2022 Fiscal Year Final Research Report
Investigation of the financial structure of the bubble period based on the unit roof contiguous processes with locally stationary high dimensional disturbance
| Project/Area Number |
19K11857
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 60030:Statistical science-related
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| Research Institution | Niigata University |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | 時系列解析 / 緩やかに爆発するモデル / 局所定常過程 / 金融工学 / 高次元データ / 非整数和分過程 / 長期記憶過程 / ランク検定 |
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| Outline of Final Research Achievements |
We constructed the asymptotic theory of unit root related processes with locally stationary innovations. In particular, the asymptotic distribution of the least squares estimator was derived. We applied the slowly explosive processes to describe the financial time series data of the bubble period and to identify the beginning and the end of the bubble period. We extended the results of consistency and asymptotic normality of quasi-Gaussian maximum likelihood estimators for I(d) processes with positive parameters, which are long memory processes related to unit roots, to negative parameters. We derived weak convergence of partial sum processes of generalized near unit root processes with locally stationary innovations to CARMA processes. For the testing problem of null hypothesis of independence against the locally stationary MA alternative hypothesis, we applied the rank test statistic and derived the asymptotic distribution of the test statistic under the alternative hypothesis.
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| Free Research Field |
統計科学
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| Academic Significance and Societal Importance of the Research Achievements |
今後は，局所定常単位根周辺過程を一般化単位根周辺過程を含む形に一般化して，より広いクラスである局所定常一般化単位根周辺過程の理論を構成する。金融時系列データ等の多様性を記述することが可能になり，大規模金融データにおけるバブル期の経済構造やコロナ感染症の流行時期の特徴等をより詳細に説明できるようになる。投資市場やCovid データにおけるイベントの従属構造を局所定常一般化単位根周辺過程を用いて可視化する。局所定常一般化単位根周辺過程の理論を様々な非定常・非正則な時系列解析手法と組み合わせることによって，大規模かつ多種多様な金融時系列やコロナ感染症のデータへの応用が可能になるという意義がある。
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