Class03 Answer:

Show a plot of the fitted line on top of the 2016 prices

I use NumPy, Pandas below.


This script should plot a fitted line on top of the 2016 prices.


import pandas as pd
import numpy  as np
import matplotlib.pyplot as plt

csvfile_s  = ''
cp_df      = pd.read_csv(csvfile_s).sort_values(['cdate'])
cp2016_sr  = (cp_df.cdate > '2016') & (cp_df.cdate < '2017')
cp2016_df  = cp_df[['cdate','cp']].loc[cp2016_sr]
daycount_i = cp2016_df.index.size

def colvec(arylst):
    # This should help me create column vectors from arrays or lists:
    rowcount_i = len(arylst)
    return np.array(arylst).reshape((rowcount_i,1))

# Study this image:
# Y is easy to get, I should get Y first.
# I should transform the prices into a column vector of y-values:
yvals_a = colvec(cp2016_df.cp)

# Next I should work with X.

# I simplify; X-values are simple integers starting at 0:
x_a = colvec(range(daycount_i))
# Notice that I reshaped it into a column.
# I should pre-pend a column vector of ones:

ones_l = [1]*daycount_i
ones_a = colvec(ones_l)

# I should build xvals_a from column of ones then integers:
xvals_a = np.hstack((ones_a,x_a))

# Now, I have X and Y, I should implement Linear Algebra with NumPy:
lhs_a = np.linalg.pinv(np.matmul(xvals_a.T,xvals_a))
rhs_a = np.matmul(xvals_a.T,yvals_a)
w_a   = np.matmul(lhs_a,rhs_a)

x_in_a = xvals_a
yhat_a = np.matmul(x_in_a, w_a)
cp2016_df['yhat'] = yhat_a

# To make a better plot I should convert X-values from integers to series of strings:
cpdate2016_df = cp2016_df.set_index(['cdate'])
# I should plot cp (closing price), and fitted line:
cpdate2016_df.plot.line(title="GSPC 2016")

# If X-axis is missing labels, I should experiment with plt.xticks():
# plt.xticks(some_tuple_orlist, another_tuple_orlist, rotation=45) 
# Ref:

# xticks1_l = [-50.,   0.,  50., 100., 150., 200., 250., 300.]
# xticks2_l = ['','Jan','Mar','May','Jul','Sep','Dec','']
# plt.xticks(xticks1_l, xticks2_l, rotation=-45)


I ran the above script and saw this:

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