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A least-squares filter for sequence-space models

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  • Rigato, Rodolfo Dinis

Abstract

Sequence-space models are becoming increasingly popular in macroeconomics, especially in the heterogeneous-agent literature. However, the econometric toolkit for users of these models remains less developed than that available for traditional state-space methods. This note introduces an algorithm for efficiently filtering unobserved shocks in linear sequence-space models. The proposed filter solves a least-squares optimization problem in closed form and returns the expectation of unobserved shocks conditional on observed data. It handles heteroskedasticity, missing observations, measurement error, and non- Gaussian shock distributions. To illustrate its properties, I apply it to data simulated from a medium-scale heterogeneous-agent New Keynesian model and show that it accurately recovers the underlying structural shocks. JEL Classification: C32, E27, E32, E37

Suggested Citation

  • Rigato, Rodolfo Dinis, 2026. "A least-squares filter for sequence-space models," Working Paper Series 3191, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:20263191
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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E27 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Forecasting and Simulation: Models and Applications
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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