'Chinese\nYuan',
'Korean\nWon', 'Ukrainian\nHryvnia'],fontsize=10)
plt.show()
# In[4]:
#this is similar to In[3]
#In[3] is r squared of each regressor in each year
#In[4] is r squared of each regressor of years cumulated
var=locals()
for i in df.columns:
if i!='rub':
var[i]=[]
for j in year:
x=sm.add_constant(df[i][:str(j)])
y=df['rub'][:str(j)]
m=sm.OLS(y,x).fit()
var[i].append(m.rsquared)
ax=plt.figure(figsize=(10,5)).add_subplot(111)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
width=0.3
colorlist=['#04060f','#03353e','#0294a5','#a79c93']
bar=locals()
for j in range(len(year)):
bar[j]=[var[i][j] for i in df.columns if i!='rub']
plt.bar(np.arange(1,len([i for i in df.columns if i!='rub'])*2+1,2)+j*width,
bar[j],width=width,label=year[j],color=colorlist[j])
plt.legend(loc=0)
plt.title('Stepwise Regression Year Cumulated')
plt.ylabel('R Squared')
plt.xlabel('Regressors')
plt.xticks(np.arange(1,len([i for i in df.columns if i!='rub'])*2+1,2)+(len(year)-1)*width/2,
['Urals Crude', 'Japanese\nYen',
'Euro', 'Henry Hub', 'Chinese\nYuan',
'Korean\nWon', 'Ukrainian\nHryvnia'],fontsize=10)
plt.show()
# In[5]:
#print model summary and actual vs fitted line chart
x=sm.add_constant(pd.concat([df['urals']],axis=1))
y=df['rub']
m=sm.OLS(y['2017':'2018'],x['2017':'2018']).fit()
print(m.summary())
ax=plt.figure(figsize=(10,5)).add_subplot(111)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.plot(df.loc['2017':'2018'].index,m.predict(), \
c='#0abda0',label='Fitted')
ax.plot(df.loc['2017':'2018'].index, \
df['rub']['2017':'2018'],c='#132226',label='Actual')
plt.legend(loc=0)
plt.title('Russian Ruble 2017-2018')
plt.ylabel('RUBAUD')
plt.xlabel('Date')
plt.show()
# In[6]:
#print model summary and actual vs fitted line chart
x=sm.add_constant(pd.concat([df['urals'],df['eur']],axis=1))
y=df['rub']
m=sm.OLS(y[:'2016'],x[:'2016']).fit()
print(m.summary())
ax=plt.figure(figsize=(10,5)).add_subplot(111)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
plt.plot(df.loc[:'2016'].index,m.predict(), \
c='#c05640',label='Fitted')
plt.plot(df.loc[:'2016'].index,df['rub'][:'2016'], \
c='#edd170',label='Actual')
plt.legend(loc=0)
plt.title('Russian Ruble Before 2017')
plt.ylabel('RUBAUD')
plt.xlabel('Date')
plt.show()
# In[7]:
#normalize different regressors by 100 as the initial value
#so that we can observe the trend of different regressors in the same scale
ax=plt.figure(figsize=(10,5)).add_subplot(111)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
(df['urals']['2017':'2018']/df['urals']['2017':'2018'].iloc[0]*100).plot(label='Urals Crude',c='#728ca3',alpha=0.5)
(df['jpy']['2017':'2018']/df['jpy']['2017':'2018'].iloc[0]*100).plot(label='Japanese Yen',c='#99bfaa')
(df['eur']['2017':'2018']/df['eur']['2017':'2018'].iloc[0]*100).plot(label='Euro',c='#5c868d')
(df['rub']['2017':'2018']/df['rub']['2017':'2018'].iloc[0]*100).plot(label='Russian Ruble',c='#000000')
plt.legend(loc=0)
plt.title('2017-2018 Trend')
plt.ylabel('Normalized Value by 100')
plt.xlabel('Date')
plt.show()
# In[8]:
#plot actual vs fitted line chart for each year
#including one sigma and two sigma confidence interval
for i in df.index.year.drop_duplicates():
temp=df.loc[str(i):str(i)]
train=temp.iloc[:int(len(temp)/3)]
test=temp.iloc[int(len(temp)/3):]
x=sm.add_constant(train['urals'])
y=train['rub']
m=sm.OLS(y,x).fit()
forecast=m.predict(sm.add_constant(test['urals']))
resid=np.std(train['rub']-m.predict())
ax=plt.figure(figsize=(10,5)).add_subplot(111)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.plot(test.index, \
forecast, \
label='Fitted',c='#f5ca99')
test['rub'].plot(label='Actual',c='#ed5752')
ax.fill_between(test.index, \
forecast+resid, \
forecast-resid, \
color='#1e1f26', \
alpha=0.8, \
label='1 Sigma')
ax.fill_between(test.index, \
forecast+2*resid, \
forecast-2*resid, \
color='#d0e1f9', \
alpha=0.7, \
label='2 Sigma')
plt.legend(loc='best')
plt.title(f'{i} Russian Ruble Positions\nR Squared {round(m.rsquared*100,2)}%\n')
plt.ylabel('RUBAUD')
plt.xlabel('Date')
plt.legend()
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.