基隆港外海有義波高時間序列不同轉換法之ARMA模式模擬研究

A Time Series Research on the Different Transformation Methods of the Significant Wave Height near the Keelung Harbor

何秉均(Ping-Chun Ho) ； 尹彰(John Z. Yim)

《海洋工程學刊》 2卷1期 (2002/07) Pp. 73-92

https://doi.org/10.6266/JCOE.2002.0201.05

摘要

本文利用ARMA模式模擬基隆港外海逐日最大有義波高時間序列。以Bruce法、Box-Cox法及Guedes Soares與Ferreira兩人(1996)所建議的方法［本文將之簡稱為GF法］等三種不同轉換法，將原始波高時間序列轉換成適合套配ARMA模式的時間序列後，再模擬基隆港外海的波高。除了藉著一些常用的評斷標準一如自相關函數、偏自相關函數、四階動差一來判斷轉換結果的好壞外，並利用AIC值及SBC等值來判定參數的多寡。更進一步地利用比對原始與所模擬的波高時間序列機率分佈的套配結果，來評估這三種不同的轉換法的優劣。就本文所用的，1985年基隆港外海每日最大有義波高時間序列來說，以Box-Cox轉換法所得的結果最佳。

關鍵字

Box-Cox轉換 ； 時間序列分析 ； ARMA

並列摘要

Simulations of time series were considered here in this paper. Maximal significant wave heights on a daily basis for the year 1985 measured near the Keelung Harbor were used as target. Three data transformation methods, namely, the Bruce method, the Box-Cox method, and the one due to Guedes Soares & Ferreira, were considered. Transformed data were then used to estimate the coefficients of the autocorrelation moving-average (ARMA) model. The ”goodness-of-the-fit” of these simulated series were then examined by conducting the ”usual” tests carried out for simulated time series. These ”usual” tests include, the moments, the autocorrelation functions (ACF), and the partial autocorrelation functions (PACF). It is shown that using the AIC and SBC criteria the optimal numbers of the coefficients of the autoregressive (AR) and moving average (MA) models can be determined as ARMA(4, 4). As a further verification, the statistical distributions of simulated time series were compared with those of the original. Based upon these results, it is shown that among the models considered, the Box-Cox transformation model has the best performance in simulating the time series of wave significant heights.

並列關鍵字

time series ； ARMA ； Box-Cox transformation ； significant wave height