由靜態到動態之依時拆分－－臺灣工業部門實質GDP之按月推估

FROMSTATIC TOWARDS DYNAMIC TEMPORAL DISAGGREGATION:MONTHLY REAL GDP ESTIMATE OF THE INDUSTRIAL SECTOR FOR TAIWAN

時間數列資料由低頻依時拆分（temporally disaggregate） 為高頻的形式，雖不是當下最時髦的計量課題， 卻是實務上經常被遇到、亟需審慎處理的問題， 其重要性不可等閒視之。本文探討10 種依時拆分的方法， 並劃分成三類：一類是只利用自身低頻數列， 如Boot et al. （1967）； 另一類則是輔以相關高頻參考指標數列， 如Denton （1971）、Ginsburgh （1973）、Guerrero （1990）、Chow and Lin （1971）、Fern´andez （1981）、Litterman （1983）、Salazar et al. （1997a， 1997b）、Santos Silva and Cardoso （2001） 等； 第三類則是應用狀態空間（statespace）法，如Harvey and Pierse （1984）、Harvey （1989）以及Moauro and Savio （2005）。其中特別值得強調的是， 傳統依時拆分在設定模型時， 礙於變數取對數後加總不等於變數加總後再取對數， 對所要推估之高頻變數並不取其對數，也不考慮自我遞延項的影響，雖其拆分過程簡便，但可能引起變異數不齊一問題， 而且模型停留在靜態的形式。Salazar et al. （1997a， 1997b） 及Santos Silva and Cardoso （2001）引人入勝之處為導入動態設定，前者更巧妙地利用泰勒展開法化解對數加總的障礙， 使其模型更符合當代計量理論之要求。

This paper reviews ten kinds of universally applied temporal disaggregationmethods. These tenmethods can be classified into three categories. The first uses the unique information of the low-frequency series during disaggregation, e.g., Boot, Feibes and Lisman (1967); The second requires the help of related high-frequency indicators to disaggregate the low-frequency data, such as Denton (1971), Ginsburgh (1973), Guerrero (1990), Chow and Lin (1971), Fern´andez (1981), Litterman (1983), Salazar et al. (1997a, 1997b), Santos Silva and Cardoso (2001), etc. The last utilizes the state-space approach like Harvey and Pierse (1984)、Harvey (1989), and Moauro and Savio (2005). A crucial aspect worthy of attention is that the traditional static disaggregation method may lead to a heteroscedasticity problem, because the dependent variable is repressed in level form. The major reason is that the logarithms of high-frequency estimates do not add up to the logarithm of their aggregate. Salazar et al. (1997a, 1997b) and Santos Silva and Cardoso (2001) first introduce the dynamic structure linking the indicator variables to the interpoland. Salazar et al. also employ Taylor’s approximation to tackle the adding-up obstacle of the logarithmtransformation. In the paper, I’ll utilize the first nine methods to derive themonthly real GDP estimate of the industrial sector for Taiwan and compare the results.