Time Series Analysis of AirPassengers: Unraveling Trends and Forecasting Future Demands

Introduction:

In the realm of data analysis, understanding trends, patterns, and behaviors over time is a crucial aspect. Time Series Analysis, a powerful statistical method, provides us with the tools to dissect temporal data and extract meaningful insights. In this blog, we’ll embark on a journey through the fundamental concepts, techniques, and applications of Time Series Analysis.

What is Time Series:

A time series is a sequence of data points collected or recorded at regular intervals over time. These data points can represent various phenomena, such as stock prices, temperature readings, sales figures, and more. Time Series Analysis aims to unveil inherent structures within the data, allowing us to make predictions, identify patterns, and gain a deeper understanding of the underlying processes.

Applications of Time Series Analysis:

Time series analysis finds widespread applications across various domains. In finance, it is employed for predicting stock prices, identifying market trends, and assessing risk. In healthcare, time series analysis is utilized for forecasting patient admissions, tracking disease outbreaks, and monitoring vital signs over time. Weather prediction relies on time series modeling to anticipate climate patterns and trends. Additionally, businesses leverage time series analysis to predict demand, manage inventory, and optimize production schedules, contributing to more informed decision-making.

Now lets dive deep into the example to understand time series analysis better.

Lets delve into the captivating realm of time series data with a focus on air passenger traffic. Air travel has not only transformed the way we connect with the world but has also become a key barometer of economic activity. Leveraging the widely-used AirPassengers dataset, which spans monthly air passenger counts from 1949 to 1960, we aim to unravel underlying trends, patterns, and seasonality within this temporal data. This exploration provides a valuable opportunity to showcase the power of time series analysis in understanding historical trajectories and making informed predictions for future demands in the aviation sector. As we navigate through the data, we will employ statistical methods and visualization techniques to extract meaningful insights, shedding light on the dynamics of air travel over the studied period.

library(tidyverse)

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library(ggplot2)
library(forecast)

## Warning: package 'forecast' was built under R version 4.3.2

## Registered S3 method overwritten by 'quantmod':
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# Load AirPassengers dataset
url <- "https://raw.githubusercontent.com/Naik-Khyati/data_621/main/blogs/blog%204/AirPassengers.csv"
air_passengers <- read.csv(url)

# Convert the 'Month' column to a Date format
air_passengers$Month <- as.Date(paste(air_passengers$Month, "-01", sep=""), format = "%Y-%m-%d")

# Check the structure of the dataset
str(air_passengers)

## 'data.frame':    144 obs. of  2 variables:
##  $ Month       : Date, format: "1949-01-01" "1949-02-01" ...
##  $ X.Passengers: int  112 118 132 129 121 135 148 148 136 119 ...

# Convert the 'Month' column to a Date format
air_passengers$Month <- as.Date(paste(air_passengers$Month, "-01", sep=""), format = "%Y-%m-%d")

# Visualize the time series
ggplot(air_passengers, aes(x = Month, y = X.Passengers)) +
  geom_line() +
  labs(title = "AirPassengers Time Series",
       x = "Month",
       y = "Passengers")

# Time series decomposition
air_passengers_ts <- ts(air_passengers$X.Passengers, frequency = 12)
decomposition <- decompose(air_passengers_ts)
plot(decomposition)

# Check for seasonality and trend
autoplot(air_passengers_ts) +
  labs(title = "AirPassengers Time Series",
       x = "Year",
       y = "Passengers")

# Fit a time series model
fit <- auto.arima(air_passengers_ts)
summary(fit)

## Series: air_passengers_ts 
## ARIMA(2,1,1)(0,1,0)[12] 
## 
## Coefficients:
##          ar1     ar2      ma1
##       0.5960  0.2143  -0.9819
## s.e.  0.0888  0.0880   0.0292
## 
## sigma^2 = 132.3:  log likelihood = -504.92
## AIC=1017.85   AICc=1018.17   BIC=1029.35
## 
## Training set error measures:
##                  ME     RMSE     MAE      MPE     MAPE     MASE        ACF1
## Training set 1.3423 10.84619 7.86754 0.420698 2.800458 0.245628 -0.00124847

# Forecast future values
forecast_values <- forecast(fit, h = 24)
plot(forecast_values, main = "AirPassengers Forecast")

Analysis

The time series plot shows a clear increasing trend and seasonality.
The decomposition plot reveals the trend, seasonality, and remainder components.
The autocorrelation plot confirms the seasonality, with a clear pattern every 12 months.
The fitted ARIMA model indicates significant coefficients for the trend and seasonality components.
The forecast plot provides future predictions based on the time series model.

Conclusion

The AirPassengers dataset exhibits a strong increasing trend and seasonality, suggesting a consistent growth in the number of passengers over the years with recurring patterns. The ARIMA model successfully captures these components, providing a basis for forecasting future passenger counts. The analysis aids in understanding the underlying patterns in air passenger data, which is valuable for making informed predictions and decisions related to the aviation industry.