This question requires a thorough analysis of the Exports for France using the global$\_$economy dataset in R Studio. The task involves applying at least two forecasting techniques learned in the course to forecast Exports for the next $10$ years. Your analysis should include data visualization, exploratory data analysis, model selection and estimation, model evaluation, and forecasting. All steps should be implemented and demonstrated using R Studio. Make sure you load the fpp$2$ and fpp$3$ library before you answer Questions $4-6.$

Question $4$

This question requires you to use the dataset, global$\_$economy. Your task is to analyse the

Exports for France and use at least two forecasting techniques you have learnt in the course

to forecast Exports for the next $10$ years. Pay attention to whether the data needs to be

transformed. Discuss all your results carefully, writing down estimated models where

required and performing model evaluation. The analysis needs to be thorough.

Instructions for the Expert:

Data Visualization:

Load the global$\_$economy dataset in R$.$

Extract and plot the historical exports data for France.

Identify if the data needs transformation $($e$.$g$.,$ log transformation to stabilize variance$).$

Exploratory Data Analysis:

Describe the patterns observed in the data $($e$.$g$.,$ trend, seasonality$).$

Use ACF and PACF plots to understand the data characteristics and inform model selection.

Model Selection and Estimation:

Select and fit at least two forecasting models $($e$.$g$.,$ ARIMA, Exponential Smoothing$).$

Write down the estimated models with coefficients, ensuring to include any transformations applied to the data.

Provide the R code used for fitting these models.

Model Evaluation:

Evaluate the models using appropriate criteria such as AIC, residual diagnostics, and goodness$-$of$-$fit measures.

Compare the performance of the models and justify your choice of the best model based on the evaluation.

Include the R code used for model evaluation.

Forecasting:

Generate forecasts for the next $10$ years using the selected models.

Plot the forecasts and include prediction intervals to convey the uncertainty of the forecasts.

Provide the R code used for generating and plotting the forecasts.

Discussion:

Discuss your findings and conclusions, explaining why you chose the specific models and how they perform relative to each other.

Relate your analysis to the forecasting techniques and model evaluation methods covered in the course.

Provide insights gained from the analysis and how they align with the lecture notes and tutorials.

Note:

Ensure to discuss your steps and reasoning clearly to demonstrate understanding.

Relate the explanation and calculations to the concepts of forecasting, transformations, model fitting, and evaluation covered in the course.

Use relevant plots, charts, or tables to support your analysis and conclusions.

Example Structure for Response:

Data Visualization:

Plot the historical data of French Exports.

Identify if the data needs transformation.

Exploratory Data Analysis:

Analyze the trend and seasonality in the data.

Use ACF and PACF plots.

Model Selection and Estimation:

Fit ARIMA and Exponential Smoothing models.

Write down the estimated models with coefficients.

Model Evaluation:

Evaluate models using AIC, residual diagnostics, etc.

Compare the models.

Forecasting:

Generate and plot forecasts for the next $10$ years.

Discussion:

Discuss findings and conclusions.

Explain the choice of models and their performance.