SignalY provides a comprehensive methodological framework for extracting latent signals from panel data through the integration of spectral decomposition methods, Bayesian variable selection, and automated technical interpretation. The package is designed for researchers working with multivariate time series who seek to distinguish underlying structural dynamics from phenomenological noise.
The package operationalizes a distinction between latent structure and phenomenological dynamics. In complex systems, observed variables often represent the superposition of: (1) underlying generative processes that exhibit persistent, structured behavior; and (2) transient perturbations, measurement noise, and stochastic fluctuations. SignalY provides tools to decompose this mixture and identify which candidate variables contribute meaningfully to the latent structure of a target signal.
This framework recognizes that panel data exhibit multivariate non-linear interdependence: the relationships between variables may be complex, non-additive, and evolve over time. The methods implemented here are robust to such complexities while remaining interpretable.
1. Spectral Decomposition (Signal Filtering)
The package implements three complementary approaches to extract trend components from time series:
Wavelet Multiresolution Analysis: Using the maximal overlap discrete wavelet transform (MODWT) with configurable Daubechies wavelets, the signal is decomposed into scale-specific components. Lower-frequency detail levels (e.g., D3, D4) capture structural dynamics while higher-frequency levels capture transient noise.
Empirical Mode Decomposition (EMD): A data-adaptive method that decomposes signals into intrinsic mode functions (IMFs) without requiring pre-specified basis functions. The residual component captures the underlying trend.
Grant-Chan Embedded Hodrick-Prescott Filter: A Bayesian implementation embedding the HP filter within an unobserved components model, allowing for principled uncertainty quantification around the extracted trend via Markov Chain Monte Carlo sampling.
2. Bayesian Variable Selection (Horseshoe Regression)
When the target signal Y is constructed from or influenced by a set of candidate variables X, identifying which candidates are structurally relevant versus informationally redundant is crucial. The regularized Horseshoe prior provides:
Adaptive shrinkage: Coefficients for irrelevant variables are strongly shrunk toward zero (high kappa), while relevant variables escape shrinkage (low kappa).
Uncertainty quantification: Full posterior distributions over coefficients enable credible interval construction.
Automatic sparsity detection: The effective number of non-zero coefficients (m_eff) is estimated as part of the model.
3. Dimensionality Reduction and Factor Analysis
For high-dimensional panels, the package provides:
Principal Component Analysis (PCA): With bootstrap significance testing to identify which variables load significantly on each component.
Dynamic Factor Models (DFM): For extracting common factors that drive co-movement in the panel.
Entropy-based interpretation: Shannon entropy of loadings distinguishes between diffuse systemic movement (high entropy) and concentrated structural signals (low entropy).
4. Unit Root and Stationarity Testing
Comprehensive suite of tests to characterize the persistence properties of extracted signals:
Augmented Dickey-Fuller (ADF) tests with drift and trend options
Elliott-Rothenberg-Stock (ERS) DF-GLS and P-tests
Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests
Phillips-Perron tests
SignalY generates automated technical interpretations based on:
Signal smoothness: Comparing variance of second differences between original and filtered series
Trend persistence: Whether extracted trends are deterministic or stochastic based on unit root tests
Information topology: Entropy and distributional fit of PCA loadings indicating structural concentration
Sparsity ratio: Proportion of candidate variables shrunk to zero under Horseshoe regression
Regime detection: Identification of structural breakpoints in mean or volatility
SignalY provides methodology, not theory. The statistical identification of relevant variables does not establish causal or structural relationships without supporting domain theory. Users must:
Justify variable inclusion based on domain knowledge
Interpret sparsity results in theoretical context
Recognize that statistical significance is necessary but not sufficient for structural claims
Jose Mauricio Gomez Julian isadore.nabi@pm.me
Daubechies, I. (1992). Ten Lectures on Wavelets. SIAM.
Grant, A. L., & Chan, J. C. C. (2017). Reconciling output gaps: Unobserved components model and Hodrick-Prescott filter. Journal of Economic Dynamics and Control, 75, 114-121.
Huang, N. E., et al. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society A, 454(1971), 903-995.
Percival, D. B., & Walden, A. T. (2000). Wavelet Methods for Time Series Analysis. Cambridge University Press.
Piironen, J., & Vehtari, A. (2017). Sparsity information and regularization in the horseshoe and other shrinkage priors. Electronic Journal of Statistics, 11(2), 5018-5051.
signal_analysis: Master function for complete analysis
filter_wavelet: Wavelet multiresolution analysis
filter_emd: Empirical mode decomposition
filter_hpgc: Grant-Chan HP filter
fit_horseshoe: Regularized Horseshoe regression