ECON1061: Forecasting and Quantitative Analysis

Assignment Overview

Part A 

The aim in this part of the assignment is to understand the data, perform transformation (if required), and use simple forecasting models to produce forecasts.

Question 1

Produce appropriate plots in order to become familiar with your data. Make sure you label your axes and plots appropriately. Comment on the plots. What do you see? (50 words per plot).

Question 2

Would transforming your data be useful? If transformation is required, compare two approaches graphically. Choose the best transformation, justifying your choice (100 words).

Question 3

Apply the two most appropriate benchmark (simple forecasting) methods, justifying your choices 
Question 4

Perform a thorough residual analysis for each model. Do the residuals appear to be white noise? 

Question 5

Generate and plot forecasts and forecast intervals for the next 2 years from the two benchmark methods, also plotting the observed data. You may choose to provide a separate plot for each model (along with the observed data) for better visualisation. You may also choose to plot on a shorter period of say 5 last years for clearer visualisation. Compare and discuss your findings, commenting on the merits/limitations of either or both modelling approaches (100 words).

Part B (25 marks)

The aim in this part of the assignment is to build an ARIMA model and use it to forecast.

Question 6

Visually inspect your transformed data and decide what differencing is required to achieve stationarity. Analyse using relevant plots at every step, commenting on each plot and justifying your actions. (50 words per plot).

Question 7

Estimate an ARIMA model using the auto-ARIMA function in R. Tabulate your results.

Question 8

Perform a thorough residual diagnostics analysis for your estimated model. Discuss your results. 

Question 9

Generate and plot forecasts and forecast intervals for the next two years. Comment on the results 

Part C (20 marks)

You have now built three models with your dataset. Next, the aim is to evaluate the three models.

Question 10

Create a training set with your data by leaving two years’ worth of observations as the test set. Generate forecasts for the last two years (the period of the test set), from the three models you have estimated in Parts A (two benchmark models) & B (ARIMA model). Plot the forecasts (both point forecasts and prediction intervals) together with the observed data and comment on these (100 words). You may choose to plot on a shorter period of say 5 last years for clearer visualisation. Make sure the visualisations are clear.

Question 11

Compute the accuracy of your forecasts generated from the three models in a table. Which model does best and why? 

Assessment Summary: Forecasting and Quantitative Analysis

Overview of Assessment Requirements

This assessment focuses on developing skills in data analysis, forecasting, and model evaluation using quantitative techniques. It is divided into three key parts (A, B, and C), each designed to progressively enhance the student’s understanding of time series forecasting, model building, and validation.

• Part A emphasizes understanding the dataset, performing necessary data transformations, and applying simple benchmark forecasting models to generate forecasts.

• Part B focuses on building an ARIMA model, conducting residual diagnostics, and producing forecasts using the model.

• Part C involves evaluating and comparing the three models (two from Part A and one from Part B) using test data and accuracy measures to determine the best-performing model.

The key components covered in the assessment include:

1. Visual exploration of data using appropriate plots.

2. Data transformation and justification for the chosen method.

3. Application of benchmark forecasting models.

4. Residual and diagnostic analysis.

5. Generation and comparison of forecasts and confidence intervals.

6. Model selection and evaluation using statistical accuracy measures.

Academic Mentor’s Step-by-Step Approach

The academic mentor guided the student through the assessment using a systematic, concept-driven, and applied learning approach. Each section was explained with practical reasoning and theoretical grounding to ensure conceptual clarity and correct application of forecasting techniques.

Step 1: Understanding the Dataset (Part A – Question 1)

The mentor first assisted the student in exploring the dataset visually.

• The student was guided to generate time series plots to identify trends, seasonality, and irregular fluctuations.

• The mentor emphasized labeling axes, titles, and legends clearly for professional presentation.

• The visual inspection helped the student observe patterns such as long-term trends or seasonal variations, laying the foundation for subsequent analysis.

Outcome: The student learned how to interpret visual data patterns and recognize underlying structures that influence forecasting models.

Step 2: Data Transformation (Part A – Question 2)

The mentor introduced the concept of data transformation to stabilize variance and achieve stationarity.

• The student was guided to apply logarithmic and square root transformations, comparing both graphically.

• The mentor explained how to select the best transformation based on visual results and variance stability.

Outcome: The student learned to assess when and why transformations are necessary and to justify the most suitable transformation using visual and statistical evidence.

Step 3: Applying Benchmark Forecasting Models (Part A – Question 3)

The mentor helped the student understand simple forecasting models such as:

• Naïve Model (using the last observation as the forecast).

• Mean or Drift Model (based on average or trend extrapolation).

The student applied both models and discussed their suitability, with the mentor explaining the significance of these models as baseline comparisons before building complex models.

Outcome: The student understood the logic and purpose of benchmark forecasting and gained confidence in implementing and justifying basic models.

Step 4: Residual Analysis (Part A – Question 4)

The mentor guided the student in evaluating model residuals to determine if the models captured all patterns in the data.

• The student analyzed residual plots and conducted statistical checks to test for white noise properties.

• The mentor explained how randomness in residuals indicates a well-fitted model, while patterns suggest room for improvement.

Outcome: The student learned to interpret residual plots, identify non-random patterns, and understand the importance of diagnostic checks in forecasting accuracy.

Step 5: Forecast Generation and Comparison (Part A – Question 5)

Next, the mentor instructed the student to generate forecasts and forecast intervals for two years using both benchmark models.

• Separate plots were created for each model for better visual clarity.

• The student compared performance visually and described the strengths and weaknesses of each method.

Outcome: The student developed the ability to visualize and interpret forecasts, including confidence intervals, and critically compare model performance.

Step 6: ARIMA Model Development (Part B – Questions 6 & 7)

The mentor introduced ARIMA modeling, explaining the concepts of stationarity, differencing, and autocorrelation.

• The student was guided to visually assess the transformed data and apply differencing to remove trends and achieve stationarity.

• Using the auto-ARIMA function in R, the student estimated the best-fitting ARIMA model.

• The mentor emphasized understanding ARIMA parameters (p, d, q) and interpreting the model output table.

Outcome: The student gained hands-on experience in ARIMA model construction and parameter interpretation.

Step 7: Residual Diagnostics for ARIMA (Part B – Question 8)

The mentor directed the student to perform residual diagnostics to validate model adequacy.

• The student examined ACF and PACF plots of residuals and applied Ljung-Box tests to check for randomness.

• The mentor explained how these diagnostics ensure that the ARIMA model effectively captures the time series patterns.

Outcome: The student understood how to confirm model validity and ensure residual independence, a key requirement for reliable forecasting.

Step 8: Forecasting with ARIMA (Part B – Question 9)

After validating the model, the student generated two-year forecasts and intervals using the ARIMA model.

• The mentor guided the student on proper visualization of forecasts alongside historical data for interpretability.

• The student commented on the model’s performance, noting forecast behavior and uncertainty levels.

Outcome: The student learned to interpret ARIMA-based forecasts and visually assess prediction accuracy.

Step 9: Model Evaluation and Comparison (Part C – Questions 10 & 11)

Finally, the mentor guided the student in evaluating all three models — the two benchmark models from Part A and the ARIMA model from Part B.

• The dataset was split into training and test sets, keeping the last two years as the test period.

• The student plotted forecasts versus actual test data, comparing prediction intervals and trends.

• The forecast accuracy metrics (such as MAE, RMSE, and MAPE) were calculated and tabulated to identify the most accurate model.

• The mentor explained that model performance should be judged not only by numerical accuracy but also by interpretability and predictive stability.

Outcome: The student successfully identified the model with the best predictive performance and developed analytical reasoning for model selection.

Final Outcome and Learning Objectives Achieved

By the end of the assessment, the student demonstrated strong analytical and practical forecasting skills. Through mentor guidance, the student learned to:

• Explore and visualize time series data effectively.

• Apply transformations and benchmark models accurately.

• Build, interpret, and validate ARIMA models using statistical tools.

• Compare multiple models objectively using diagnostic checks and accuracy measures.

• Present clear, evidence-based conclusions supported by data visualization.

Learning Objectives Covered

 Understanding and interpretation of time series data.
Application of statistical and forecasting models.
 Development of analytical reasoning in model selection.
 Proficiency in using software tools like R for forecasting.
Critical evaluation of model performance and residual behavior.
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