Forecasting Associations, Not Interventions: A Preregistered Causal Audit of Covariate-Aware Time Series Foundation Models

Zong-Han Bai

cs.LGOct 22, 2026

Forecasting Associations, Not Interventions: A Preregistered Causal Audit of Covariate-Aware Time Series Foundation Models

Authors: Zong-Han Bai

Organizations: National Tsing Hua University, Hsinchu, Taiwan.

Abstract

Covariate-aware time series foundation models (TSFMs) accept a future path for a control variable and return a forecast, inviting what-if queries. The query is interventional; the models are trained on observational data. We determine whether their answers are the conditional slope $\partial E[Y|X]$ or the interventional effect $\partial E[Y|do(X)]$ , at three levels. Theory: a Bayes-optimal observational predictor answers interventional queries associationally unless the adjustment set is available and used; for in-context least squares we derive the resulting confounding gap -- a model's effect estimate under an observational minus under a randomized context -- in closed form, a parameter-free reference line. Behaviour: on a preregistered grid with exact counterfactual ground truth, Chronos-2, TiRex-2, TabPFN-TS and TimesFM-2.5 all track this line ( $R^2$ 0.90-1.00) and respond more confounded than regression itself (slopes 1.3-1.8), on linear and nonlinear structural models. Pairs of models with identical observational laws prove this is not an identifiability limit: when the effect is identifiable, least squares recovers 100% of the true effect difference, Chronos-2 75%, TiRex-2 34%. Representation: linear probes decode the data-generating regime (94-96%) and the true effect ( $R^2$ 0.7-0.9) from embeddings that the forecasts ignore. On two physical systems with randomized actuators, pretrained models under-respond by 2-5x and ignore in-window confounding. Minutes of interventional post-training on 3,000 synthetic series cut the gap by up to 83% and transfer outside the training prior. Its forecasting cost is a replay-distribution effect: replaying the model's own pretraining prior cuts it from +47% to +10% MASE, and with low-rank adaptation yields a recipe meeting the preregistered criterion over three seeds (52-61% gap reduction at +1-3% cost) while improving the DoTime benchmark.

Figures & tables

Figure 1: Foundation models forecast associations, not interventions. (a) One what-if query is posed under two contexts from the same structural model: observational (

Z

drives both

X

and

Y

) and randomized (the edge is cut). A model that estimates the effect answers the same number in both. (b) Chronos-2 does not: under observational context its response to

\operatorname{do}(X{+}\delta)

is inflated by the confounding. The difference at the first intervened step is the confounding gap , derived in closed form for in-context least squares ( Proposition 1 ). (c) Supplying the confounder’s future should close the gap (star: least squares does); three models fail in three ways.

Figure 2: Measured confounding gap against the Proposition 1 prediction , one point per

(\alpha,\gamma)

cell (slopes and

R^{2}

in Table 1 ). The identity line is in-context least squares; the horizontal line is a causal predictor. All four TSFMs lie on or above the line with the confounder hidden (

\mathrm{V0}

) or past-only (

\mathrm{V1}

); supplying the confounder’s future (

\mathrm{V2}

, theory 0) removes only part of the gap and, for TiRex-2 and TimesFM-2.5, little or none of it. Right: the least-squares control validates the harness (

R^{2}=1.000

Model	Vis.	slope ( $R^{2}$ )	$\overline{\mathrm{CG}}$	$\mathrm{CG}_{\mathrm{V2}}/\mathrm{CG}_{\mathrm{V1}}$	$\hat{b}_{\mathrm{int}}$
Chronos-2	$\mathrm{V0}$	1.64 (0.99)	0.77		0.84
	$\mathrm{V1}$	1.78 (0.83)	0.73		0.81
	$\mathrm{V2}$	–	0.40	0.58	0.97
TiRex-2	$\mathrm{V0}$	1.34 (1.00)	0.62		0.95
	$\mathrm{V1}$	1.56 (0.83)	0.62		0.97
	$\mathrm{V2}$	–	0.77	1.07	0.63

Table 1: E1 confounding gap (

L=512

; slope and

R^{2}

of the measured impact-coefficient gap on the Proposition 1 prediction over confounded cells, 95% cell-bootstrap CIs in Table 6 ).

\mathrm{CG}_{\mathrm{V2}}/\mathrm{CG}_{\mathrm{V1}}

: residual gap when

Z

’s future is supplied (theory 0);

\hat{b}_{\mathrm{int}}

: randomized-context estimate of

\beta=1

. † relative to

\mathrm{V0}

(TabPFN-TS drops past-only covariates).

Figure 3: Causal compass. Each point is a confounded cell. A causal predictor sits at the origin, an associational one on the vertical axis; covariate dominance pushes left. Chronos-2 (

\mathrm{V2}

) moves toward the origin but stops; TabPFN-TS does not move; TiRex-2 (

\mathrm{V2}

) moves left : supplying

Z

’s future collapses its response to

X

Figure 6: Nonlinear structural model (E11).

X

responds to

\tanh(Z)

Y

1.5\tanh(X)

and a convex function of

Z

; the reference is an in-context kernel ridge regression with the same three visibility rules, and its own observational-minus-randomized gap is the

x

-axis. Chronos-2 and TiRex-2 again sit above the reference under

\mathrm{V0}

(slopes 1.35 and 1.53,

R^{2}

0.82 and 0.92); post-training on the linear family transfers (gap 0.57

\to

0.15 under

\mathrm{V0}

, 0.58

\to

0.02 under

\mathrm{V1}

); the linear least-squares control is itself close to the nonparametric reference (slope 0.92,

R^{2}

0.90).

Figure 7: Causal Chambers. (a) Wind tunnel: horizon-average effect of

\operatorname{do}(\text{load\_in}+\delta)

on downwind pressure versus the in-window confounding bias predicted from context (septile bins). An associational predictor has slope 1 (least squares,

\mathrm{V1}

), an adjusting one slope 0 (least squares,

\mathrm{V2}

). Pretrained models have slope

\approx 0

at every visibility and a response one third to one half of the identified effect: they ignore the covariate rather than adjust for it. (b) Response scale on both systems: on the light tunnel the post-trained model overshoots by

1.6

–

2.1\times

	Repair	$\mathrm{CG}$ red. $\mathrm{V1}$	$\mathrm{CG}$ red. $\mathrm{V2}$	$\hat{b}_{\mathrm{int}}$ ( $\mathrm{V1}$ )	spurious	MASE mean / med.	DoTime
inference	context dither ( $0.5\sigma\times 4$ )	$-6\%$	$-34\%$	0.78	–	0	–
	in-context randomization, $K{=}2$	$-19\%$	$+5\%$	0.90	–	0	–
	in-context randomization, $K{=}8$	$-22\%$	$+20\%$	0.88	–	0	–
	do-flag without training	$-4\%$	$+13\%$	0.74	–	0	–
post-training	v2: $\mathrm{V1}$ contexts, $\beta$ incl. 0	$-85\%$	$-44\%$	0.96	0.28	$+71$ / $+21\%$	0.693
	v3: $\mathrm{V2}$ contexts	$-70\%$	$\mathbf{-97\%}$	0.64	0.21	$+46$ / $+13\%$	0.697

Table 2: Repairs (Chronos-2 unless stated;

3\times 3

confounded grid; KS = KernelSynth). Gap reduction relative to the pretrained model;

\hat{b}_{\mathrm{int}}

under

\mathrm{V1}

; spurious effect at

\beta=0

under observational

\mathrm{V1}

context (pretrained 0.47; least squares 0.42); change in M4-hourly MASE (mean / median over 200 series); DoTime effect-direction accuracy (pretrained 0.684). Preregistered success (

\checkmark

\geq 50\%

reduction on both visibilities and MASE change

\leq 5\%

on both the mean and the median.

Figure 8: The repair trade-off. Gap reduction against forecasting cost for every variant of Table 2 (filled diamonds: median cost; open circles: mean; ICR = in-context randomization). (a) Variants without pretraining-prior replay form a curve on which reductions above 50% cost at least 10% median MASE. (b) KernelSynth replay (green) removes the mean-cost tail at full-parameter learning rates (v11) and, with low-rank adaptation, moves the curve into the preregistered region (v18, v19).

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Model	Vis.	slope (dyn.)	$R^{2}$	RMSE	slope (static)	$R^{2}$	RMSE
Chronos-2	$\mathrm{V0}$	1.64	0.99	0.40	1.17	0.95	0.12
Chronos-2	$\mathrm{V1}$	1.78	0.83	0.46	1.07	0.94	0.10
TiRex-2	$\mathrm{V0}$	1.34	1.00	0.23	0.95	0.94	0.15
TiRex-2	$\mathrm{V1}$	1.56	0.83	0.35	0.94	0.94	0.15
TabPFN-TS	$\mathrm{V0}$	1.00	0.98	0.04	0.71	0.84	0.40
TimesFM-2.5 + XReg	$\mathrm{V0}$	1.26	0.90	0.40	1.01	1.00	0.01

Appendix

Table 3: Dynamic versus static reference. Slope,

R^{2}

and RMSE of each model’s measured impact gap on the Proposition 1 (dynamic) and Proposition 3 (static) references over the confounded cells; last column: ratio of the two references.

Encoder	regime acc.	$\beta$ $R^{2}$ (rand.)	$\beta$ $R^{2}$ (obs.)	bias $R^{2}$
Chronos-2 pretrained	0.96	0.80	0.71	$-0.03$
Chronos-2 + IPT (v4)	0.99	0.90	0.82	0.24
TiRex-2 pretrained	0.94	0.90	0.86	0.15
TiRex-2 + IPT (one round)	0.96	0.94	0.87	0.24
raw in-window OLS statistics	1.00	1.00	–	–

Appendix

Table 4: Linear probes (5-fold held-out) on pretrained and post-trained encoders of both architectures.

Model	$s_{\mathrm{V1}}$	$\rho$	$d_{\mathrm{int}}$	$e_{\mathrm{int}}$	Mode
In-context OLS	1.00	0.00	0.00	0.00	adjusts ( $\mathrm{V1}$ associational by construction)
Chronos-2	1.78	0.58	$+0.16$	0.03	partial adjustment, A +
TabPFN-TS	1.00	0.89	$+0.01$	0.11	no adjustment
TiRex-2	1.56	1.07	$\mathbf{-0.34}$	0.37	covariate dominance, A +
TimesFM-2.5 + XReg	1.62	0.88	$0.00$	0.32	no adjustment, A +
TimesFM-2.5 (univariate)	0.00	–	0.00	1.00	unresponsive (pattern D)

Appendix

Table 5: Failure-mode classifier applied to the E1 grid.

Model	Vis.	cells	slope	95% CI
Chronos-2	$\mathrm{V0}$	16	1.64	[1.57, 1.71]
Chronos-2	$\mathrm{V1}$	16	1.78	[1.36, 2.29]
TiRex-2	$\mathrm{V0}$	16	1.34	[1.31, 1.36]
TiRex-2	$\mathrm{V1}$	16	1.56	[1.21, 2.03]
TabPFN-TS	$\mathrm{V0}$	9	1.00	[0.85, 1.13]
In-context OLS	$\mathrm{V0}$ / $\mathrm{V1}$	16	1.00	[1.00, 1.00]

Appendix

Table 6: Cell-bootstrap 95% confidence intervals for the impact slopes of Table 1 (2,000 resamples of the confounded cells).

Figure 9: Gap path over the horizon

\mathrm{CG}_{t}=\mathbb{E}_{\mathrm{obs}}[\Delta\hat{y}_{t}]/\delta-\mathbb{E}_{\mathrm{int}}[\Delta\hat{y}_{t}]/\delta

, averaged over the 16 confounded cells. In-context least squares answers with the contemporaneous coefficient at

t=1

(0.40 under

\mathrm{V0}

, 0.33 under

\mathrm{V1}

) and then accumulates through the autoregressive carry (to 0.15 and 0.65). Chronos-2 and TiRex-2 answer with the long-run association from the first step: their gap is 0.6–0.8 at

t=1

and 0.85–0.9 thereafter. This is why the impact slope exceeds 1 while the cumulative slope is close to 1.

Figure 10: Sensitivity versus context length. Under randomized context

S

rises monotonically toward 1 with

L

( Proposition 2 ); under observational context it stays at 1.3–1.4 at every

L

: the confounding does not wash out. TiRex-2 under

\mathrm{V2}

moves the other way as the known-future covariate increasingly dominates.

Model	Vis.	$L=128$	$L=512$	$L=2048$
Chronos-2	$\mathrm{V0}$ / $\mathrm{V1}$ / $\mathrm{V2}$	0.69 / 0.64 / 0.77	0.86 / 0.84 / 0.96	0.94 / 0.93 / 0.99
TiRex-2	$\mathrm{V0}$ / $\mathrm{V1}$ / $\mathrm{V2}$	0.79 / 0.80 / 0.65	0.85 / 0.84 / 0.56	0.88 / 0.87 / 0.52

Appendix

Table 7: E3 sensitivity versus context length (randomized context,

3\times 3

cells, seed 0).

Cell	Relation to training prior	pretrained $\mathrm{CG}$	IPT $\mathrm{CG}$	reduction	effect RMSE (obs.)
in-distribution $3\times 3$	–	0.98 / 0.55	0.22 / 0.10	78% / 82%	0.76 $\to$ 0.15
$\alpha,\gamma\in\{2,2.5\}$	outside ( $\leq 1.5$ in training)	1.62 / 1.10	0.35 / 0.24	78% / 79%	1.11 $\to$ 0.23
$\beta=0.5$	inside	0.83 / 0.37	0.21 / 0.15	74% / 60%	0.63 $\to$ 0.20
$\delta=4\sigma$	intervention magnitude outside	0.97 / 0.65	0.35 / 0.30	64% / 54%	0.89 $\to$ 0.13
$\beta=-1$	inside, but confounding sign fixed positive	0.38 / 0.39	0.33 / 0.22	15% / 44%	0.63 $\to$ 0.46
$\beta=-1$ , v5 (signed $\gamma$ )	–	0.38 / 0.39	0.54 / 0.33	$-40\%$ / $+15\%$	–

Appendix

Table 8: E8 transfer of IPT outside the training prior (

\mathrm{V1}

\mathrm{V2}

): full-parameter v4 (top) and the low-rank recipe v19 (bottom).

Model	Vis.	impact slope ( $R^{2}$ )	cumul. slope ( $R^{2}$ )	mean $\mathrm{CG}$	$\hat{b}_{\mathrm{int}}$	$S_{\mathrm{int}}$	$S_{\mathrm{obs}}$	cells
In-context OLS	$\mathrm{V0}$	1.00 (1.00)	$-0.10$ (0.05)	0.41	0.92	1.27	1.36	25
	$\mathrm{V1}$	1.00 (1.00)	1.00 (1.00)	0.33	1.00	1.00	1.32	25
	$\mathrm{V2}$	–	0.88 (0.70)	0.00	1.00	1.00	1.00	25
Chronos-2	$\mathrm{V0}$	1.64 (0.99)	0.98 (0.64)	0.77	0.84	0.89	1.31	25
	$\mathrm{V1}$	1.78 (0.83)	1.58 (0.94)	0.73	0.81	0.88	1.31	25
	$\mathrm{V2}$	–	–	0.40	0.97	0.97	1.09	25

Appendix

Table 9: E1 in full : impact and cumulative coefficients.

Model	Vis.	observational	least-squares pred.	randomized	FP obs.	FP rand.
Chronos-2	$\mathrm{V1}$	0.47	0.42	0.00	100%	11%
Chronos-2	$\mathrm{V2}$	0.16	0.00	0.00	100%	56%
TiRex-2	$\mathrm{V1}$	0.48	0.42	0.00	100%	0%
TiRex-2	$\mathrm{V2}$	0.31	0.00	$-0.01$	100%	78%
TabPFN-TS	$\mathrm{V2}$	0.44	0.00	0.00	100%	11%
TimesFM-2.5 + XReg	$\mathrm{V1}$	0.72	0.42	$-0.01$	–	–

Appendix

Table 10: E2 null effect (

\beta=0

; mean spurious impact coefficient over nine cells; false-positive rate = cells whose 95% CI excludes 0). Randomized-context false positives with

|\text{effect}|\leq 0.04

are trivially significant at

n=600

( Wasserstein and Lazar, 2016 ) ; the magnitude column is the informative one.

Figure 11: Left: E2 spurious effects. Right: E8 out-of-prior transfer of post-training (confounding gap before and after IPT).

Model	Regime	$\mathrm{V0}$ median (97.5%)	$\mathrm{V1}$ median (97.5%)	$\mathrm{V2}$ median (97.5%)
Chronos-2	obs.	0.002 (0.006)	0.001 (0.006)	0.003 (0.030)
Chronos-2	rand.	0.011 (0.331)	0.012 (0.495)	0.013 (0.065)
TiRex-2	obs.	0.001 (0.004)	0.001 (0.004)	0.001 (0.008)
TiRex-2	rand.	0.008 (0.071)	0.008 (0.068)	0.035 (1.796)

Appendix

Table 11: E3 anticipation leak (onset

H/2

; ratio of pre-onset to post-onset response energy; the preregistered claim requires a CI lower bound

>0.05

). No systematic leak; heavy right tail under randomized context.

Method	dir. acc.	NMSE	back-door	front-door	IV	bow
Zero / Mean / AR(1)	0.53 / 0.53 / 0.53	1.03 / 0.68 / 0.95	0.50–0.53	0.51–0.53	0.51–0.54	0.54–0.56
Naive OLS (no adjustment)	0.77	0.57	0.79	0.70	0.81	0.81
Back-door OLS	0.60	0.63	0.81	0.53	0.54	0.54
VAR-OLS / IV-2SLS	0.53 / 0.55	0.82 / 0.67	0.52 / 0.53	0.54 / 0.53	0.52 / 0.61	0.54 / 0.54
Oracle	1.00	0.00	1.00	1.00	1.00	1.00
Chronos-2	0.684	0.44	0.68	0.60	0.74	0.73

Appendix

Table 12: E4 DoTime dot-Identifiability-v1 (12,150 episodes; effect-direction accuracy, NMSE, and direction accuracy on key structures).

Model	$\mathrm{V0}$	$\mathrm{V1}$	$\mathrm{V2}$	$\mathrm{V0}$	$\mathrm{V1}$	$\mathrm{V2}$	$\mathrm{V0}$	$\mathrm{V1}$	$\mathrm{V2}$
	Wind tunnel: effect / truth			slope on predicted bias			RMSE (truth 16.4)
In-context OLS	0.42	0.79	0.77	0.43	1.00	0.00	21.2	34.8	7.9
Chronos-2	0.33	0.41	0.47	0.07	0.01	$-0.03$	13.1	11.3	10.5
TiRex-2	0.18	0.19	0.22	0.04	0.04	0.01	15.9	15.2	14.1
Chronos-2 + IPT	0.65	0.63	0.73	0.41	0.22	0.03	17.9	13.6	8.3
Chronos-2 + IPT v19	0.46	0.42	0.56	0.14	0.02	$-0.03$	13.1	12.2	10.1

Appendix

Table 13: E6 real systems in full. Mean horizon-average effect (fraction of the identified effect), slope on the in-window predicted bias (1 associational, 0 adjusting), and RMSE against the identified effect. Light tunnel: the in-window least-squares reference is itself unstable (six unobserved LED/polariser settings and persistent random walks within 512 steps), so the slope reference is weaker than on the wind tunnel; the identified effect from the pooled regression is reliable (

R^{2}

0.976).

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