한국 멸치어업의 어획량 분석과 예측 ARIMA 모델 및 스펙트럼 해석 = Analysis and Prediction of Anchovy Fisheries in Korea ARIMA Model and Spectrum Analysis

다국어 초록 (Multilingual Abstract)

Forecasts of the monthly catches of anchovy in Korea were carried out by the seasonal Autoregressive Integrated Moving Average (ARIMA) model and spectral analysis. The seasonal ARIMA model is as follows: $$(1-0.431B)(1-B^{12})Z_t=(1-0.882B^{12})e_t$$ where: $Z_t=value$ at month $t;\;B^{p}$ is a backward shift operator, that is, $B^pZ_t=Z_{t-p};$ and $e_t=error$ term at month t, which is to forecast 24 months ahead the anchovy catches in Korea. The prediction error by the Box-Cox transformation on monthly anchovy catches in Korea was less than that by the logarithmic transformation. The equation of the Box-Cox transformation was $Y'=(Y^{0.58}-1)/0.58$. Forecasts of the monthly anchovy catches for $1991\~1992$, which were compared with the actual catches, had an absolute percentage error (APE) range of $1.0\~63.2\%$. Total observed annual catches in 1991 and 1992 were 170,293 M/T and 168,234 M/T respectively, while the predicted catches were 148,201 M/T and 148,834 M/T $(API\;13.0\%\;and\;11.5\%,\;respectively)$. The spectrum analysis of the monthly catches of anchovy showed some dominant fluctuations in the periods of 2.2, 6.1, 10.2 12.0 and 14.7 months. The spectrum analysis was also useful for selecting the ARIMA model.