how to get correct correlation plot on time series data with matplotlib/seaborn?

Question

I have time-series data that collected weekly basis, where I want to see the correlation of its two columns. to do so, I could able to find a correlation between two columns and want to see how rolling correlation moves each year. my current approach works fine but I need to normalize the two columns before doing rolling correlation and making a line plot. In my current attempt, I don't know how to show 3-year, 5 year rolling correlation. Can anyone suggest a possible idea of doing this in matplotlib?

current attempt:

Here is my current attempt:

import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

dataPath="https://gist.github.com/jerry-shad/503a7f6915b8e66fe4a0afbc52be7bfa#file-sample_data-csv"

def ts_corr_plot(dataPath, roll_window=4):
    df = pd.read_csv(dataPath)
    df['Date'] = pd.to_datetime(df['Date'])
    df['week'] = pd.DatetimeIndex(df['date']).week
    df['year'] = pd.DatetimeIndex(df['date']).year
    df['week'] = df['date'].dt.strftime('%W').astype('uint8')
    
    def find_corr(x):
        df = df.loc[x.index]
        return df[:, 1].corr(df[:, 2])
    
    df['corr'] = df['week'].rolling(roll_window).apply(find_corr)
    fig, ax = plt.subplots(figsize=(7, 4), dpi=144)
    sns.lineplot(x='week', y='corr', hue='year', data=df,alpha=.8)
    plt.show()
    plt.close

update:

I want to see rolling correlation in different time window such as:

plt_1 = ts_corr_plot(dataPath, roll_window=4)
plt_2 = ts_corr_plot(dataPath, roll_window=12)
plt_3 = ts_corr_plot(dataPath, roll_window=24)

I need to add 3-years, 5-years rolling correlation to the plots but I couldn't find a better way of doing this. Can anyone point me out how to make a rolling correlation line plot for time series data? How can I improve the current attempt? any idea?

desired plot

this is my expected plot that I want to obtain:

Answer 1

Customizing the legend in esaborn is painstaking, so I created the code in matplotlib.

1. Corrected the method for calculating the correlation coefficient. Your code gave me an error, so please correct me if I'm wrong.
2. The color of the line graph seems to be the color of the tableau from the desired graph color, so I used the 10 colors of the tableau defined in matplotlib.
3. To calculate the correlation coefficient for 3 years, I am using 156 line units, which is 3 years of weekly data. Please correct this logic if it is wrong.
4. I am creating 4-week and 3-year graphs in a loop process respectively.

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

dataPath="https://gist.githubusercontent.com/jerry-shad/503a7f6915b8e66fe4a0afbc52be7bfa/raw/414a2fc2988fcf0b8e6911d77cccfbeb4b9e9664/sample_data.csv"

df = pd.read_csv(dataPath)
df['Date'] = pd.to_datetime(df['Date'])
df['week'] = df['Date'].dt.isocalendar().week
df['year'] = df['Date'].dt.year
df['week'] = df['Date'].dt.strftime('%W').astype('uint8')

def find_corr(x):
    dfc = df.loc[x.index]
    tmp = dfc.iloc[:, [1,2]].corr()
    tmp = tmp.iloc[0,1]
    return tmp

roll_window=4
df['corr'] = df['week'].rolling(roll_window).apply(find_corr)
df3 = df.copy() # three year
df3['corr3'] = df3['year'].rolling(156).apply(find_corr) # 3 year = 52 week x 3 year = 156 

fig, ax = plt.subplots(figsize=(12, 4), dpi=144)
cmap = plt.get_cmap("tab10")

for i,y in enumerate(df['year'].unique()):
    tmp = df[df['year'] == y]
    ax.plot(tmp['week'], tmp['corr'], color=cmap(i), label=y)

for i,y in enumerate(df['year'].unique()):
    tmp = df3[df3['year'] == y]
    if tmp['corr3'].notnull().all():
        ax.plot(tmp['week'], tmp['corr3'], color=cmap(i), lw=3, linestyle='--', label=str(y)+' 3 year avg')

ax.grid(axis='both')
ax.legend(loc='upper left', bbox_to_anchor=(1.0, 1.0), borderaxespad=1)
plt.show()
# plt.close