Econstellar: AI-Driven Financial Econometrics

• Econstellar is an open-source, AI-augmented research engine for computational financial econometrics that addresses reproducibility, cost, and accessibility challenges.
• It integrates 17 rigorous econometric methods via a parameterized compute endpoint, detailed provenance tracking, and an AI analyst layer for reliable analysis interpretation.
• The platform emphasizes transforming non-stationary price levels to log returns, ensuring that every computation is live, verified, and traceable for financial contagion studies.

Econstellar is an open-source, publicly served, AI-augmented research engine for computational financial econometrics. It is designed to run publication-grade econometric analyses from an ordinary web browser, expose the same code that produced figures in associated research, and return “verified live values” that can be re-run, varied, and traced through explicit provenance. Its defining design choices are a parameterized-only compute endpoint, an AI analyst layer that selects and interprets analyses but never originates a number, and a single methodological discipline in which price levels are treated as non-stationary and the exposed methods operate on returns by default (Bhandari, 4 Jun 2026).

1. Identity, scope, and nomenclature

Econstellar was introduced as a response to three linked problems in empirical financial econometrics: the cost of publication-grade estimation, the reproducibility gap between published figures and executable computation, and the accessibility barrier created by local environments and specialist tooling. The platform is described as the working core of an active research programme spanning three software releases and three preprints, and it is served live as a portal, a browser workbench, and a compute API (Bhandari, 4 Jun 2026).

Its main contributions are specified narrowly. These are a public compute endpoint that executes 17 econometric methods in an isolated R subprocess; a provenance system carrying method and version, engine revision, parameters, data vintage, timestamp, and a permalink that re-runs the identical analysis; an AI analyst layer implemented with Gemini 2.5 via Vertex AI that selects and interprets analyses but never originates a number; on-demand regeneration of an accompanying financial contagion study from the same code that produced the manuscript figures; and a delivery stack composed of a dependency-free browser SPA, a compute engine on Cloud Run, and a longitudinal news-intelligence warehouse called NEURICX (Bhandari, 4 Jun 2026).

The term also appears in an unrelated arXiv-linked context associated with the EXoplanetary Circumstellar Environments and Disk Explorer (EXCEDE), a NASA-selected technology maturation concept for circumstellar-disk imaging (Guyon et al., 2012). In the dedicated 2026 preprint, however, Econstellar denotes the financial-econometrics platform rather than an astrophysical instrument (Bhandari, 4 Jun 2026).

2. Methodological discipline and data transformation

The platform’s central econometric discipline is explicit: price levels are treated as non-stationary, and all methods are applied to returns unless a method intrinsically requires levels, as in cointegration analysis. The engine tests levels and returns separately and refuses to treat a price level as stationary. This design is motivated by the stylized facts of asset prices and by the aim of avoiding spurious inference from unit-root behavior and inappropriate cointegration leakage (Bhandari, 4 Jun 2026).

The paper defines weak stationarity in the standard way: the mean is constant, the variance is finite and constant, and the autocovariance depends only on lag. A unit root is introduced through the random-walk level process $y_t = y_{t-1} + u_t$. For testing, Econstellar exposes the Augmented Dickey–Fuller, Phillips–Perron, and KPSS procedures. The ADF regression is

$$\Delta y_t = \alpha + \beta t + \phi y_{t-1} + \sum_{j=1}^{p}\theta_j \Delta y_{t-j} + \epsilon_t,$$

with null $H_0:\phi=0$. KPSS reverses the null and uses

$$\text{KPSS} = \frac{1}{T^2}\sum_{t=1}^{T}\frac{S_t^2}{\widehat{\sigma}_\xi^2},$$

where $S_t$ is the partial sum of residuals and $\widehat{\sigma}_\xi^2$ is a HAC estimator of long-run variance (Bhandari, 4 Jun 2026).

Returns are computed and analyzed by default as log returns,

$r_t = \ln P_t - \ln P_{t-1},$

with simple returns $r_t = (P_t/P_{t-1}) - 1$ available where relevant. The stated rationale is that log returns make aggregation and scaling natural, align with multiplicative pricing, and stabilize variance relative to simple returns. Where methods require levels, the engine applies the proper transformation internally while preserving the stationarity gate (Bhandari, 4 Jun 2026).

Preprocessing policy is equally restrictive. Methods that require zero-mean inputs internally center returns within the analysis window; regression-based methods typically use intercepts rather than blanket demeaning; no arbitrary scaling is applied; multi-series methods operate on the intersection of trading days; holidays and market closures reduce that intersection; and missing values are handled by listwise deletion rather than forward-filling. Each output carries a data-vintage stamp and the actual sample size used. A plausible implication is that Econstellar treats transformation policy as part of inferential validity rather than as a front-end convenience setting (Bhandari, 4 Jun 2026).

3. Exposed econometric methods

Econstellar exposes 17 methods through a uniform interface that accepts typed parameters such as series names, date ranges, lag orders, windows, quantiles, and frequency bands, executes an R runner under sandboxing, and returns JSON with results and provenance. The method menu spans stationarity diagnostics, cointegration, impulse responses, volatility, long memory, wavelet decompositions, information-theoretic contagion, spillovers, and network topology (Bhandari, 4 Jun 2026).

Family	Methods	Brief function
Stationarity and cointegration	unit_root; live_unit_root; panel_unit_root; vecm	Unit roots, panel stationarity, Johansen cointegration
Dynamic dependence and volatility	var_irf; garch; rolling_dcc; quantile_var; granger	IRFs, conditional variance, DCC, tail dynamics, predictive causality
Scale and information flow	dfa_hurst; wavelet; wavelet_coherence; wqte; soch_profile	Long memory, MODWT variance, coherence, transfer entropy, contagion profile
Connectedness and topology	connectedness; spillover_rolling; network	Diebold–Yilmaz spillovers, rolling TCI, graph/community structure

Several defaults are fixed by the verified-value discipline. For unit-root analysis, the default is ADF with drift and lag selection via AIC up to a maximum $p=12$, with KPSS trend optional. For VAR impulse responses, the defaults are $p=7$ and horizon $$\Delta y_t = \alpha + \beta t + \phi y_{t-1} + \sum_{j=1}^{p}\theta_j \Delta y_{t-j} + \epsilon_t,$$0, with stability requiring the maximal root to remain below unity. VECM estimation uses Johansen’s maximum-likelihood procedure and is gated so that it is applied only when series are $$\Delta y_t = \alpha + \beta t + \phi y_{t-1} + \sum_{j=1}^{p}\theta_j \Delta y_{t-j} + \epsilon_t,$$1. GARCH defaults to a Gaussian-likelihood $$\Delta y_t = \alpha + \beta t + \phi y_{t-1} + \sum_{j=1}^{p}\theta_j \Delta y_{t-j} + \epsilon_t,$$2, with the persistence summary $$\Delta y_t = \alpha + \beta t + \phi y_{t-1} + \sum_{j=1}^{p}\theta_j \Delta y_{t-j} + \epsilon_t,$$3 reported; the example for India gives $$\Delta y_t = \alpha + \beta t + \phi y_{t-1} + \sum_{j=1}^{p}\theta_j \Delta y_{t-j} + \epsilon_t,$$4, indicating high persistence (Bhandari, 4 Jun 2026).

The scale-based menu is unusually prominent. Detrended fluctuation analysis estimates the Hurst exponent $$\Delta y_t = \alpha + \beta t + \phi y_{t-1} + \sum_{j=1}^{p}\theta_j \Delta y_{t-j} + \epsilon_t,$$5 from the scaling of $$\Delta y_t = \alpha + \beta t + \phi y_{t-1} + \sum_{j=1}^{p}\theta_j \Delta y_{t-j} + \epsilon_t,$$6 against window size $$\Delta y_t = \alpha + \beta t + \phi y_{t-1} + \sum_{j=1}^{p}\theta_j \Delta y_{t-j} + \epsilon_t,$$7, with linear detrending and dyadic windows as defaults; the cited India example yields $$\Delta y_t = \alpha + \beta t + \phi y_{t-1} + \sum_{j=1}^{p}\theta_j \Delta y_{t-j} + \epsilon_t,$$8. The wavelet method uses MODWT, such as LA(8), with boundary reflection and unbiased variance estimators, reporting per-scale shares and cumulative fractions; the India example reports $$\Delta y_t = \alpha + \beta t + \phi y_{t-1} + \sum_{j=1}^{p}\theta_j \Delta y_{t-j} + \epsilon_t,$$9 of variance. Wavelet coherence measures localized co-movement in the time–scale plane; the USA–India example reports mean coherence $H_0:\phi=0$0 with a peak at $H_0:\phi=0$1 (Bhandari, 4 Jun 2026).

The information-theoretic methods define one of the platform’s distinctive domains. Wavelet–quantile transfer entropy estimates directed information flow $H_0:\phi=0$2 in tail regions and at multiple scales using Kozachenko–Leonenko differential entropy, KSG nearest-neighbor mutual information, and phase-preserving surrogate significance. The default is $H_0:\phi=0$3 over four scales; for USA $H_0:\phi=0$4 India, the aggregate is reported as $H_0:\phi=0$5. The scale-ordered contagion profile, exposed through the published sochcontagion package, reports USA $H_0:\phi=0$6 India per-scale gains $H_0:\phi=0$7 under $H_0:\phi=0$8, with an aggregated value $H_0:\phi=0$9 for four scales and a five-scale aggregate in the paper of $$\text{KPSS} = \frac{1}{T^2}\sum_{t=1}^{T}\frac{S_t^2}{\widehat{\sigma}_\xi^2},$$0 (Bhandari, 4 Jun 2026).

Connectedness analysis follows the Diebold–Yilmaz framework with generalized FEVD and a frequency decomposition into short, medium, and long bands. The total connectedness index is

$$\text{KPSS} = \frac{1}{T^2}\sum_{t=1}^{T}\frac{S_t^2}{\widehat{\sigma}_\xi^2},$$1

For the India/USA/UK example, the reported result is $$\text{KPSS} = \frac{1}{T^2}\sum_{t=1}^{T}\frac{S_t^2}{\widehat{\sigma}_\xi^2},$$2, decomposed as $$\text{KPSS} = \frac{1}{T^2}\sum_{t=1}^{T}\frac{S_t^2}{\widehat{\sigma}_\xi^2},$$3, $$\text{KPSS} = \frac{1}{T^2}\sum_{t=1}^{T}\frac{S_t^2}{\widehat{\sigma}_\xi^2},$$4, and $$\text{KPSS} = \frac{1}{T^2}\sum_{t=1}^{T}\frac{S_t^2}{\widehat{\sigma}_\xi^2},$$5. Rolling connectedness recomputes these quantities over sliding windows; an example reports mean $$\text{KPSS} = \frac{1}{T^2}\sum_{t=1}^{T}\frac{S_t^2}{\widehat{\sigma}_\xi^2},$$6 with a $$\text{KPSS} = \frac{1}{T^2}\sum_{t=1}^{T}\frac{S_t^2}{\widehat{\sigma}_\xi^2},$$7–$$\text{KPSS} = \frac{1}{T^2}\sum_{t=1}^{T}\frac{S_t^2}{\widehat{\sigma}_\xi^2},$$8 range. Network analysis then builds directed dependency graphs from significant edges and applies modularity-based community detection; the example six-market graph has 18 edges, directed density $$\text{KPSS} = \frac{1}{T^2}\sum_{t=1}^{T}\frac{S_t^2}{\widehat{\sigma}_\xi^2},$$9, and 6 communities (Bhandari, 4 Jun 2026).

4. Compute architecture, provenance, and the AI layer

Econstellar’s implementation places heavy compute on Cloud Run CPU containers rather than on accelerators. The paper states that information-theoretic primitives such as KSG $S_t$0-NN over $S_t$1-d trees are CPU workloads because of branch-divergent control flow and memory latency, and that GPU/SIMT execution would serialize divergent branches. Volatility and VAR methods are likewise treated as CPU-suitable workloads (Bhandari, 4 Jun 2026).

The orchestration layer is a zero-dependency Node.js service exposing a parameterized-only registry. Each accepted call spawns a disposable, network-isolated R subprocess with read-only root, ephemeral scratch space, and a wall-clock timeout. Invalid method names and malformed parameters are rejected before process creation. Load management includes per-address rate limits, exemplified by 20/min for compute, global concurrency ceilings that shed load rather than queue unboundedly, and daily ceilings on paid analyst calls. NEURICX uses a disk cache when upstream rate limits occur so that the system degrades gracefully (Bhandari, 4 Jun 2026).

The software stack is divided cleanly. Node.js is used for orchestration, R runners for econometrics, a dependency-free JavaScript SPA for the portal and workbench, Cloud Run for service containers, Vertex AI for the agent interface, Gemini 2.5 for interpretation and news classification, Google Cloud Storage for artifacts, and BigQuery for the NEURICX longitudinal warehouse. Public repositories are listed for compute-engine, econstellar, NEURICX, sochcontagion, contagionchannels, and ManyIVsNets; the paper records that sochcontagion passes 44/44 unit tests and a clean package check, while contagionchannels and ManyIVsNets have CRAN releases (Bhandari, 4 Jun 2026).

The provenance system is central to the platform’s epistemic claims. A “verified live value” is defined as a number computed by the sandboxed engine at call time, or retrieved from a deterministic cache keyed by inputs and revision, and reproducible by any reader via the same registered call. Provenance stamps include method version, engine revision, parameters, data vintage, timestamp, and a permalink that re-runs the identical analysis. The parameterized-only registry prevents arbitrary execution, and outputs are traceable to code identity, including commit hashes referenced in the paper (Bhandari, 4 Jun 2026).

The AI assistant is tightly constrained. It is given exactly one tool, run_analysis(method, params), with schema derived from the same registry used by the compute layer. It can request only registered analyses with validated arguments and sees the engine’s JSON before composing prose. The model never originates numbers; if it attempts to assert a number not present in the engine’s JSON, the reply fails validation and is rejected. This architecture separates language generation from numeric computation at the level of executable enforcement rather than editorial policy (Bhandari, 4 Jun 2026).

5. Public interface and regeneration of the contagion study

The public deployment comprises a portal, a research workbench, a reproduce-the-paper page, and a compute API. The listed interfaces are the portal at https://avishekb9.github.io/econstellar/, the workbench at https://avishekb9.github.io/econstellar/research-engine.html, the reproduce page at https://avishekb9.github.io/econstellar/reproduce.html, and the compute API base at https://shssm-compute-b7ui3oxaqq-el.a.run.app, which exposes GET /health, GET /api/compute/catalog, and POST /api/compute/run (Bhandari, 4 Jun 2026).

The browser workflow is parameterized rather than notebook-like. One example selects instruments such as India and USA, sets a date window and $S_t$2, runs var_irf, and reads impulse-response plots and stability metrics. Another selects USA $S_t$3 India, $S_t$4, runs soch_profile, and compares per-scale gains and the aggregate. The API workflow mirrors this structure: GET /api/compute/catalog returns the JSON list of methods with typed parameters and defaults, while POST /api/compute/run executes a method with explicit arguments. The paper gives an illustrative unit_root response containing ADF and KPSS statistics and a provenance block with engine revision d2df994, data vintage G20 panel v2026-06-30, a timestamp, and a permalink (Bhandari, 4 Jun 2026).

The platform also regenerates, on demand, the headline result of an accompanying financial contagion study from the same sochcontagion package that generated the manuscript figures. The stored dataset is a G20 equity panel of 18 markets, daily log-returns, spanning 2006–2026, with live sources from Yahoo and FRED. Directed contagion is defined operationally by statistically significant transfer entropy at quantile $S_t$5 across wavelet scales, with surrogate significance

$S_t$6

For the headline USA $S_t$7 India result at $S_t$8, the live four-scale profile rises monotonically with gains $S_t$9 and aggregate $\widehat{\sigma}_\xi^2$0. The manuscript’s five-scale aggregate of $\widehat{\sigma}_\xi^2$1 is attributed to the additional 32–64-day band rather than to a computational discrepancy (Bhandari, 4 Jun 2026).

A common misconception is that the platform merely visualizes precomputed research outputs. The paper instead states that the engine a visitor exercises is the same code that produced the figures in the associated research, and that every result carries a permalink that re-runs the identical analysis. This suggests that the reproduce page functions not as a static archive but as a live verification surface (Bhandari, 4 Jun 2026).

6. Validation, limitations, and research significance

Validation is reported at the level of downstream stress classification and internal methodological checks. A systemic-risk index built on directed-flow primitives attains $\widehat{\sigma}_\xi^2$2 for one-day early warning in classifying COVID-19 stress in a US equity sample, while the VIX benchmark is reported at $\widehat{\sigma}_\xi^2$3 with higher contemporaneous discrimination. For trade-policy-induced stress in India, an augmented index attains $\widehat{\sigma}_\xi^2$4 versus India VIX $\widehat{\sigma}_\xi^2$5, with $\widehat{\sigma}_\xi^2$6 by the DeLong correlated-AUC test. The paper also reports that live unit-root diagnostics confirm the expected pattern of levels $\widehat{\sigma}_\xi^2$7 and returns $\widehat{\sigma}_\xi^2$8, and that verified connectedness and cointegration outputs remain stable under the discipline gates (Bhandari, 4 Jun 2026).

The limitations are equally explicit. Econstellar is not financial advice and not a forecasting oracle. Data coverage depends on the stored G20 panel and on live Yahoo/FRED availability. Quantile methods require sufficient tail mass, and transfer entropy requires adequate sample length for $\widehat{\sigma}_\xi^2$9-NN consistency. The platform prioritizes reproducibility and transparency over maximal speed, and exact KSG on full panels is deferred pending a dedicated CPU-HPC node. Correlation-based contagion formulations with variance-shift adjustments, such as Forbes–Rigobon, are acknowledged in the literature but are not the default framework for regeneration on the platform (Bhandari, 4 Jun 2026).

The paper also identifies misuse risks and mitigations. Multiple testing can inflate network density, so surrogate ensembles and adjusted $r_t = \ln P_t - \ln P_{t-1},$0-values are recommended, including BH or stepwise corrections in network construction. Model mis-specification is addressed through the stationarity gate, stability checks, and mandatory provenance. Outliers may still affect GARCH and DCC residuals, though quantile methods and surrogate significance reduce sensitivity. AI-related fabrication risk is addressed structurally through strict separation of compute and language layers, schema validation, and rejection of prose that contains numbers absent from engine JSON (Bhandari, 4 Jun 2026).

Future work is framed around scaling and extensibility rather than changing the core discipline. Planned directions include a dedicated CPU-HPC node for full 18-market panels and exact $r_t = \ln P_t - \ln P_{t-1},$1-NN transfer entropy at scale, extension of the method menu through registration against a compact substrate of eight primitives, additional volatility models where needed, and a software-paper submission that would provide a citable artifact linking code identity to public endpoints. In that sense, Econstellar occupies a specific position in computational financial econometrics: it is less a general-purpose notebook environment than a reproducible execution and interpretation layer in which every quantitative claim is tied to a registered computation, an identified code revision, and an explicit data vintage (Bhandari, 4 Jun 2026).