  State Space Models (SSMs) have emerged as a potent tool in sequence modeling
tasks in recent years. These models approximate continuous systems using a set
of basis functions and discretize them to handle input data, making them
well-suited for modeling time series data collected at specific frequencies
from continuous systems. Despite its potential, the application of SSMs in time
series forecasting remains underexplored, with most existing models treating
SSMs as a black box for capturing temporal or channel dependencies. To address
this gap, this paper proposes a novel theoretical framework termed Dynamic
Spectral Operator, offering more intuitive and general guidance on applying
SSMs to time series data. Building upon our theory, we introduce Time-SSM, a
novel SSM-based foundation model with only one-seventh of the parameters
compared to Mamba. Various experiments validate both our theoretical framework
and the superior performance of Time-SSM.
