Helsinki Urban Noise Analysis: Hourly LAeq Time-Series Modelling

This repository contains a comprehensive time-series analysis of hourly $L_{Aeq}$ (equivalent continuous sound pressure level) measurements from a single sensor in Helsinki, recorded during 2018. The project focuses on characterizing the temporal structure of urban noise and evaluating a seasonal ARIMA (SARIMA) model for short-term forecasting.

Abstract

Urban noise exhibits strong intraday seasonality driven by anthropogenic activities. This analysis explores how a parsimonious SARIMA model can capture these 24-hour cycles and the implications of residual seasonal dependence.

Key Findings

• Strong Seasonality: The series shows a pronounced 24-hour cycle.
• Model Fit: A $\text{SARIMA}(2,1,2) \times (1,1,1)_{24}$ model was selected via AIC as the best-performing candidate.
• Residual Insights: While the model captures the primary daily cycle, Ljung-Box tests at lag 24 indicate remaining seasonal correlation, suggesting complex non-linear dynamics or exogenous shocks (e.g., sirens, construction) not fully captured by the linear specification.

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Methodology

The analysis follows a rigorous time-series workflow:

1. Data Aggregation: Minute-level measurements were aggregated to hourly means ($N=8,575$ observations).
2. Stationarity Testing: ADF and KPSS tests were used to assess stationarity.
3. Differencing: To stabilize the series, both regular and seasonal differencing were applied: $$(1-B)(1-B^{24})x_t$$
4. Model Identification: ACF and PACF analysis of the differenced series guided parameter selection.
5. Estimation & Diagnostics: SARIMA parameters were estimated, and residuals were evaluated for Gaussianity and autocorrelation.

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Visual Analysis

1. Data Overview

The raw hourly series shows significant non-stationary behavior and a clear daily pattern.

Full Year Overview	7-Day Zoom (Daily Cycle)

2. Differencing & Stationarity

After applying $(1-B)(1-B^{24})$, the series becomes mean-stable and suitable for modeling.

Full Year (Differenced)	7-Day Window (Differenced)

3. Model Diagnostics & Forecast

The following plots illustrate the model's performance and residual characteristics.

Forecast (7-Day Horizon):

Residual Analysis:

Residual ACF	Residual Histogram

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Model Results Summary

Metric	Value
Selected Model	$\text{SARIMA}(2,1,2) \times (1,1,1)_{24}$
AIC	$34245.22$
Mean ($L_{Aeq}$)	$48.08 \text{ dB(A)}$
Std Dev ($L_{Aeq}$)	$6.33 \text{ dB(A)}$
Ljung-Box (Lag 24)	$p \approx 0.0004$ (Significant)

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Repository Structure & Replication

Project Structure

• analysis.ipynb: Core analysis and modeling (R kernel).
• datasource/: Data preprocessing scripts and raw data.
• plots/: All generated diagnostic and forecast plots (PDF and PNG).
• tex/: LaTeX source for the full report and presentation slides.

Replication Guide

To reproduce the results:

1. Data Preparation: Generate the hourly dataset using the Python preprocessing script:

   python datasource/databuilder.py

2. Analysis: Execute the analysis.ipynb notebook in an R-enabled Jupyter environment. This will perform the statistical tests, model fitting, and regenerate all plots.

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Author: Tommi Bimbato
Data Source: Forum Virium Helsinki (mySMARTLife)