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变量投影稀疏函数主成分分析：可解释降维及拉曼光谱应用AI 解读

Functional principal component analysis (FPCA) provides low-rank representations of functional data but generally produces dense components, making it difficult to identify the localised regions contributing to dominant modes of variation. This limitation is particularly relevant in Raman spectroscopy, where spectra are observed over an ordered domain and interpretation often focuses on chemically meaningful spectral regions. This study proposes variable-projection sparse…

广义动态函数主成分分析AI 解读

In this paper, we explore dimension reduction for functional time series. We propose a generalized dynamic functional principal component analysis (GDFPCA) which does not rely on spectral density estimation and demonstrates strong empirical performance for both stationary and nonstationary functional time series. We define the generalized dynamic functional principal components (GDFPCs) as static factor time series in a functional dynamic factor model and obtain their…

马尔可夫切换时空 ARCH 模型AI 解读

Stock market indices are volatile by nature, and sudden shocks are known to affect volatility patterns. The autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) models neglect structural breaks triggered by sudden shocks that may lead to an overestimation of persistence, causing an upward bias in the estimates. Different regime-switching models that have abrupt regime-switching governed by a Markov chain were developed to model volatility in…