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Time Series Analysis in R Studio using AirPassengers dataset

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Time Series Analysis in R Studio using AirPassengers dataset

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  1. Time Series Analysis in R Studio using Air Passengers dataset www.statisticshelpdesk.com

  2. Introduction Let’s dive into time series analysis using a popular dataset in R. We'll use the Air Passengers dataset, which is widely used for time series analysis. This dataset includes the total count of the international airline passengers (in thousands) from the year 1949 to 1960 in monthly terms. The objective here will be to make uses of ARIMA (AutoRegressive Integrated Moving Average) model and explore the patterns, decompose the series, as well as predict future values. www.statisticshelpdesk.com

  3. Research Question How well can we model and forecast the number of international airline passengers for future periods using the historical data from 1949-1960? www.statisticshelpdesk.com

  4. Step-by-Step Analysis www.statisticshelpdesk.com

  5. Step 1: Loading the Dataset and Packages We will load the AirPassengers dataset and the necessary libraries in R. Output: This will show the monthly passenger counts over the time span of 1949-1960. # Load necessary libraries library(forecast) library(tseries) library(ggplot2) # Load the AirPassengers dataset data("AirPassengers") # Convert to a time series object if not already AP_ts <- ts(AirPassengers, frequency = 12, start = c(1949,1)) # View the first few rows print(AP_ts) www.statisticshelpdesk.com

  6. Step 2: Visualizing the Time Series Data Let’s plot the dataset to observe any trends, seasonality, or cyclical patterns. # Plot the time series plot(AP_ts, of Passengers (Thousands)", xlab="Year") main="Monthly Airline Passengers (1949-1960)", ylab="Number Interpretation of Plot: • There is a noticeable upward trend, indicating a growing number of airline passengers over time. • There also appears to be some seasonality, as the number of passengers fluctuates regularly each year. www.statisticshelpdesk.com

  7. Step 3: Decomposing the Time Series To better understand the components (trend, seasonality, noise), we’ll decompose the time series into these parts. # Decompose the time series decomposed_AP <- decompose(AP_ts) plot(decomposed_AP) Interpretation of Plot: •Trend: The upward trend is confirmed, with more passengers as time progresses. •Seasonality: There is a recurring pattern every year, indicating a seasonal component. •Random/Noise: The irregular part seems random, with no obvious structure. www.statisticshelpdesk.com

  8. Step 4: Making the Time Series Stationary Before applying ARIMA, we need to make the series stationary. We'll use the Augmented Dickey-Fuller (ADF) test to check for stationarity and differentiate the series if necessary. # Perform the Augmented Dickey-Fuller Test adf_test <- adf.test(AP_ts) print(adf_test) Output: If the p-value is greater than 0.05, the series is non-stationary, and we need to differentiate it. Since the data is likely non-stationary, we’ll apply differencing: # Differencing the data to make it stationary diff_AP_ts <- diff(AP_ts) plot(diff_AP_ts, main="Differenced Time Series") www.statisticshelpdesk.com

  9. Step 5: Fitting an ARIMA Model # Fit the ARIMA model fit <- auto.arima(AP_ts) print(fit) Now that we have a stationary series, we can fit an ARIMA model. Output: This will show the best ARIMA model chosen based on the AIC criterion. Interpretation of the ARIMA Model: The output might suggest a model like ARIMA(0,1,1)(0,1,1)[12]. This means: •Non-seasonal difference: 1 (d=1) •Seasonal difference: 1 (D=1) One Moving Average term (MA(1)) for both seasonal and non-seasonal components. www.statisticshelpdesk.com

  10. Step 6: Forecasting with ARIMA We’ll now use the ARIMA model to forecast future airline passenger counts # Forecasting for the next 24 months (2 years) forecast_AP <- forecast(fit, h=24) plot(forecast_AP) Interpretation: •The forecast shows the expected number of airline passengers for the next two years. •The shaded area represents the confidence interval around the forecast values. www.statisticshelpdesk.com

  11. Step 7: Model Diagnostics # Plot diagnostics for the ARIMA model tsdiag(fit) We need to check the residuals to ensure our model is well-fitted. We should check if: •The residuals appear to be white noise (i.e., they are randomly distributed with no apparent structure). •The p-values from the Ljung-Box test (part of the diagnostic plot) should be greater than 0.05, suggesting that residuals are uncorrelated. www.statisticshelpdesk.com

  12. Step 8: Conclusion and Interpretation of Results 01. Trend Analysis The upward trend of airline passengers indicate an increased demand for international travel in the specific period of 1949-1960. We can also identify the differences between seasons of the year where the number of passengers is likely to be greater than expected (for instance during holidays). Forecasting Seasonality 02. 03. The analysis performed by the ARIMA model can be considered to give a fairly accurate forecast for the next two years. From the above analysis, we observed that the model is able to capture both the trend in the data as well as the seasonal trend. •The residuals from the ARIMA model appear random, indicating a well- fitted model. Diagnostics 04.

  13. Struggling with time series analysis? www.statisticshelpdesk.com

  14. Our Time Series Assignment Help service aims to cater students who find themselves struggling with complex data sets as well as the forecasting models. In time series analysis understanding the trends, seasonality and noise in data over time can be quite problematic. Our skilled statisticians explain these concepts and provide you with detailed instructions on how to work through the examples of ARIMA models, stationarity, decomposition, etc. www.statisticshelpdesk.com

  15. Why opt for our service? Seek quality assistance from statistics academic experts and industry professionals who are conversant with time series modeling procedures. Expert Guidance We provide detailed worked out solution along with R codes to make the learning process easy Detailed Explanations Tight deadlines? No problem! We provide quick, accurate solutions. On-Time Delivery Develop deep understanding of time series data, gain confidence and improve your grades. Enhanced Learning Choose our service and get help with your time series assignments to gain confidence in handling time series data. www.statisticshelpdesk.com

  16. Thanks! www.statisticshelpdesk.com homework@statisticshelpdesk.com +44-166-626-0813

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