Dynamic Multi-period Experts for Online Time Series Forecasting

Seungha Hong; Sukang Chae; Suyeon Kim; Sanghwan Jang; Hwanjo Yu

cs.LGMar 10, 2026

Dynamic Multi-period Experts for Online Time Series Forecasting

Authors: Seungha Hong, Sukang Chae, Suyeon Kim, Sanghwan Jang, Hwanjo Yu

Organizations: Pohang University of Science and Technology, Pohang, Republic of Korea · Kyungpook National University, Daegu, Republic of Korea

Abstract

Online Time Series Forecasting (OTSF) requires models to continuously adapt to concept drift. However, existing methods often treat concept drift as a monolithic phenomenon. To address this limitation, we first redefine concept drift by categorizing it into two distinct types: Recurring Drift, where previously seen patterns reappear, and Emergent Drift, where entirely new patterns emerge. We then propose DynaME (Dynamic Multi-period Experts), a novel hybrid framework designed to effectively address this dual nature of drift. For Recurring Drift, DynaME employs a committee of specialized experts that are dynamically fitted to the most relevant historical periodic patterns at each time step. For Emergent Drift, the framework detects high-uncertainty scenarios and shifts reliance to a stable, general expert. Extensive experiments on several benchmark datasets and backbones demonstrate that DynaME effectively adapts to both concept drifts and significantly outperforms existing baselines.

Figures & tables

Figure 1. Effect of recurring drift on PROCEED and Weekly-LR performance on the Traffic dataset, showing the time series segment (top) and corresponding MSE (bottom).

Figure 2. Autocorrelation Function (ACF) analysis on the ECL (top) and Traffic (bottom) datasets. Each plot compares the correlation strength of the daily (Lag-24) and weekly (Lag-168) patterns.

Figure 3. DynaME architecture. The solid-bordered components ( $\phi$ , $f_{0}$ , $g$ ) are parameterized and trained, while the dash-bordered components ( $f_{1}$ , $f_{2}$ , $f_{3}$ ) are non-parametrically fitted.

	Dataset	ETTh2			ETTm1			Traffic			ECL			Weather
	Horizon ( $H$ )	$24$	$48$	$96$	$24$	$48$	$96$	$24$	$48$	$96$	$24$	$48$	$96$	$24$	$48$	$96$
PatchTST	GD	2.062	3.412	5.838	0.524	0.675	0.763	0.511	0.541	0.533	4.225	4.926	6.096	0.927	1.304	1.589
	SOLID	1.924	3.439	5.801	0.498	0.645	0.779	0.403	0.557	0.544	4.191	4.897	6.122	0.897	1.226	1.612
	DSOF	1.850	3.591	6.242	0.595	0.822	0.950	0.478	0.536	0.546	6.363	7.742	8.441	0.998	1.532	1.920
	PROCEED	1.711	2.905	5.752	0.494	0.659	0.776	0.395	0.435	0.457	4.153	4.705	5.871	0.855	1.212	1.578
	DynaME (ours)	1.676	2.871	5.049	0.439	0.589	0.703	0.376	0.398	0.431	4.073	4.541	5.837	0.845	1.146	1.456

Table 1. Comparison of methods across different backbones and prediction horizons. Performance is measured in MSE (Mean Squared Error), with the best performance in each column highlighted in bold. The table presents the Mean Squared Error (MSE) for five different time series forecasting methods (GD, SOLID, DSOF, PROCEED, DynaME (ours)) using three different transformer backbones (PatchTST, iTransformer, xPatch). The best (lowest) MSE value in each combination of dataset and horizon is highlighted in bold.

Method	PatchTST	iTransformer	xPatch
GD	0.0277	0.0174	0.0082
SOLID	0.0283	0.0176	0.0084
DSOF	0.0321	0.0255	0.0163
PROCEED	0.0422	0.0367	0.0234
DynaME-primal	0.1252	0.1092	0.0754
DynaME-dual (ours)	0.0489	0.0423	0.0279

Table 2. Average wall-clock time per step.

	ETTh2	ETTm1	Traffic	ECL	Weather
Simple Average	3.001	0.467	0.407	4.962	1.005
Learnable Gate	2.556	0.446	0.386	4.327	0.906
Detached Gate	2.201	0.451	0.386	4.593	0.941
Dynamic Gate (ours)	1.676	0.439	0.376	4.073	0.845

Table 3. Performance comparison of different gating variants.

Backbone	PatchTST		iTransformer		xPatch
Dataset	ETTh2	Electricity	ETTh2	Electricity	ETTh2	Electricity
w/o $d_{t}$	1.906	4.905	2.318	4.719	2.281	5.136
w/ $d_{t}$	1.676	4.073	1.854	3.834	1.845	4.177

Table 4. Performance comparison with and without

d_{t}

Figure 4. Per-step MSE of " w/

d_{t}

" and " w/o

d_{t}

" with danger signal

d_{t}

during Emergent Drift . The danger signal rises when an MSE spike is detected.

Period selection	ETTh2	ETTm1	Traffic	ECL	Weather
Fixed	1.855	0.460	0.378	4.355	0.886
Dynamic	1.676	0.439	0.376	4.073	0.845

Table 5. Performance comparison of dynamic vs. fixed period selection.

Figure 5. Performance comparison with varying Maximum Sample Size (

n

) and Number of Experts (

k

) on the ETTh2 and ETTm1 datasets.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Dataset	ETTh2	ETTm1	Traffic	ECL	Weather
Length	17,420	69,680	17,544	26,304	52,696
Channels	7	7	862	321	21

Appendix

Table 6. Statistics of the datasets.

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May 20, 2026J/K move · Enter open · S save

Dynamic TMoE: A Drift-Aware Dynamic Mixture of Experts Framework for Non-Stationary Time Series Forecasting

Jiawen Zhu, Shuhan Liu, Di Weng, Yingcai Wu

School of Software Technology, Zhejiang University, Ningbo, China · State Key Lab of CAD&CG, Zhejiang University, Hangzhou, China

Concept Drift Mixture of Experts Communication-Efficient Mixture-of-Experts Non-Stationary Time Series Forecasting Mixture-of-Experts Models Temporal Distribution Shift

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Non-stationary time series forecasting is challenged by evolving distribution shifts that static models struggle to capture. While Mixture-of-Experts (MoE) architectures offer a promising paradigm for decoupling complex drift patterns, existing approaches are limited by fixed expert pools and memoryless routing, hampering their ability to adapt to abrupt regime shifts. To address this, we propose Dynamic TMoE, a framework that unifies architectural evolution with temporal continuity during learning phase. By detecting distribution shifts via Maximum Mean Discrepancy (MMD), we dynamically instantiate heterogeneous experts and prune redundant ones to optimize capacity. Additionally, a temporal memory router leverages recurrent states and an anomaly repository to ensure stable, context-aware expert selection without requiring test-time updates. Experiments on nine benchmarks demonstrate state-of-the-art performance, reducing MSE by 10.4% and MAE by 7.8%. Code is available at https://github.com/andone-07/Dynamic-TMoE.

Abstract

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