| Abstract: | 由大量多維度資料的出現, 假設所有變數的波動都僅由少數幾個重要共同因子所決定 的 「因子模型j 以及其變化模型在近年的文獻研究上也逐漸受到重視。 其中, 為了能讓因 子所蘊含的經濟意義更為清晰, 納入更多經濟結構設定的 「階層式因子模型j 也因而被 引進於實證研究中。 然而, 目前文獻上的 「階層式因子模型j 中皆隱含了兩個重要的限 制: 一為其只能分析定態資料, 男一則為每一階層的因子數目必須由研究者事先給定以 利後續估計方法 (如最大概似估計或貝式估計) 的進行。 此一兩年期的計畫, 即試圖在保 留 「階層式因子模型j 的結構優點下, 突破這兩大限制。 我們的模型允許可能非定態的資 料、 因子及干擾項的存在, 同時每一階層的因子數目將由資料來客觀決定。 並且, 我們提 出的估計方法將僅倚賴主成分分析法, 以逐層分析的方式進行估計。 相較於大部分文獻 所採用的估計方式, 這是一個相對容易執行的估計方法。 我們在此計畫中的第一年中將 會完整探討此模型及其延伸, 與對應的極限性質等, 並於第三年提出兩個針對小型開放 經濟體的實證應用模型。 基本而言, 由於多數資料皆非定態, 而這些非定態特徵可能存在 值得探討的共同趨勢, 因此, 此計畫所提出的分析架構在文獻上是一套新的嘗試, 而且可 與現有的 「階層式因子模型j 相抗衡。
While facing the large dimensional data, the factor model, which assumes the main fluctuations of all variables of interest are driven by only a few common factors, has thus become popular, and lots of its variants are introduced in the literature. In particular, to gain a better understanding of factors, the so-called top- down hierarchical factor model is established by imposing more economic structures on factors. Nevertheless, there are a couple of limitations in the exiting hierarchical factor models: (1) they work for the stationary data only, and (2) the number of factors of each layer must be presumed by researchers in advance of employing the maximum likelihood estimation or Bayesian methods. This two-year project thus aims to get round these limitations, while keeping the advantages of top- down hierarchical factor model. The non-stationary data as well as non-stationary factors and idiosyncratic errors are allowed, the number of factors of each layer is determined by the data instead of presumption by researchers, and the proposed estimation procedure is implementable by applying principal component analysis from top layer to bottom layer recursively. The extensions, the corresponding asymptotic properties of the proposed approach, and two interesting empirical applications to small-open economy will also be discussed in detailed in this project. In essence, the proposed framework is new in the literature and can be a comparable alternative to the existing top-down hierarchical factor models, while facing the possible non-stationary data. |
