New developments from heteroskedastic models in non-negative integer-valued time series analysis

2022 Fiscal Year Final Research Report

• Project/Area Number: 21K20338
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year Fund
• Review Section: 0201:Algebra, geometry, analysis, applied mathematics,and related fields
• Research Institution: Kyushu University (2022); Waseda University (2021)
• Principal Investigator: Goto Yuichi 九州大学, 数理学研究院, 助教 (90907073)
• Project Period (FY): 2021-08-30 – 2023-03-31
• Keywords: 計数時系列 / 分散不均一性 / 一致性 / 漸近正規性

Outline of Final Research Achievements

In this project, we proposed a model that incorporates an autoregressive structure not only for the conditional expectation but also for the conditional variance in order to introduce a model corresponding to the ARMA-GARCH model to counted time series analysis. The unknown parameters of this model can be estimated in two steps, and their consistency and asymptotic normality are proved. We found that the model can be applied to other testing problems that have not been proposed before. Although we had struggled to show the stationarity of the model, we were able to find clues. These contents will be submitted to an international journal as soon as they are ready. In addition, four papers were published in international journals and presented at domestic and international conferences.

Free Research Field

時系列解析

Academic Significance and Societal Importance of the Research Achievements

本研究成果の学術的意義として, 計数時系列のモデリングの柔軟性が広がることが挙げられる。実際、ARMA-GARCH モデルは, 実証研究にも用いられている実用的なモデルである。さらに、条件付き分散不均一性がINGARCHモデルでは正しく表現できていないため、条件付き分散不均一性を正しく考慮したモデルであるという点にも学術的な価値がある. 研究期間中に出版した論文のうちのひとつは, 統計のトップジャーナルである.