# This Python 3 environment comes with many helpful analytics libraries installed
# It is defined by the kaggle/python Docker image: https://github.com/kaggle/docker-python
# For example, here's several helpful packages to load


import numpy as np # linear algebra
import pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)


import matplotlib as mpl
import matplotlib.pyplot as plt   # data visualization
import seaborn as sns             # statistical data visualization


# Input data files are available in the read-only "../input/" directory
# For example, running this (by clicking run or pressing Shift+Enter) will list all files under the input directory

import os
for dirname, _, filenames in os.walk('/kaggle/input'):
    for filename in filenames:
        print(os.path.join(dirname, filename))

# You can write up to 5GB to the current directory (/kaggle/working/) that gets preserved as output when you create a version using "Save & Run All" 
# You can also write temporary files to /kaggle/temp/, but they won't be saved outside of the current session

path = 'https://raw.githubusercontent.com/pik1989/TimeSeriesAnalysis/main/AirPassengers.csv'

df = pd.read_csv(path)

df.head(10)

df.columns = ['Date','Number of Passengers']

df.head()

def plot_df(df, x, y, title="", xlabel='Date', ylabel='Number of Passengers', dpi=100):
    plt.figure(figsize=(15,4), dpi=dpi)
    plt.plot(x, y, color='tab:red')
    plt.gca().set(title=title, xlabel=xlabel, ylabel=ylabel)
    plt.show()
    

plot_df(df, x=df['Date'], y=df['Number of Passengers'], title='Number of US Airline passengers from 1949 to 1960')

x = df['Date'].values
y1 = df['Number of Passengers'].values

# Plot
fig, ax = plt.subplots(1, 1, figsize=(16,5), dpi= 120)
plt.fill_between(x, y1=y1, y2=-y1, alpha=0.5, linewidth=2, color='seagreen')
plt.ylim(-800, 800)
plt.title('Air Passengers (Two Side View)', fontsize=16)
plt.hlines(y=0, xmin=np.min(df['Date']), xmax=np.max(df['Date']), linewidth=.5)
plt.show()

def plot_df(df, x, y, title="", xlabel='Date', ylabel='Number of Passengers', dpi=100):
    plt.figure(figsize=(15,4), dpi=dpi)
    plt.plot(x, y, color='blue')
    plt.gca().set(title=title, xlabel=xlabel, ylabel=ylabel)
    plt.show()
    

plot_df(df, x=df['Date'], y=df['Number of Passengers'], title='Trend and Seasonality')

from statsmodels.tsa.seasonal import seasonal_decompose
from dateutil.parser import parse


# Multiplicative Decomposition 
multiplicative_decomposition = seasonal_decompose(df['Number of Passengers'], model='multiplicative', period=30)

# Additive Decomposition
additive_decomposition = seasonal_decompose(df['Number of Passengers'], model='additive', period=30)

# Plot
plt.rcParams.update({'figure.figsize': (16,12)})
multiplicative_decomposition.plot().suptitle('Multiplicative Decomposition', fontsize=16)
plt.tight_layout(rect=[0, 0.03, 1, 0.95])

additive_decomposition.plot().suptitle('Additive Decomposition', fontsize=16)
plt.tight_layout(rect=[0, 0.03, 1, 0.95])

plt.show()

rand_numbers = np.random.randn(1000)
pd.Series(rand_numbers).plot(title='Random White Noise', color='b')

# Using scipy: Subtract the line of best fit
from scipy import signal
detrended = signal.detrend(df['Number of Passengers'].values)
plt.plot(detrended)
plt.title('Air Passengers detrended by subtracting the least squares fit', fontsize=16)

# Using statmodels: Subtracting the Trend Component
from statsmodels.tsa.seasonal import seasonal_decompose
result_mul = seasonal_decompose(df['Number of Passengers'], model='multiplicative', period=30)
detrended = df['Number of Passengers'].values - result_mul.trend
plt.plot(detrended)
plt.title('Air Passengers detrended by subtracting the trend component', fontsize=16)

# Subtracting the Trend Component


# Time Series Decomposition
result_mul = seasonal_decompose(df['Number of Passengers'], model='multiplicative', period=30)


# Deseasonalize
deseasonalized = df['Number of Passengers'].values / result_mul.seasonal


# Plot
plt.plot(deseasonalized)
plt.title('Air Passengers Deseasonalized', fontsize=16)
plt.plot()

# Test for seasonality
from pandas.plotting import autocorrelation_plot

# Draw Plot
plt.rcParams.update({'figure.figsize':(10,6), 'figure.dpi':120})
autocorrelation_plot(df['Number of Passengers'].tolist())

from statsmodels.tsa.stattools import acf, pacf
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

# Draw Plot
fig, axes = plt.subplots(1,2,figsize=(16,3), dpi= 100)
plot_acf(df['Number of Passengers'].tolist(), lags=50, ax=axes[0])
plot_pacf(df['Number of Passengers'].tolist(), lags=50, ax=axes[1])

from pandas.plotting import lag_plot
plt.rcParams.update({'ytick.left' : False, 'axes.titlepad':10})

# Plot
fig, axes = plt.subplots(1, 4, figsize=(10,3), sharex=True, sharey=True, dpi=100)
for i, ax in enumerate(axes.flatten()[:4]):
    lag_plot(df['Number of Passengers'], lag=i+1, ax=ax, c='firebrick')
    ax.set_title('Lag ' + str(i+1))

fig.suptitle('Lag Plots of Air Passengers', y=1.05)    
plt.show()

from statsmodels.tsa.stattools import grangercausalitytests
data = pd.read_csv('/kaggle/input/dataset/dataset.txt')
data['date'] = pd.to_datetime(data['date'])
data['month'] = data.date.dt.month
grangercausalitytests(data[['value', 'month']], maxlag=2)

	Month	#Passengers
0	1949-01	112
1	1949-02	118
2	1949-03	132
3	1949-04	129
4	1949-05	121
5	1949-06	135
6	1949-07	148
7	1949-08	148
8	1949-09	136
9	1949-10	119

	Date	Number of Passengers
0	1949-01	112
1	1949-02	118
2	1949-03	132
3	1949-04	129
4	1949-05	121

Complete Guide on Time Series Analysis in Python¶

I hope you find this notebook useful and your UPVOTES keep me motivated.¶

Table of Contents¶

1. Introduction to Time-Series Analysis ¶

Components of a Time-Series¶

2. Types of data ¶

3. Time Series terminology ¶

4. Time Series Analysis ¶

4.1 Basic set up ¶

4.2 Import data ¶

5. Visualize the Time Series ¶

6. Patterns in a Time Series ¶

Trend¶

Seasonality¶

Cyclic behaviour¶

7. Additive and Multiplicative Time Series ¶

Additive time series:¶

Multiplicative Time Series:¶

8. Decomposition of a Time Series ¶

9. Stationary and Non-Stationary Time Series ¶

10. How to make a time series stationary? ¶

10.1 Introduction to Differencing ¶

10.2 Reasons to convert a non-stationary series into stationary one before forecasting ¶

11. How to test for stationarity? ¶

11.1 Augmented Dickey Fuller test (ADF Test) ¶

11.2 Kwiatkowski-Phillips-Schmidt-Shin – KPSS test (trend stationary) ¶

11.3 Philips Perron test (PP Test) ¶

12. Difference between white noise and a stationary series ¶

13. Detrend a Time Series ¶

14. Deseasonalize a Time Series ¶

15. How to test for seasonality of a time series? ¶

16. Autocorrelation and Partial Autocorrelation Functions ¶

17. Computation of Partial Autocorrelation Function ¶

18. Lag Plots ¶

19. Granger Causality Test ¶

20. Smoothening a Time Series ¶

Moving Average¶

Localized Regression¶

21. References ¶