台北市養殖魚類價格分析──向量ARMA模型之應用

An Analysis of Major Aquaculture Products’ Prices in Taipei: An Application of Vector ARMA Models

本文以台北市魚市場之虱目魚、吳郭魚、鯛類及鱸類等主要之養殖魚類產品批發價量為研究對象，應用ADF（augmented Dickey-Fuller）單根檢定1991年1月至1998年10月價格時間數列，共計282筆旬別資料的特性，進行養殖魚類批發價格之時間數列分析與預測。ADF單根檢定結果顯示四種魚類批發價格皆呈現定態，而多變量完整參數向量ARMA模型之估計殘差變異數明顯地小於單變量ARIMA模型殘差變異數。增加考量季節週期之多變量向量ARMA模型，對虱目魚及吳郭魚價格之殘差變異數皆增大，而對鯛類及鱸類價格的殘差變異數皆縮小，顯示鯛類及鱸類價格較虱目魚及吳郭魚價格有季節週期。最後根據所有模型模擬結果顯示，實際觀察值均落在模擬值95％信賴區間上、下限之間，均方根百分比誤差約為6.32％～12.12％，依不損失模型配適度及節約變數原則之模型估計結果顯示，虱目魚價格（MP）與吳郭魚價格（TP）均有相互顯著影響，可說明兩者關係極為密切；鯛類價格（BP）並不與其它變數有明顯相關，表示鯛類價格並不受其它三類養殖魚種之價量變動而影響；而鱸類價格（PP）明顯受前1及前37期鱸類自身價格顯著影響。 Based on both quantity and value production, aquaculture plays a very important role in Taiwan fishery production. Among aquaculture products, tilapia, milkfish, sea bream and sea perch are the most important species to the Taiwanese aquaculture sector. This paper examines prices and quantities of these four species in Taipei fish market. The ADF unit root test results show that the prices of milkfish, sea bream and sea perch are all stationary and reject the null hypothesis of unit root. Nine time series models including univariate and multivariate ARMA with yearly cycle models have been established. Estimation results show that the full model of multivariate ARMA models provide the most efficient estimates of the variance for four relative price variables than both the univariate and restricted multivariate models. From the simulation results, all models exhibit the actual values fall within the 95% confidence interval of respective simulated values and the root-mean-square percentage error (RMSPE) are 6.32% - 12.12%. According to the likihood value and rule of pasimony, the chosen restricted model shows that there is a significant mutual impact between the prices of milkfish and tilipia. Especially, the price of sea bream does not significantly influenced by three other aquaculture species.