StaFIR improves filtering of persistent time series while keeping data close to original
StaFIR: Convex Learning of Stationarity-Aware Causal Filters
Machine Learning
Summary
Time series data, like financial market readings, often change in ways that make them hard to analyze. The authors introduce StaFIR, a new method that carefully removes patterns in the data that cause this instability while keeping the data as close as possible to its original form. This balance helps maintain important information for tasks like forecasting. Their tests show StaFIR adjusts its filtering depending on how persistent the changes in the data are, avoiding unnecessary alterations when the data is already stable.
What this means in practice
- •For financial data analysts: Enhance preprocessing of financial time series to maintain signal integrity while improving stationarity for statistical modeling.
- •For economic forecasters: Improve volatility forecasting by adjusting time series filtering strength adaptively based on data persistence.
Authors
Lorena Egger, Mathis Linger
Abstract
Reducing nonstationarity in a persistent time series entails deciding how much of its temporal dependence to remove. In finance, fractional differencing is often tuned using the Augmented Dickey--Fuller (ADF) test, limiting the search to a one-parameter family of lag profiles and addressing input preservation only indirectly. We propose StaFIR, a causal finite-impulse-response filter with a learned nonnegative mixture of exponential lag profiles. Its convex learning objective balances empirical stationarity with similarity to the input. We evaluate StaFIR on ARFIMA--GARCH controlled settings and rolling financial series, including a realized-volatility forecasting task. The experiments show that StaFIR adjusts its filtering strength to persistence while limiting unnecessary transformation in stationary regimes. In downstream forecasting, there is no clear accuracy difference from fixed half-order differencing, while StaFIR achieves higher measured similarity to the raw signal. A complementary direct forecasting experiment finds that greater input similarity is associated with smaller forecasting penalties, although the raw representation remains stronger.