ARMA Modelling and Forecasting for Linear Time Series

Authors: Clijo JOSE and Oliver HANNAOUI

Description

This project performs a comprehensive time series analysis of the Wine Industrial Production Index (IPI) data from INSEE (Institut national de la statistique et des études économiques). The analysis includes data exploration, trend detection, stationarity testing, ARMA/ARMAX modelling, and forecasting.

Project Structure

rproj/
├── main.R              # Main analysis script
├── figures/            # Generated plots
├── tables/             # Generated LaTeX tables
├── report.pdf          # Project report
├── LICENSE             # MIT License
└── README.md           # This file

Requirements

The following R packages are required and will be automatically installed if missing:

• zoo - Time series infrastructure
• tidyverse - Data manipulation and visualization
• tseries - Time series analysis
• forecast - Forecasting functions
• tsoutliers - Outlier detection
• insee - INSEE data access
• gridExtra - Grid graphics
• strucchange - Structural change detection
• ellipse - Ellipse plotting
• FinTS - Financial time series
• nortest - Normality tests
• knitr - Table generation

Analysis Overview

The script performs three main parts:

Part I: Data Exploration

• Downloads Wine IPI data from INSEE (ID: 010767676)
• Performs trend regression analysis
• Detects structural breakpoints using Bai-Perron test
• Generates summary statistics across different periods
• Creates visualizations of the original and break-adjusted series

Part II: Model Fitting

• Tests for stationarity (ADF, PP, KPSS tests)
• Examines ACF and PACF plots
• Fits multiple ARMA models and evaluates them
• Performs residual diagnostics
• Fits ARMAX model with outlier detection
• Compares ARMA and ARMAX model performance

Part III: Forecasting

• Generates 2-step ahead forecasts using AR(1) model
• Creates forecast plots with confidence intervals
• Visualizes forecast uncertainty using confidence ellipses

Outputs

Figures (figures/)

• raw_ts_plot.png - Original and break-adjusted time series
• bp_bic_rss_plot.png - Breakpoint selection criteria
• ts_comparison.png - Comparison of original and adjusted series
• ACF_PACF.png - Autocorrelation and partial autocorrelation functions
• ARMA_1_0_residual_diagnostics_plt.png - Residual diagnostic plots
• ARMAX_1_0_residual_hist.png - ARMAX residual histogram
• fitted_series_comparison.png - ARMA vs ARMAX fitted values
• AR1_forecast.png - Forecast visualization
• confidence_elipse.png - Forecast confidence ellipse

Tables (tables/)

• ols_trend_regression.tex - OLS trend regression results
• summary_stats_by_period.tex - Summary statistics by period
• stationarity_tests.tex - Stationarity test results
• arma_well_adjusted_valid.tex - ARMA model evaluation
• arma_coefficients_all.tex - ARMA model coefficients
• ARMA_1_0_residual_diagnostics_tbl.tex - Residual diagnostics
• ARMA_1_0_coefficients.tex - ARMA(1,0) coefficients
• ARMA_1_0_performance.tex - ARMA(1,0) performance metrics
• ARMA_0_4_performance.tex - ARMA(0,4) performance metrics
• ARMAX_1_0_coefficients.tex - ARMAX coefficients
• ARMAX_1_0_performance.tex - ARMAX performance metrics

Data Source

Data is retrieved from INSEE using the insee package. The specific series used is Wine IPI (ID: 010767676).

License

This project is licensed under the MIT License - see the LICENSE file for details.