| Abstract: | 由大量資料的出現，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「動 態因子模型」在近年的文獻硏究上逐漸受到重視。一般而言，我們可以用無母數估計中 的主成分分析法去估計模型，抑或是利用狀態空間轉換以及卡曼平滑法與EM演算法 而得到對應的最大概似估計。值得注意的是，大部分的模型或方法，都必須建立在所有資 料皆爲定態的假設上。由於我們對於大部分的實證資料是否爲定態並沒有先驗上的認知， 因此，在進行模型估計之前，我們都必須倚賴常用的單根檢定辦別資料特性，並據之適當 轉換成定態資料。如人所熟知，常用的這些單根檢定對於某些對立假設的檢定力不高並 可能因資料長短不同而有不同判定，因此將連帶使得後續的分析受到此判定誤差的波及。 由於大量維度資料中，可能具有定態、非定態、缺漏某段時期的資料，也可能具有發佈的 頻率等重要特性，爲了要能捕捉這些特性，相較於文獻上已知的硏究，我於此三年計畫中 針對因子模型提出了一個較爲全面性的分析方法。我以Bai and Ng (2004)允許定態與 非定態特性共存的因子模型爲基礎，並進一步建立其對應之一階差分因子的向量自我迴 歸模型。簡而言之，這個新的分析架構有以下特性:(1)它不會受到因爲單根檢定所產生 之誤差的影響；（2)它可以納入僅具有較爲短期資料的重要變數或是不同頻率的變數於 分析中；（3)可以提高因子或缺漏資料推估的效率性；（4)在此架構下可以進一步探討很 多有趣的實證議題，例如，插補、預測、推估當期資料以及衡量資料對預測某變數的重要 程度等。
While facing thousands of data, the dynamic factor model (DFM) model, which assumes the main uctuations of all variables of interest are driven by only a few common factors, has thus attracted lots of attention in the literature. Typically, we may estimate the model by adopting the nonparametric approach based on principal component analysis, or obtain the (quasi-)maximum likelihood estimators based on the associated state-space representations with Kalman smoothers or expectation maximization (EM) algorithm. Almost all related studies require the panels are stationary, but it is not known a priori whether the series in the panel are stationary in most applications. Therefore, it is common to pretest these series for unit roots and determine the appropriate transformations which render the data stationary. As is well-known, however, unit root pretests may lack powers against some alternatives, and it would thus a ect the following analysis. In order to capture the important features of large dimensional data|they may be stationary, non-stationary or mixed, may be missing for some periods, or may be published at di erent frequencies, I go beyond the studies in the literature to propose a new comprehensive framework to extract factors by combining PANIC model of Bai and Ng(2004) with parametric VAR models for the factors and idiosyncratic errors in the deduced rst-di erenced data. In brief, some attractive features of this proposed approach are: (1) it is free of the biases induced by unit root pretests; (2) important variables with shorter history or released in relatively low frequency can be included; (3) the e?ciency of the estimates for the missing values, latent factors can be improved (especially for small samples); (4) many interesting empirical issues|bakdating, interpolating, forecasting, nowcasting, information evaluation, recovering the structural shocks, etc.|can be further addressed. |
