本文提出了一種新穎的即時多維度偵測系統，對於結構中出現的共同因子或
共同參數改變透過向量自回歸模型（Vector Autoregression）近似方式進行即
時偵測(Real Time Monitory)。
本文中提出的方式計算成本非常低，因為它無需為多變量系統中的每個短記
憶(short memory)和長記憶(long memory)的參數進行估計。然而，偵測檢定
(monitoring test)的極限分佈(limiting distribution)遵循布朗橋(Brownian
bridge)，並且在沒有共同因子(common factor)或共同參數改變(common break)
的虛無假設(null hypothesis)下對於長記憶(long memory)的參數沒有限制。
蒙特卡洛（Monte Carlo）模擬為這種即時多維度偵測系統在有限樣本中的
實用性提供了證據。本文也將即時多維度偵測系統應用於偵測全球市場的即時模
式。

This paper proposes a novel real-time multivariate monitoring procedure for detecting common breaks or factors in the multivariate fractional system via a vector autoregressive (VAR) approximation framework.
The computational cost of this test is extremely mild, in that it is free from estimating the short and long memory parameters for each series of the multivariate system. Thus, the limiting distribution of the monitoring test follows a Brownian bridge and is free of long memory parameters under the null hypothesis of no common factor or break.
Monte Carlo simulations provide the evidence on the usefulness of this multivariate monitoring test in finite samples as well as indicate . The procedure is then applied to monitor the real time pattern of global markets.

摘要
目錄
1. Introduction .......................................................................................................1
2. Model .................................................................................................................2
2.1 Common breaks in a multivariate long memory process ...............................2
2.2 Common factors in a multivariate long memory process ...............................3
3. The VAR( k ) approximation of multivariate fractional processes ......................4
4. Multivariate real time monitoring test ..............................................................5
5. Monte Carlo Simulation .....................................................................................7
5.1 Experiment designs ........................................................................................7
5.2 Monte Carlo Outcomes ..................................................................................8
6. Global Equity Market Volatility Data .................................................................9
7. Conclusion ........................................................................................................11
8. Reference .........................................................................................................23

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