Learning Agentic Time Series Forecasting via Trajectory Distillation and Memory-Based Reinforcement Learning

Xiaoyu Tao; Mingyue Cheng; Yaguo Liu; Xingpeng Gao; Qingsong Wen; Shijin Wang; Enhong chen

cs.LGFeb 14, 2026

Learning Agentic Time Series Forecasting via Trajectory Distillation and Memory-Based Reinforcement Learning

Authors: Xiaoyu Tao, Mingyue Cheng, Yaguo Liu, Xingpeng Gao, Qingsong Wen, Shijin Wang, Enhong chen

Organizations: State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei, Anhui Province, China

Abstract

Recent agentic time series forecasting (TSF) approaches use large language models (LLMs) to autonomously orchestrate analytical and forecasting tools and reason about temporal patterns using the resulting evidence. However, many such approaches rely on powerful LLMs in training-free, prompt-driven workflows, leaving open whether smaller models can learn these interaction and reasoning capabilities. In this paper, we introduce Cast-R1, an 8Bparameter agentic forecasting model trained through trajectory distillation and multi-turn reinforcement learning with structured memory. First, we develop a forecasting agent harness with specialized analysis and prediction tools to generate multi-turn interaction trajectories using a teacher LLM, which are subsequently evaluated and selected for supervised fine-tuning. Second, we apply group relative policy optimization (GRPO) across multi-turn forecasting episodes, with structured memory preserving diagnostic evidence and intermediate forecasts for state construction. Rewards based on prediction accuracy and temporal structure guide tool selection, model routing, and forecast refinement. A difficulty-aware curriculum combines sample filtering and progressive sample ordering during training. Extensive experiments on multiple datasets demonstrate the effectiveness of Cast-R1. These findings highlight the potential of forecasting-specific post-training to equip smaller LLMs with multi-turn, tool-augmented forecasting capabilities within structured workflows.

Figures & tables

Figure 1: Overview of Cast-R1 as a learned agentic forecasting framework that combines structured memory for state construction with tool-augmented sequential decision-making and policy training.

Figure 2: Structured memory for state construction. The environment updates $M_{k}=(D_{k},Q_{k})$ with tool observations and constructs the next policy state.

	LTSF (Historical Inputs) ( $L=96$ , $H=96$ )					EPF (Forecast-Origin Context) ( $L=168$ , $H=24$ )
Model	ETTh1	ETTh2	ETTm1	ETTm2	Wind	BE	DE	FR	NP	PJM
ARIMA	10.879	12.567	9.898	22.527	2166.64	869.444	362.487	963.997	55.507	149.281
Prophet	46.697	23.525	12.225	31.525	8071.24	749.864	340.371	1024.401	40.754	53.777
PatchTST	9.300	11.358	5.838	16.386	2024.83	512.834	201.705	807.512	29.428	27.164
iTransformer	7.505	10.161	5.771	12.751	1591.64	645.760	265.310	824.473	34.591	53.751
ConvTimeNet	8.032	18.072	6.358	12.253	1660.13	668.275	198.431	789.035	29.903	34.638

Table 1: MSE results for two benchmark families, not a controlled context ablation. EPF provides forecast-origin context; input access follows Appendix A.4 . Lower values are better. Best results are bold ; second-best results are underlined . MAE results appear in Appendix Table 8 .

Dataset	Length	Variables	Frequency
ETTh1 & ETTh2	17,420	7	1 hour
ETTm1 & ETTm2	69,680	7	15 mins
Wind	48,673	7	15 mins
BE	14,496	3	1 hour
DE	14,496	4	1 hour
FR	14,496	3	1 hour

Table 2: Statistics of the benchmark datasets, including length, variables, and sampling frequency.

Variant	ETTh1		ETTm1		Wind		DE		NP		PJM
Variant	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
w/o Features	7.145	1.988	4.979	1.548	1743.431	23.122	194.672	9.864	28.714	4.260	30.641	4.251
w/o Prediction	15.993	2.144	13.134	2.258	4047.163	28.113	564.157	12.965	64.813	5.267	91.122	7.135
Cast-R1	6.062	1.320	3.465	1.160	1331.513	16.125	183.781	7.400	24.750	3.255	26.905	3.877

Table 3: Toolkit ablations on representative datasets. Removing feature extraction or model prediction increases error. Best results are bold .

Figure 3: MSE comparisons for (a) memory-based state construction, (b) trajectory distillation (SFT) and RL, (c) curriculum learning, and (d) backbone size. ETTh/ETTm denote ETTh1/ETTm1.

Figure 4: Qualitative ETTh1 oil-temperature forecasting case with $L=96$ and $H=96$ , illustrating statistical diagnosis, routing to Chronos, and forecast refinement. Dashed lines mark the history–forecast boundary.

Variant	ETTh1		ETTm1		Wind
Variant	MSE	MAE	MSE	MAE	MSE	MAE
w/o Length	6.102	1.928	3.982	1.378	1575.997	22.445
w/o Error	13.444	2.832	12.731	2.681	3146.645	32.329
w/o Trend	8.452	2.347	6.684	1.614	1830.842	25.219
w/o Align.	7.847	2.031	5.984	1.483	1744.896	24.786
Cast-R1	6.062	1.320	3.465	1.160	1331.513	16.125

Table 4: Reward ablations, where Length denotes length weighting, Error measures prediction accuracy, Trend captures both trend and seasonality effects, and Align represents alignment.

Figure 5: Training reward curves comparing (a) initialization by trajectory distillation (SFT) with pure RL and (b) different backbones.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Target	Freq.	Task	Covariate fields
NP	Electricity price	1 h	EPF	Grid load and wind generation forecasts.
PJM	Electricity price	1 h	EPF	System-wide and zonal load forecasts.
BE	Electricity price	1 h	EPF	National load and French generation forecasts.
FR	Electricity price	1 h	EPF	Grid load and domestic generation forecasts.
DE	Electricity price	1 h	EPF	Zonal load, wind, and solar generation forecasts.
ETTh1/ETTh2	Oil temperature	1 h	LTSF	Six power load variables accompanying oil temperature.

Appendix

Table 5: Forecast targets and original covariate fields. EPF additionally uses forecast-horizon covariates and textual context available at the forecast origin. LTSF uses covariates only within the historical window. Textual context is additional to the listed fields.

Family	$L$	$H$	Duration	Split
EPF	168	24	24 hours	7:1:2
ETTh1/ETTh2	96	96	96 hours	6:2:2
ETTm1/ETTm2	96	96	24 hours	6:2:2
Wind	96	96	24 hours	7:1:2

Appendix

Table 6: Forecasting task configuration.

L

and

H

count time steps; duration gives the physical length of the forecasting horizon. Split denotes chronological train/validation/test proportions.

Hyperparameter	SFT	GRPO
Base Model	Qwen3-8B
Precision	BF16
Optimizer	AdamW	AdamW
Learning Rate	$1.0\times 10^{-5}$	$1.0\times 10^{-6}$
LR Scheduler	Cosine	Cosine
Epochs	1	1

Appendix

Table 7: Hyperparameter settings for Cast-R1 training.

	LTSF (Historical Inputs) ( $L=96$ , $H=96$ )					EPF (Forecast-Origin Context) ( $L=168$ , $H=24$ )
Model	ETTh1	ETTh2	ETTm1	ETTm2	Wind	BE	DE	FR	NP	PJM
ARIMA	2.429	3.248	2.513	4.325	28.767	13.549	11.150	13.224	4.116	8.481
Prophet	4.592	3.548	2.504	3.781	56.059	14.988	12.238	14.422	3.941	5.739
PatchTST	1.638	2.008	1.397	1.945	20.465	10.400	8.029	8.287	3.474	4.103
iTransformer	1.513	1.930	1.460	1.661	18.186	14.375	11.230	12.618	4.039	5.501
ConvTimeNet	1.439	2.578	1.252	2.057	18.343	10.804	9.405	8.993	3.365	4.313

Appendix

Table 8: MAE results for the same benchmark families and input regimes as Table 1 . The groups do not constitute a controlled context ablation; input access follows Appendix A.4 . Lower values are better. Best values are bold ; second-best values are underlined .

Component	Score	Weight
Length constant	$1$	$0.10$
Prediction accuracy	$q(e_{\mathrm{pred}})$	$0.70$
Seasonality	$q(e_{\mathrm{seas}})$	$0.05$
Trend	$q(e_{\mathrm{trend}})$	$0.15$
Maximum alignment	Maximum hit rate	$0.10$
Minimum alignment	Minimum hit rate	$0.10$

Appendix

Table 9: Components of the valid-output reward before multiplication by the length factor

p

Variant	ETTh1		NP
Variant	MSE	MAE	MSE	MAE
w/o Basic Stats	9.814	2.384	36.781	4.715
w/o Channel Dynamics	7.012	1.532	24.711	3.386
w/o Residual Diagnostics	6.543	1.341	23.774	3.335
w/o Data Quality	6.942	1.574	23.557	3.227
w/o Event Patterns	7.571	1.642	27.154	3.646

Appendix

Table 10: Diagnostic tool ablations on ETTh1 and NP.

Figure 6: Forecast comparison on ETTh1 oil temperature with $L=96$ and $H=96$ . Dashed lines separate the 96 historical observations from the 96-step forecasting horizon.

Variant	ETTh1		NP
Variant	MSE	MAE	MSE	MAE
w/o ARIMA	6.614	1.413	24.788	3.334
w/o Chronos	8.414	1.622	55.418	7.097
w/o PatchTST	14.261	3.014	37.191	4.277
w/o iTransformer	13.512	2.825	30.387	4.054
Cast-R1	6.062	1.320	24.750	3.255

Appendix

Table 11: Forecasting model ablations on ETTh1 and NP.

Variant	ETTh1		NP
Variant	MSE	MAE	MSE	MAE
w/o Planning	18.184	3.914	38.540	5.549
w/o Refinement	9.142	1.542	25.413	3.841
Cast-R1	6.062	1.320	24.750	3.255

Appendix

Table 12: Agent component ablations on ETTh1 and NP, removing planning or refinement.

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CastFlow: Bridging Evidence Acquisition and Accurate Prediction in Agentic Time Series Forecasting

Bokai Pan, Mingyue Cheng, Xiaoyu Tao, Zhiding Liu+5

State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei 230026, China

Time Series Forecasting LLM-Based Time Series Forecasting Agentic Time Series Forecasting

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Time series forecasting is a fundamental task in temporal data analytics, and large language model (LLM)-based agents offer a promising paradigm through autonomous tool interaction and evidence-grounded reasoning. However, two fundamental challenges remain: how to acquire forecast-relevant evidence through adaptive tool interactions, and how to translate such evidence into accurate numerical predictions. To address these challenges, we propose CastFlow, a role-specialized agentic forecasting framework that bridges general-purpose tool reasoning and specialized temporal forecasting. Specifically, CastFlow introduces an Experience Memory that distills successful tool-use trajectories from training data, guiding a frozen LLM to orchestrate a multi-view toolkit for evidence acquisition. A lightweight specialized LLM then performs evidence-grounded temporal reasoning to refine an ensemble forecasting prior. To enhance this capability, we develop a two-stage training strategy combining supervised fine-tuning and reinforcement learning with verifiable rewards, where final forecasting outcomes of the overall workflow guide the optimization of the specialized model. Extensive experiments on ten real-world benchmarks demonstrate that CastFlow outperforms competitive baselines on nine datasets. Our findings highlight the importance of bridging autonomous evidence acquisition and specialized temporal reasoning for accurate and adaptive agentic forecasting. The source code is available at https://github.com/Forever-Pan/CastFlow.

Abstract

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