Vector Autoregression (VAR) of Longitudinal Sleep and Self-report Mood Data

TL;DR

Quantify sleep–mood dynamics in a long-running, single-subject study by linking four years of Oura Ring sleep scores with daily mood reports via a $VAR(2)$ model. The analysis uses Granger causality and impulse response functions to reveal that sleep quality predicts depressed and anxious moods and can Granger-cause these states, with effects peaking around day 3. This demonstrates that affordable consumer wearables can yield actionable, time-resolved insights for mood management, while acknowledging stationarity assumptions and bidirectional influences for future work. The work suggests avenues for automatic episode labeling and integration with machine-learning time-series methods to support proactive self-care.

Abstract

Self-tracking is one of many behaviors involved in the long-term self-management of chronic illnesses. As consumer-grade wearable sensors have made the collection of health-related behaviors commonplace, the quality, volume, and availability of such data has dramatically improved. This exploratory longitudinal N-of-1 study quantitatively assesses four years of sleep data captured via the Oura Ring, a consumer-grade sleep tracking device, along with self-reported mood data logged using eMood Tracker for iOS. After assessing the data for stationarity and computing the appropriate lag-length selection, a vector autoregressive (VAR) model was fit along with Granger causality tests to assess causal mechanisms within this multivariate time series. Oura's nightly sleep quality score was shown to Granger-cause the presence of depressed and anxious moods using a VAR(2) model.

Figures (3)

• Figure 1: Decomposition of sleep time series
• Figure 2: Partial autocorrelation of sleep time series
• Figure 3: Plot of Impulse Response Function, Lag 0 to 10