TemporalDisaggregations.jl

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TemporalDisaggregations.jlRecover signals from interval averages

Reconstruct instantaneous time series from overlapping, irregular interval-averaged observations — with uncertainty estimates.

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Four Methods

B-spline, sinusoid, Gaussian Process, and Kalman-filter GP — all sharing the same interface. Switch by passing a different algorithm struct.

Uncertainty Estimates

Every method returns a spatially-varying sandwich std alongside the reconstructed signal — lower where observations are dense, higher where they are sparse.

Robust to Outliers

All methods support L1 loss via IRLS, automatically down-weighting suspicious observations.

Overview ​

Many real-world measurements are temporal averages rather than point observations:

  • Remote sensing: satellite image-pair velocities averaged over a revisit period

  • Hydrology: stream-gauge discharge totals over reporting intervals

  • Climatology: monthly or seasonal summaries of daily observations

  • Finance: period-average prices or returns

When intervals are irregular, overlapping, or sparse, standard interpolation fails. TemporalDisaggregations.jl solves this inverse problem: given interval averages, recover the underlying instantaneous signal on a regular output grid.

In math: yᵢ ≈ (1/Δtᵢ) ∫_{t1ᵢ}^{t2ᵢ} x(t) dt