An Alternative Proof Of Minimum Trace Reconciliation
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An Alternative Proof of Minimum Trace Reconciliation
Author: Mr. Sakai Ando
language: en
Publisher: International Monetary Fund
Release Date: 2022-07-08
Minimum trace reconciliation, developed by Wickramasuriya et. al. (2019), is an innovation in the literature of forecast reconciliation. The proof, however, is indirect and not easy to extend to more general situations. This paper provides an alternative proof based on the first-order condition in the space of non-square matrix and argues that it is not only simpler but also can be extended to incorporate more general results on minimum weighted trace reconciliation in Panagiotelis et. al. (2021). Thus, our alternative proof not only has pedagogical value but also connects the results in the literature from a unified perspective.
Smooth Forecast Reconciliation
Author: Mr. Sakai Ando
language: en
Publisher: International Monetary Fund
Release Date: 2024-03-22
How to make forecasts that (1) satisfy constraints, like accounting identities, and (2) are smooth over time? Solving this common forecasting problem manually is resource-intensive, but the existing literature provides little guidance on how to achieve both objectives. This paper proposes a new method to smooth mixed-frequency multivariate time series subject to constraints by integrating the minimum-trace reconciliation and Hodrick-Prescott filter. With linear constraints, the method has a closed-form solution, convenient for a high-dimensional environment. Three examples show that the proposed method can reproduce the smoothness of professional forecasts subject to various constraints and slightly improve forecast performance.
Final Report of the Truth and Reconciliation Commission of Canada, Volume One: Summary
Author: Truth and Reconciliation Commission of Canada
language: en
Publisher: James Lorimer & Company
Release Date: 2015-07-22
This is the Final Report of Canada's Truth and Reconciliation Commission and its six-year investigation of the residential school system for Aboriginal youth and the legacy of these schools. This report, the summary volume, includes the history of residential schools, the legacy of that school system, and the full text of the Commission's 94 recommendations for action to address that legacy. This report lays bare a part of Canada's history that until recently was little-known to most non-Aboriginal Canadians. The Commission discusses the logic of the colonization of Canada's territories, and why and how policy and practice developed to end the existence of distinct societies of Aboriginal peoples. Using brief excerpts from the powerful testimony heard from Survivors, this report documents the residential school system which forced children into institutions where they were forbidden to speak their language, required to discard their clothing in favour of institutional wear, given inadequate food, housed in inferior and fire-prone buildings, required to work when they should have been studying, and subjected to emotional, psychological and often physical abuse. In this setting, cruel punishments were all too common, as was sexual abuse. More than 30,000 Survivors have been compensated financially by the Government of Canada for their experiences in residential schools, but the legacy of this experience is ongoing today. This report explains the links to high rates of Aboriginal children being taken from their families, abuse of drugs and alcohol, and high rates of suicide. The report documents the drastic decline in the presence of Aboriginal languages, even as Survivors and others work to maintain their distinctive cultures, traditions, and governance. The report offers 94 calls to action on the part of governments, churches, public institutions and non-Aboriginal Canadians as a path to meaningful reconciliation of Canada today with Aboriginal citizens. Even though the historical experience of residential schools constituted an act of cultural genocide by Canadian government authorities, the United Nation's declaration of the rights of aboriginal peoples and the specific recommendations of the Commission offer a path to move from apology for these events to true reconciliation that can be embraced by all Canadians.