Time Series Analysis with Python

Time series analysis comprises various statistical methods to analyze time series data points that are indexed in sequential order. The primary goal is to extract meaningful data and understand any underlying patterns and trends.

Time Series Analysis With Python

This article will delve deep into the core aspects of Python-based Time Series Analysis. Whether you are a beginner or an experienced data scientist working with Python, this article will help you master the complexities of Time Series Analysis.

1. Introduction to Time Series
2. Components of Time Series
3. Python Libraries for Time Series Analysis
4. Practical Examples using Python
5. Conclusion and FAQs

1. Introduction to Time Series

A series of data points ordered in time is a simple description of time series. We see it everywhere – monthly sales data, daily temperature data, stock prices and many more. The increasing capability to collect and analyze massive quantities of data has lured many industries into using time series analysis for forecasting and decision-making processes.

2. Components of Time Series

Time Series data generally has four components:

Trend: An increasing or decreasing value in the series.
Seasonality: A repeating short-term cycle in the series.
Cyclical: A long-term cycle in the series.
Irregularity: Random variance in the series.

3. Python Libraries for Time Series Analysis

Python, with its robust libraries, is a popular language for time series analysis. Key libraries include:

Pandas: Essential for data manipulation and analysis. It provides efficient data structures and functionalities to work with structured data.
Numpy: A library that provides support to handle large multidimensional arrays and matrices of numerical data. Also provides high-level mathematical functions to operate on these arrays.
Matplotlib: Used for constructing 2D and 3D graphics.
Seaborn: An advanced data visualization library based on Matplotlib. It provides a high-level interface for drawing attractive statistical graphics.
Statsmodels: A powerful library built specifically for statistics. It provides tools for the estimation of statistical models, conducting statistical tests and more. It’s the go-to library for time series analysis in Python.
Scipy: A free and open-source Python library used for scientific computing and technical computing.

To install these libraries, use the pip command: pip install libraryname

4. Practical Examples using Python

Now, let’s dive into some practical examples. We’ll start by importing the necessary libraries.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from statsmodels.tsa.arima_model import ARIMA
from statsmodels.tsa.stattools import adfuller
import warnings
warnings.filterwarnings('ignore')
%matplotlib inline

For this tutorial, we will analyze a dataset from Yahoo Finance containing the daily closing price and trading volume of the S&P 500 Index from 2010 until present day.

df = pd.read_csv('S&P500.csv')
print(df.head())

Exploratory Data Analysis

First, let’s analyze the data from different angles and visualize its different aspects.

# Plotting the closing prices
plt.figure(figsize=(10, 6))
plt.grid(True)
plt.xlabel('Dates')
plt.ylabel('Close Prices')
plt.plot(df['Close'])
plt.title('S&P500 closing price')
plt.show()

# Plotting the volume
df['Volume'].plot(kind='bar', title ="V comp", figsize=(10, 6), legend=True, fontsize=12)

This analysis will give us the first insights into the data we are dealing with. Check the trends, possible patterns and irregularities in the graphs.

Testing for Stationarity

A stationary series has constant mean and variance over time. Stationarity is an essential assumption for time series forecasting. We can perform the Augmented Dickey Fuller (ADF) test to check stationarity.

def adf_test(timeseries):
  adft = adfuller(timeseries, autolag='AIC')
  output = pd.Series(adft[0:4], index=['Test Statistic','p-value','#Lags Used','Number of Observations Used'])
  for key,value in adft[4].items():
     output['Critical Value (%s)'%key] = value
  print (output)

adf_test(df['Close'])

Implementing the ARIMA Model

ARIMA(p,d,q) model is commonly used in time series analysis. Here, p is the order of the ‘Auto Regressive’ (AR) term, q is the order of the ‘Moving Average’ (MA) term, and d is the number of differencing required to make the time series stationary.

model=ARIMA(df['Close'],order=(1,1,1)) #(p,d,q)
model_fit=model.fit(disp=0)
print(model_fit.summary())

We then plot the actual vs fitted values to understand the accuracy of our model.

model_fit.plot_predict(dynamic=False)
plt.show()

5. Conclusion and FAQs

This article aimed to provide an insight into time series analysis using Python. The Python libraries discussed and the practical examples should help get you started on your journey. Remember, practice is key when dealing with time series analysis.

FAQs

Why is stationarity important in time series analysis?
Stationarity is crucial because most of the time series models work on the assumption that the time series data are stationary. Furthermore, the theories related to stationary series are more mature and easier to implement.

Sources:

Brownlee, Jason. Python Machine Learning: Machine Learning and Deep Learning with Python, Scikit-Learn, and TensorFlow, 2nd Edition. Packt Publishing, 2020.
McKinney, Wes. Python for Data Analysis: Data Wrangling with Pandas, NumPy, and IPython. O’Reilly Media, Inc., 2018.
Ljungqvist, Lars, and Thomas J. Sargent. Recursive Macroeconomic Theory. The MIT Press, 2018.

Time Series Analysis With Python