資料頻率對風險值衡量的影響－變異數比例檢定的應用

本研究以匯率資料探討在不同資料頻率下，估計的外匯報酬率變異數是否有顯著的差別。由於變異數常用做風險值的估計基礎，變異數估計若有差異也影響風險值估計的結果。許多實證研究都假設資產價格服從對數常態分配且其變動無自我相關或價格過程符合幾何布朗運動的前提下，估計資產報酬的變異數與風險值。所以，理論上，不同資料頻率所估計的結果經時間的調整後應是相同的。然而，實際的資產價格過程不必然服從上述的假設。因此，若以實際資料估計，不同資料頻率所估計的結果可能有差異。本文使用2003年1月至2008年12月期間美元兌新台幣與美元兌歐元日資料及週資料為研究樣本，以檢定時間序列是否為隨機漫步的變異數比例檢定（Variance Ratio Test）來檢測不同資料頻率是否有顯著差異。研究結果發現，就新台幣而言，以日資料估計的結果無法接受變異數相同的假說；而以新台幣的週資料與歐元的日資料估計的結果皆接受變異數相同的假說。因此，實務上，10天（兩週）的美元兌新台幣匯率的市場風險值，若以日資料估計再以10天天數調整並無法正確估計10天的風險值；以週資料估計再以時間調整（2週）較能正確估計10天的風險值。而以日資料估計美元兌歐元匯率的10天風險值，則無上述的問題。

關鍵字

變異數；風險值；資料頻率；變異數比例檢定

並列摘要

This paper uses daily and weekly exchange rate data to test if there is significantly different in estimating the variances of exchange rates. This issue is important for computing the value at risk (VAR) because estimated variances are often the input for VAR computation. Under the assumption that the exchange rate follows geometric Brownian motion, that is, the exchange rate follows a lognormal distribution and there is no autocorrelation, the variances estimated from different data frequencies shouldn't be significantly different after adjusting the square root of time. However, this doesn't have to be true if the assumption violated. By examining daily and weekly Taiwan dollar-US dollar (NT/US) and daily Euro-US dollar (Euro/US) data from January 2003 to December 2008 by the variance ratio tests, the results show there is significantly different for daily NT/US exchange rates, but no significant difference for other exchange rate data. As the variance or standard deviation is often used for the estimation of value at risk, it implies the daily NT/US is not appropriate for the 10-day VAR calculation. However, such problem doesn't show up for the weekly NT/US exchange rates or daily Euro/US exchange rates.

並列關鍵字

Variance ； Value at Risk ； Data Frequency ； Variance Ratio Test

國際替代計量

資料頻率對風險值衡量的影響－變異數比例檢定的應用

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