Mô hình không gian trạng thái liên tục- rời rạc của dữ liệu bảng với các thuật toán lọc phi tuyến

AStA Advances in Statistical Analysis - Tập 95 - Trang 375-413 - 2011
Hermann Singer1
1Lehrstuhl für angewandte Statistik und Methoden der empirischen Sozialforschung, FernUniversität in Hagen, Hagen, Germany

Tóm tắt

Mô hình thời gian liên tục với dữ liệu lấy mẫu có nhiều lợi thế hơn so với các mô hình chuỗi thời gian rời rạc và bảng thông thường (xem, ví dụ, số đặc biệt Stat. Neerl. 62(1), 2008). Ví dụ, dữ liệu có khoảng thời gian không bằng nhau giữa các làn sóng có thể được xử lý một cách hiệu quả, vì các tham số mô hình của mô hình hệ động lực không bị ảnh hưởng bởi quy trình đo lường. Mô hình không gian trạng thái liên tục-rời rạc là sự kết hợp của động lực thời gian liên tục (phương trình vi phân ngẫu nhiên, SDE) và các phép đo ồn định thời gian rời rạc. Phương pháp ước lượng cực đại khả năng (ML) của các mô hình bảng tuyến tính được thảo luận sử dụng bộ lọc Kalman và các mô hình phương trình cấu trúc (SEM). Dữ liệu chuỗi thời gian thuần túy và dữ liệu bảng có tương quan (ví dụ, với các hiệu ứng thời gian ngẫu nhiên) có thể được xử lý chính xác bằng các phương pháp SEM. Các mô hình bảng phi tuyến được ước lượng bằng các phương pháp lọc xấp xỉ như bộ lọc Kalman mở rộng (EKF), bộ lọc đường thẳng cục bộ (LLF), bộ lọc Gauss–Hermite (GHF) và bộ lọc Kalman không tiêu chuẩn (UKF). Một lần nữa, các bảng có tương quan được xử lý bằng cách xếp chồng các đơn vị bảng trong một phương trình vector Itô. Cuối cùng, các mô hình động lực không gian được thảo luận. Các biến trạng thái là các trường ngẫu nhiên được cho là các nghiệm của các phương trình vi phân riêng phần ngẫu nhiên (SPDE), được dẫn dắt bởi một tiếng ồn trắng không gian-thời gian. Hơn nữa, các trường này được lọc và ước lượng bằng các phép đo ồn và lấy mẫu.

Từ khóa


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