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Mastering Time Series Analysis from Scratch: A Data Scientist’s Roadmap

Source: Medium

In this comprehensive exploration, we delve deep into the world of time series analysis, an intricate yet accessible domain within data science. Time series data, representing events measured over time, offer a wealth of information and challenges.

Take the example of a company’s daily sales totals — each day’s figure is a mesh of various influencing factors, sometimes extending from previous days. Navigating through this complexity requires not just analytical skills but also a nuanced understanding of the underlying dynamics.

1. Introduction to Time Series Data: Understanding the fundamentals of time series data, focusing on daily sales totals as an example, and highlighting the importance of recognizing influencing factors and their temporal relationships.

2. The Role of Statistical Techniques: Emphasizing the predominance of statistical methods in time series analysis, with a particular focus on understanding and validating underlying assumptions for accurate analysis.

3. Understanding ARIMA Models: Exploring the ARIMA model in-depth, discussing its reliance on the assumption of stationarity, and the implications of not validating this critical aspect.

4. Data Preparation and Analysis: Detailing the steps to prepare the time series data, including setting the date as an index and understanding the significance of chronological order.

5. Stationarity and Differencing: Demonstrating the importance of checking for stationarity using the Augmented Dickey-Fuller test and applying differencing to achieve stationarity in non-stationary data.

6. Modeling and Forecasting with ARIMA: Discussing the process of fitting an ARIMA model to the data, including the selection of parameters (p, d, q) and forecasting future sales.

7. Visualization of Forecasting Results: Providing visual representations of the ARIMA model forecasts, comparing predicted sales with historical data to offer a practical perspective for future planning.

This journey through time series analysis and ARIMA modeling is designed to not only enhance theoretical understanding but also provide practical skills applicable in diverse business scenarios. Whether you are new to the field or seeking to deepen your knowledge, this exploration offers a comprehensive guide to mastering time series analysis with ARIMA.

Introduction to Time Series Analysis and Forecasting

Our project focuses on time series analysis, a broad and multifaceted topic encompassing the analysis of time series data, the modeling of such data, and forecasting future trends. Time series analysis is pivotal in understanding and predicting data trends over time, playing a crucial role in numerous business and scientific applications.

import pandas as pd

# Loading the dataset
file_path = '/mnt/data/vendas.csv'
data = pd.read_csv(file_path)

# Display the first and last five rows of the dataset
first_five_rows = data.head()
last_five_rows = data.tail()

first_five_rows, last_five_rows

Understanding the Nature of Our Time Series Data

The dataset we are working with, ‘sales.csv’, exemplifies a typical univariate time series. This characterization stems from the fact that, aside from the date, it contains only one variable — sales volume. In time series analysis, it’s crucial to understand the role of each column in your dataset.

A key point to note is that in our dataset, the date is not just another variable; it serves as the index. While the pandas library, which we’ll be using for analysis, automatically generates a numerical index starting from zero, it’s the analyst’s responsibility to recognize that the date should be the actual index in time series analysis. This understanding transforms the sales column into our focal point, representing the phenomenon or event (i.e., sales volume) that we observe over time.

# Converting the 'Date' column to datetime 
data['Date'] = pd.to_datetime(data['Date'])

# Setting it as the index of the dataframe
data.set_index('Date', inplace=True)

# Displaying the modified dataframe

The ‘Date’ column in our dataset has now been converted to a datetime type and set as the index of the DataFrame. This modification is a crucial step in time series analysis, as it allows us to leverage the temporal aspect of the data effectively.

With the dates now serving as the index, our DataFrame is correctly formatted for time series analysis, focusing on the sales volume as the primary variable of interest. This format facilitates various time series functionalities and analysis techniques that we will explore in the subsequent stages of our project.

Analyzing Trends in Time Series Data

In time series analysis, we have several techniques to identify trends, each suitable for different scenarios. Here’s a brief overview:

import pandas as pd
import matplotlib.pyplot as plt
import statsmodels.api as sm

# Re-loading the dataset and preparing it again
file_path = 'sales.csv'
sales_data = pd.read_csv(file_path)
sales_data['Date'] = pd.to_datetime(sales_data['Data'])
sales_data.set_index('Date', inplace=True)
sales_data.rename(columns={'Vendas': 'Sales'}, inplace=True)

# Decomposing the time series into trend, seasonal and residual components
decomposition = sm.tsa.seasonal_decompose(sales_data['Sales'], model='additive')

# Plotting the decomposition
plt.figure(figsize=(14, 7))
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