## Smooth Forecast Reconciliation

_IMF Working Papers, March 22, 2024_

## Source details

**Canonical URL:** [Smooth Forecast Reconciliation](https://www.imf.org/en/publications/wp/issues/2024/03/22/smooth-forecast-reconciliation-546654)

## Other formats

- [Markdown version](/en/publications/wp/issues/2024/03/22/smooth-forecast-reconciliation-546654/index.md)
- [Structured JSON version](/en/publications/wp/issues/2024/03/22/smooth-forecast-reconciliation-546654/index.json)
- [Bundle manifest](/en/publications/wp/issues/2024/03/22/smooth-forecast-reconciliation-546654/bundle-manifest.json)

## Bibliographic details
- Authors: Sakai Ando
- Published: March 22, 2024
- Series: IMF Working Papers
- DOI: https://doi.org/10.5089/9798400268922.001

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### Summary
- Research question: How to make forecasts that (1) satisfy constraints, like accounting identities, and (2) are smooth over time?
- Motivation: Solving this common forecasting problem manually is resource-intensive, and the existing literature provides little guidance on how to achieve both objectives.
- Main contribution: Proposes a new method to smooth mixed-frequency multivariate time series subject to constraints by integrating the minimum-trace reconciliation and Hodrick-Prescott filter.
- Closed-form result: With linear constraints, the method has a closed-form solution, convenient for a high-dimensional environment.
- Empirical claim: Three examples show that the proposed method can reproduce the smoothness of professional forecasts subject to various constraints and slightly improve forecast performance.

### Method
- Components integrated:
  - Minimum-Trace Reconciliation
  - Hodrick-Prescott filter
- Problem scope:
  - Mixed-frequency multivariate time series
  - Constraints include accounting identities (linear constraints)
- Solution properties:
  - Closed-form solution when constraints are linear
  - Suitable for high-dimensional settings

### Key findings and performance
- Examples:
  - Three examples are used to evaluate the method.
- Outcomes reported:
  - The method can reproduce the smoothness of professional forecasts subject to various constraints.
  - The method slightly improves forecast performance (described qualitatively as "slightly improve forecast performance").

### Implications and applications
- Use cases:
  - GDP forecasting
  - National accounts
  - Any multivariate forecasting task requiring both constraint satisfaction and temporal smoothness
- Advantages:
  - Reduces manual effort required to enforce accounting identities while preserving smooth time paths
  - Computationally convenient in high-dimensional environments due to closed-form solution under linear constraints

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## Content in this bundle

- **Working Paper**
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_Source: https://www.imf.org/en/publications/wp/issues/2024/03/22/smooth-forecast-reconciliation-546654_