ARIMA Modelling and Forecasting Using R - Assignment -17

 

ARIMA Modelling and Forecasting Using R

Problem Title

Forecasting Monthly Electricity Consumption Using an ARIMA Model

Problem Statement

An electricity distribution company has recorded the following monthly electricity consumption (in thousand units) over three years.

The company wants to analyze the historical consumption pattern and forecast electricity consumption for the next six months using an ARIMA model.

Monthly Electricity Consumption Data

125, 132, 128, 140, 145, 150,
148, 155, 160, 158, 165, 170,

172, 178, 175, 185, 190, 195,
192, 200, 205, 202, 210, 215,

218, 225, 222, 235, 240, 248,
245, 255, 260, 258, 268, 275

Tasks to be Performed by Students

Using R, perform the following:

1. Create a Time Series

Create a monthly time series starting from January 2023.

2. Visualize the Original Time Series

Plot the electricity consumption data and identify whether the data show:

  • A trend
  • Seasonal variation
  • Random fluctuations

3. Check the Need for Differencing

Perform first-order differencing and plot the differenced series.

Compare the original and differenced series.

4. Generate ACF and PACF Plots

Create:

  • An ACF plot
  • A PACF plot

Use these plots to identify possible values for:

  • pp — AutoRegressive order
  • qq — Moving Average order

Since first-order differencing is performed:

d=1d = 1

5. Build Candidate ARIMA Models

Based on the ACF and PACF plots, students should try at least three possible models, for example:

ARIMA(1,1,0)ARIMA(1,1,0) ARIMA(1,1,1)ARIMA(1,1,1) ARIMA(2,1,0)ARIMA(2,1,0)

6. Compare the Models

Compare the candidate models using:

  • AIC
  • BIC

Identify the model that provides the best fit.

Generally, a model with lower AIC and BIC values is preferred.

7. Forecast Future Values

Using the selected ARIMA model, forecast the electricity consumption for the next six months.

Display:

  • Point forecasts
  • 80% prediction interval
  • 95% prediction interval

8. Plot the Forecast

Create a graph showing:

  • Historical electricity consumption
  • Forecasted values
  • Prediction intervals

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