I FORECASTING PELAGIC FISH in MALAYSIA USING ETS STATE
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CORE Metadata, citation and similar papers at core.ac.uk Provided by UTHM Institutional Repository i FORECASTING PELAGIC FISH IN MALAYSIA USING ETS STATE SPACE APPROACH HADIZA YAKUBU BAKO A thesis submitted in fulfillment of the requirement for the award of the Master of Science Faculty of Science, Technology and Human Development University Tun Hussein Onn Malaysia DECEMBER, 2014 v ABSTRACT Modelling and forecasting fish catch has been undertaken for a long time over the world. However, From time to time, researchers are always looking for a new model that can predict more accurately the number of fish catch. The objective of this study is to propose the Error Trend and Seasonal (ETS) state space approach.In this study, two techniques of time series analysis were used to forecast fish catch of three commercial fish species found in the Malaysian waters. One of such techniques is the Box-Jenkins method which concerns the building of linear and stochastic dynamic models with minimum data requirements. The second technique is the Error Trend and Seasonal (ETS) state space exponential method which requires no assumptions about the correlations between successive values of the time series. The two class models were used to model and forecast two years monthly catches of the three fish species based on the collected data for the period 2007 – 2011. The SARIMA(1,1,1)(0,0,1)[12], SARIMA(1,1,4)(0,0,1)[12], SARIMA(2,1,1)(0,0,1)[12] and ETS (M, A, M), ETS (M, N, M), ETS (M, A, M) for Dussumiera acuta (tamban buloh), Rastrelliger kanagurta (kembong) and Thunnus tonggol (Tongkol hitam) were proposed respectively. The diagnostic checking for all the fitted models confirmed the adequacy of the models. Results based on the root mean square error (RMSE) and mean absolute error (MAE) demonstrated that the ETS models per- formed better for Thunnus tonggol and Rastrelliger kanagurta, while SARIMA model performed better for Dussumiera acuta. This shows that ETS model which has so far not been used in fisheries in Malaysia is our main contribution in this research. Nevertheless, both models have proven successful in describing and forecasting the monthly fishery dynamics. These forecasts proves helpful in formulating the needed strategies for sustainable management and conservation of the stocks, and can also help the decision makers to establish priorities in terms of fisheries management. vi ABSTRAK Permodelan dan ramalan tangkapan ikan telah dijalankan untuk masa yang lama di seluruh dunia. Namun, terdapat masalah dalam mencari model yang sesuai yang boleh memperoleh dinamik data tang sebagai atribut kepada data tangkapan ikan. Dari masa ke semasa, penyelidik sentiasa mencari model baru yang boleh meramal lebih tepat lagi beberapa tangkapan ikan. Dalam kajian ini, dua teknik analisis siri masa telah digunakan untuk meramal hasil tangkapan ikan daripada tiga spesies ikan komersial yang terdapat di perairan Malaysia. Salah satu teknik itu adalah kaedah Box-Jenkins yang berkaitan dengan pembinaan model dinamik linear dan stokastik dengan keperluan data minimum. Teknik yang kedua ialah ETS keadaan ruang kaedah eksponen yang tidak memerlukan andaian tentang hubungan antara nilai-nilai berturut-turut siri masa. Kedua-dua kelas model digunakan untuk dimodelkan dan meramal dua tahun tangkapan bulanan daripada tiga spesies ikan berdasarkan data yang dikumpul bagi tempoh 2007 - 2011. SARIMA (1,1,1) (0,0,1)[12], SARIMA (1,1,4) (0,0,1)[12], SARIMA (2,1,1) (0,0,1)[12] dan ETS (M, A, M), ETS (M, N, M) , ETS (M, A, M) untuk Dussumiera acuta (tamban Buloh), Rastrelliger kanagurta (Kembong) dan Thunnus tonggol (Tongkol hitam), telah dibangunkan. Semakan diagnostik untuk semua model dipasang mengesahkan kecukupan model. Keputusan berdasarkan punca min ralat kuasa dua (RMSE) dan bermakna ralat mutlak (MAE) menunjukkan prestasi model ETS lebih baik untuk Thunnus tonggol dan Rastrelliger kanagurta, manakala prestasi model SARIMA lebih baik untuk Dussumiera acuta.Ini menunjukkan model ETS yang belum pernah digunakan di perikanan Malaysia ialah penyumbang utama dalam kajian ini. Walau bagaimanapun, kedua- dua model telah terbukti berjaya dalam menerangkan dan meramal dinamik peri- kanan bulanan. Ramalan boleh membantu dalam merangka strategi yang diperlukan untuk pengurusan dan pemuliharaan stok yang berterusan, malah membantu pembuat keputusan untuk menubuhkan keutamaan dari segi pengurusan perikanan. vii TABLE OF CONTENTS DECLARATION ii DEDICATION iii ACKNOWLEDGEMENTS iv ABSTRACT v ABSTRAK vi TABLE OF CONTENTS vii LIST OF TABLES x LIST OF FIGURES xii LIST OF PLATES xv LIST OF ABBREVIATIONS xvi LIST OF APPENDICES xvii CHAPTER 1 INTRODUCTION 1 1.0 Introduction 1 1.1 Background of the study 2 1.2 Important fish species found in Malaysian waters 3 1.2.1 The Tuna Fish 3 1.2.2 The Mackerel 5 1.2.3 The Sardines 7 1.3 Fishing Methods 9 1.3.1 Purse seining method 9 1.3.2 Gill-netting 10 1.3.3 Hook and Line 11 1.4 Fishing seasons in Malaysia 12 1.5 Status of Pelagic fisheries 13 1.6 Problem Statement 13 viii 1.7 Objective of the research 14 1.8 Scope of the research 14 1.9 Significance of the Study 14 1.10 Outline of the Dissertation 15 CHAPTER 2 LITERATURE REVIEW 16 2.1 Introduction 16 2.2 Time Series Analysis 16 2.3 Modelling and Forecasting Fisheries Time Series 17 2.4 Box-Jenkins Methodology on Fisheries Time Series 25 2.5 ETS state space approach on Fisheries Time Series 29 2.6 Chapter Summary 31 CHAPTER 3 METHODOLOGY 32 3.0 Introduction 32 3.1 Time Series 32 3.2 Time Series Analysis 33 3.3 Box-Jenkins Methodology 33 3.3.1 Stationarity 35 3.3.2 Seasonal ARIMA Model 36 3.3.3 Seasonal ARIMA Model Estimation 37 3.4 Models Diagnostic Checking 37 3.4.1 Ljung-Box Test 37 3.5 ETS Modeling 38 3.5.1 Time Series Components 38 3.5.2 State Space Exponential smoothing models (ETS) 40 3.5.3 ETS Model selection 42 3.5.4 Forecasting with ETS models 43 3.6 Measures of Comparison between Fitted Models 45 3.7 Chapter Summary 46 CHAPTER 4 RESULTS AND DISCUSSIONS 47 4.0 Introduction 47 4.1 Data used 47 4.2 Data Exploration 47 ix 4.2.1 Time Plot 48 4.2.2 Autocorrelation functions of the fish catch data sets 50 4.2.3 Time Series Transformation 52 4.2.4 Autocorrelation Function of first difference series 55 4.3 Seasonal ARIMA Model Estimation 58 4.3.1 Diagnostic Results for the fitted Seasonal ARIMA Models 59 4.3.2 Observed and Fitted values from SARIMA Models 62 4.3.3 Forecasts from Seasonal ARIMA models 65 4.4 ETS state space exponential smoothing modelling 70 4.4.1 Time Series components 70 4.4.2 ETS State Space Exponential Smoothing Models Estimation 73 4.4.3 Diagnostic Results for the fitted ETS Models 74 4.4.4 Observed and Fitted Values from ETS Models 77 4.4.5 Forecasts from ETS models 80 4.5 ETS State Space and SARIMA Models Comparison 86 4.6 Chapter Summary 87 CHAPTER 5 SUMMARY, CONCLUSION, RECOMMENDATION AND FUTURE WORK 88 5.1 Summary 88 5.2 Conclusion 88 5.3 Recommendation and Future work 89 REFERENCES 90 APPENDICES 97 x LIST OF TABLES 1.1 Tuna species found in Malaysian waters 4 1.2 Mackerel species found in Malaysian waters 5 1.3 Sardine species found in Malaysian water 8 2.1 Summary on Modelling and Forecasting Fisheries Time Series 21 2.2 Summary on Applications of Box-Jenkins Methodology on Fisheries Time Series 27 2.3 Summary on Applications of Exponential Smoothing Methods on Fisheries Time Series 30 3.1 ETS state space exponential smoothing models 40 3.2 15 ETS State Space Exponential smoothing models equations 41 4.1 Parameter estimates for the fitted SARIMA models 59 4.2 24 monthly forecasts of Dussumiera acuta catches with SARIMA model 66 4.3 24 monthly forecasts of Rastrelliger kangurta catches with SARIMA model 68 4.4 24 monthly forecasts of Thunnus tonggol catches with SARIMA model 66 4.5 Summary results for the fitted ETS state space exponential smoothing models parameters 73 4.6 Seasonal components monthly fish catch 74 4.7 24 monthly forecasts of Dussumiera acuta production with ETS (MAM) model 81 4.8 24 monthly forecasts of Rastrelliger kangurta production with ETS (MNM) model 83 4.9 24 monthly forecasts of Thunnus tonggol production xi with ETS (MAM) model 85 4.10 Comparison of the fitted SARIMA and ETS state space exponential smoothing models for Rastrelliger kanagurta 86 4.11 Comparison of the fitted SARIMA and ETS state space exponential smoothing models for Thunnus tonggol 87 4.11 Comparison of the fitted SARIMA and ETS state space exponential smoothing models for Dussumiera acuta 87 xii LIST OF FIGURES 3.1 Box-Jenkins methodology flowchart 35 3.2 Flowchart of ETS state space modeling 44 3.3 Flowchart summarizing the methodological framework 33 4.1 Time series plot of monthly catches of Dussumiera acuta 48 4.2 Time series plot of monthly catches of Rastrelliger kanagurta 49 4.3 Time series plot of monthly catches of Thunnus tonggol 49 4.4 ACF plot of monthly fish catch data of Thunnus tonggol 50 4.5 ACF plots of monthly fish catch data of Rastrelliger kanagurta 51 4.6 ACF plots of monthly fish catch data of Dussumiera acuta 52 4.7 Time series plot of the first difference series of monthly fish catch data of Thunnus tonggol 53 4.8 Time series plot of the first difference series of monthly fish catch data of Rastrelliger kanagurta 54 4.9 Time series plot of the first difference series of monthly fish catch data of Dussumiera acuta 55 4.10 ACF plots of the first difference series of monthly fish catch data of Thunnus tonggol 56 4.11 ACF plots of the first difference series of monthly fish catch data of Rastrelliger kanagurta 57 4.12 ACF plots of the first difference series of monthly fish catch data of Dussumiera acuta 57 4.13 Diagnostic results for the fitted SARIMA (1,1,1)(0,1,1)[12] ] xiii for Dussumiera acuta 60 4.14 Diagnostic results for the fitted SARIMA (1, 1, 4)(0, 1, 1)12 for Rastrelliger kanagurta 61 4.15 Diagnostic results for the fitted SARIMA (2, 1, 1)(0, 1, 1)12 for Thunnus tonggol 62 4.16 Comparison graph of observed vs.