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"Hierarchical time series adalah sejumlah data time series yang mengikuti struktur penggabungan hierarki, dimana data time series pada level lebih tinggi adalah hasil penggabungan dari level yang lebih rendah. Fokus utama dari penelitian ini adalah untuk mem-forecast data berjenis hierarchical time series ini. Forecasting dapat dilakukan dengan menggunakan model hierarchical forecasting. Model ini bekerja dengan memforecast semua time series yang ada pada hierarki, secara individual, masing-masingdengan menggunakan model terbaiknya. Akan tetapi, hasil forecast yang didapat dengan menggunakan model ini masih tidak koheren, yaitu penjumlahan hasil forecast pada level yang lebih bawah tidak sama dengan hasil forecast di level lebih atasnya. Hasil forecast ini dapat diperbaiki dengan merekonsiliasi hasil forecast yang telah didapat agar hasilnya koheren. Metode rekonsiliasi umum yang biasa digunakan adalah metode bottom-up atau top-down. Walau demikian, penelitian ini menggunakan metode rekonsiliasi minimum trace untuk mendapatkan hasil forecast koheren. Metode rekonsiliasi ini bekerja dengan meminimumkan variansi residual, dengan syarat hasil forecast koheren yang didapat bersifat tidak bias. Metode hierarchical forecasting dengan rekonsiliasi minimum trace ini akan diimplementasikan untuk mem-forecast jumlah pengangguran di Australia dan di setiap provinsinya pada tahun 2020, dengan menggunakan data pengangguran tahun 1979 hingga 2019. Nantinya, hasil forecast yang didapat di berbagai jenjang pada hierarki akan koheren.

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Hierarchical time series is a collection of time series that follows a hierarchical aggregation structure, where the time series collection at the higher level is a result of lower leveled time series aggregation. The focus of this research is to forecast this hierarchical time series data. The forecasting can be done using the hierarchical forecasting model. This model works by forecasting each time series in the hierarchy individually using its best model. However, the forecast result from using this model is not coherent. It means that the forecast result summation of the lower level is not equal to the corresponding upper level forecast result. This forecast result can be improved with the help of reconciliation method, that makes the forecast coherent. Basic reconciliation

method that’s widely used is the bottom-up or top-down method. Even so, this research will use the minimum trace reconciliation method to get that coherent forecasts. This reconciliation method works by minimizing the residual variance, with the condition that the coherent forecast results are already unbiased. This hierarchical forecasting with minimum trace reconciliation method will then be implemented to forecast the unemployment number in Australia and its provinces on year 2020, using the unemployment number data from year 1979 until 2019. Later on, the forecast resulted on each level of the hierarchy will be coherent."

"[ABSTRAKHierarchical clustering merupakan metode yang efektif dalam membentuk pohonfilogenetik dengan mengetahui matriks jarak antar barisan DNA. Salah satu carauntuk membuat matriks jarak yaitu dengan cara menggunakan metode -mer.Kelebihan dari metode -mer yaitu lebih efisien dalam segi waktu. Langkahlangkahdalam membuat matriks jarak dengan metode -mer dimulai denganmembentuk -mer sparse matrix dari masing barisan DNA. Selanjutnya,membentuk -mer singular value vector. Pada tahap akhir yaitu menghitung jarakantar vektor. Pada tesis ini akan dilakukan analisis terhadap barisan DNA MERSCoVdengan mengimplementasi Hierarchical clustering menggunakan -merssparse matrix sehingga dapat diketahui leluhur dari masing-masing barisan DNAMERS-CoV.

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ABSTRACTHierarchical clustering is an effective method in creating phylogenetic byknowing the distance matrix between DNA sequence. One of methods to make thedistance matrix use -mer method. -mer is more efficient than others. The stepsto make distance matrix using -mer method starts from creating -mer sparsematrix. Then, creating -mer singular value vector. The last steps is countingdistance each vectors. This thesis will analyze the sequence of DNA MERS-CoVby implementing Hierarchical clustering using k-mers sparse matrix so that willbe known the ancestor of each sequence of DNA MERS-CoV., Hierarchical clustering is an effective method in creating phylogenetic byknowing the distance matrix between DNA sequence. One of methods to make thedistance matrix use -mer method. -mer is more efficient than others. The stepsto make distance matrix using -mer method starts from creating -mer sparsematrix. Then, creating -mer singular value vector. The last steps is countingdistance each vectors. This thesis will analyze the sequence of DNA MERS-CoVby implementing Hierarchical clustering using k-mers sparse matrix so that willbe known the ancestor of each sequence of DNA MERS-CoV.]"

"Berdasarkan data WHO pada pertengahan Juli 2021 lebih dari 185,2 juta orang di seluruh dunia terinfeksi virus corona atau Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). Virus ini menyerang penapasan manusia yang dapat mengakibatkan infeksi paru-paru pada manusia dan bahkan dapat menyebabkan kematian. Tercatat bahwa lebih dari 4 juta orang di seluruh dunia meninggal akibat terinfeksi virus corona. Di Indonesia sendiri pada pertengahan Juli 2021 tercatat lebih dari 2,4 juta orang ternfeksi virus corona dan lebih dari 65,4 ribu orang meninggal akibat terinfeksi virus corona. Berdasarkan data tersebut, perlu dilakukan analisis kekerabatan virus SARS-CoV-2 untuk mengurangi penyebaran dan memberikan batasan sosial dari negara satu dengan negara lainnya. Identifikasi kekerabatan dari virus covid-19 dan penyebarannya dapat dilakukan dengan cara pembentukan pohon filogenetik dan clustering. Pada penelitian ini pohon filogenetik akan dibangun berdasarkan metode Hierarchical Clustering dengan menggunakan metode Multiple Encoding Vector dan K-Mer berdasarkan translasi DNA kodon menjadi asam amino. Jarak Euclidean akan digunakan untuk menentukan matriks jarak. Penelitian ini selanjutnya menggunakan metode K- Means Clustering untuk melihat penyebarannya, dimana nilai k ditentukan dari jumlah centroid yang dihasilkan dari metode Hierarchical Clustering. Penelitian ini mengambil sampel barisan DNA SARS-CoV-2 dari beberapa negara yang tertular. Dari hasil simulasi, nenek moyang SARS-CoV-2 berasal dari China. Hasil analisis juga menunjukkan bahwa leluhur covid-19 yang paling dekat dengan Indonesia berasal dari India, Australia dan Spanyol. Selain itu dari hasil simulasi dihasilkan bahwa barisan DNA SARS-CoV-2 terdiri dari 9 cluster dan cluster keenam adalah kelompok yang memiliki anggota paling banyak. Hasil analisis juga menunjukkan bahwa metode ini sangat opitimal dalam pengelompokan data dengan nilai 97.4%.

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Based on WHO data in middle of July 2021, Coronavirus or Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is infecting more than 185.2 million people worldwide. The virus attacks human breathing, which can cause lung infections and can even cause death. More than 4 million people worldwide have died due to being infected with the coronavirus. In Indonesia alone, in mid-July 2021, there were more than 2.4 million people infected with the corona virus and more than 65.4 thousand people died from being infected with the corona virus. Based on those covid-19 survivor data, it is necessary to carry out a kinship analysis of the coronavirus to reduce its spreading. Identification of the kinship of the covid- 19 virus and its spread can be done by forming a phylogenetic tree and clustering. This study uses the Multiple Encoding Vector method and K-mer based on translation DNA codon to amino acid in analyzing sequences and Euclidean Distance to determine the distance matrix. This research will then use the Hierarchical Clustering method to determine the number of initial centroids and cluster, which will be used later by the K-Means Clustering method kinship in SARS-CoV-2 DNA sequence. This study took samples of DNA sequences of SARS-CoV-2 from several infected countries. From the simulation results, the ancestors of SARS-CoV-2 came from China. The results of the analysis also show that the closest ancestors of covid-19 to Indonesia came from India, Australia and Spain. In addition, the ancestors of SARS-CoV-2 came from China. The SARS- CoV-2 DNA sequence is also consisted of 9 clusters, and the sixth cluster is the group that has the most members. The results also show that this method is very optimal in a grouping of data with a value of 97.4%."

"[Salah satu tujuan dalam studi ekpresi gen (DNA/Protein) adalah menemukan subbagianyang penting secara biologis dan kelompok-kelompok dari gen-gen. Pengelompokan gen tersebut dapat dilakukan dengan metode hirarki maupun metode partisi. Kedua metode pengelompokan dapat dikombinasikan, dimanadilakukan fase partisi dan hirarki secara bergantian, metode ini dikenal dengan metode Hopach. Tahap partisi dapat dilakukan dengan metode PAM, SOM, atau K-Means. Proses partisi dilanjutkan dengan proses Ordered, baru kemudian dikoreksi dengan proses agglomorative, sehingga hasil pengelompokan menjadi lebih akurat. Dalam menentukan kelompok utama digunakan ukuran MSS (Median Split Silhouette). MSS mengukur homogenitas hasil pengelompokan,dimana hasil pengelompokan yang dipilih adalah yang meminimumkan MSS. Pada pengelompokan 136 barisan DNA Virus Ebola dari GeneBank. Prosesawalnya dilakukan pensejajaran global, dan dilanjutkan dengan perhitungan jarak genetik dengan menggunakan koreksi Jukes-Cantor. Pada penelitian ini didapat jarak genetik maksimum adalah 0.6153407 sedangkan jarak genetik minimum adalah 0. Selanjutnya matriks jarak genetik dapat dijadikan dasar untuk mengelompokkan barisan-barisan tersebut dengan menggunakan metode Hopach. Pada hasil pengelompokan Hopach-PAM, diperoleh kelompok utama sebanyak 10 kelompok dengan nilai MSS sebesar 0,8873843. Kelompok-kelompok virus ebola dapat diidentifikasikan berdasarkan subspesies dan tahun pertama kali mewabah.Proses pensejajaran global dan pengelompokan Hopach-PAM menggunakan bantuan program open source R.

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One goal in the study of gene expression (DNA/Protein) is finding biologically important subsets and clusters of genes. Clustering these genes can be achieved by hierarchical and partitioning methods. Both clustering methods can be combined, where partition and hierarchy phases can be executed alternately, this method is known as a Hopach method. The partitioning step can be done by the PAM, SOM, or K-Means clustering method. The partition process continued with the process of Ordered, then corrected with agglomorative process, so that the clustminering results become more accurate. The main clusters determine by using MSS

(Median Split Silhouette). MSS is used to measure homogeneity of the clustering result, in which the clustering is selected to minimize its MSS. The clustering procceses of 136 DNA sequences of Ebola virus, are started by performing a global alignment, and continued with the genetic distance calculations using

Jukes-Cantor correction. In this research we found the maximum genetic distance is 0.6153407, meanwhile the minimum genetic distance is 0. Furthermore, the genetic distance matrix can be used as a basis for clustering sequences in Hopach-PAM clustering method. Based on, the clustering results, we obtained 10 major clusters with MSS value of 0.8873843. Ebola virus clusters can be identified by subspecies and the first occoring year of their outbreak. We implemented the global alignment process and Hopach-PAM clustering algorithm using the open source program R.;One goal in the study of gene expression (DNA/Protein) is finding biologically important subsets and clusters of genes. Clustering these genes can be achieved by hierarchical and partitioning methods. Both clustering methods can be combined, where partition and hierarchy phases can be executed alternately, this method is known as a Hopach method. The partitioning step can be done by the PAM, SOM, K-Means clustering method. The partition process continued with the process

of Ordered, then corrected with agglomorative process, so that the clustmineringresults become more accurate. The main clusters determine by using MSS (Median Split Silhouette). MSS is used to measure homogeneity of the clustering result, in which the clustering is selected to minimize its MSS. The clustering procceses of 136 DNA sequences of Ebola virus, are started by performing a global alignment, and continued with the genetic distance calculations using Jukes-Cantor correction. In this research we found the maximum genetic distance is 0.6153407, meanwhile the minimum genetic distance is 0. Furthermore, the genetic distance matrix can be used as a basis for clustering sequences in Hopach-PAM clustering method. Based on, the clustering results, we obtained 10 major clusters with MSS value of 0.8873843. Ebola virus clusters can be identified by subspecies and the first occoring year of their outbreak. We implemented the global alignment process and Hopach-PAM clustering algorithm using the open

source program R., One goal in the study of gene expression (DNA/Protein) is finding biologically

important subsets and clusters of genes. Clustering these genes can be achieved by

hierarchical and partitioning methods. Both clustering methods can be combined,

where partition and hierarchy phases can be executed alternately, this method is

known as a Hopach method. The partitioning step can be done by the PAM, SOM,

or K-Means clustering method. The partition process continued with the process

of Ordered, then corrected with agglomorative process, so that the clustminering

results become more accurate. The main clusters determine by using MSS

(Median Split Silhouette). MSS is used to measure homogeneity of the clustering

result, in which the clustering is selected to minimize its MSS. The clustering

procceses of 136 DNA sequences of Ebola virus, are started by performing a

global alignment, and continued with the genetic distance calculations using

Jukes-Cantor correction. In this research we found the maximum genetic distance

is 0.6153407, meanwhile the minimum genetic distance is 0. Furthermore, the

genetic distance matrix can be used as a basis for clustering sequences in Hopach-

PAM clustering method. Based on, the clustering results, we obtained 10 major

clusters with MSS value of 0.8873843. Ebola virus clusters can be identified by

subspecies and the first occoring year of their outbreak. We implemented the

global alignment process and Hopach-PAM clustering algorithm using the open

source program R.]"

"Model mortalitas merupakan aspek penting dalam menentukan premi untuk perusahaanasuransi jiwa ataupun dana pensiun. Model mortalitas untuk populasi tunggal umumnyamengasumsikan independensi mortalitas antar populasi. Pada tugas akhir ini akan dibahasmodel prediksi mortalitas yang mengasumsikan dependensi mortalitas antar populasiuntuk memodelkan mortalitas multi-populasi. Pendekatan yang digunakan adalah modelkredibilitas hierarki untuk memprediksi mortalitas beberapa negara (multi-populasi).Secara sederhana, model kredibilitas Bühlmann memprediksi nilai dari suatu peubah acakdi satu periode yang akan datang. Model kredibilitas hierarki adalah generalisasi darimodel kredibilitas Bühlmann dan model kredibilitas Bühlmann-Straub dengan strukturpohon hierarki empat tingkat atau lebih. Pada tulisan ini diterapkan struktur pohonhierarki 5 tingkat yang terdiri dari multi-negara, negara, jenis kelamin, usia, dan tahun.Untuk memprediksi nilai dari peubah acak yang menyatakan tingkat perubahan nilailogaritma natural dari central death rate di periode-periode berikutnya, digunakan duastrategi, yaitu Expanding Window dan Moving Window. Kedua strategi memanfaatkandata prediksi terbaru sebagai data yang digunakan untuk memprediksi tahun berikutnya,namun strategi Moving Window menghilangkan data terlama. Parameter dari model yangdigunakan akan diestimasi menggunakan pendekatan non-parametrik. Data yangdigunakan untuk penerapan model adalah data mortalitas dari Norwegia, Kanada danJepang. Pada akhir tulisan, performa dari model prediksi mortalitas dengan pendekatanmodel kredibilitas hierarki dibandingkan terhadap model Lee-Carter menggunakan nilaiAMAPE (Average of Mean Absolute Percentage Error) dan RR (Reduction Ratio).Berdasarkan hasil prediksi pada tugas akhir ini, pendekatan kredibilitas hierarki memilikiperforma yang lebih baik dibanding model Lee-Carter dalam memprediksi mortalitasmulti-populasi.

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Mortality model is an important aspect in determining premium for life insurance

company and pension fund company. Generally, mortality model for single population

assumes independence between mortality of population. This thesis discusses mortality

model that assumes dependence between mortality of population to model multipopulation

mortality. Hierarchical credibility model is the approach used to forecast

mortality of multi-country (multi-population) in this writing. Bühlmann credibility model

predicts the value of a random variable in the future. Hierarchical credibility model is the

generalization of Bühlmann credibility model and Bühlmann-Straub credibility model

with a tree structure of four or more levels. This thesis applies a five-level tree structure

consisting of multi-country, country, gender, age, and year. To predict the random

variable of the yearly decrement of the logarithm of central death rate over the following

periods, two strategies are adopted, which are Expanding Window and Moving Window.

Both strategies utilize the newest predicted data as a part of the data used to predict the

next period, however Moving Window removes the oldest data. The parameters used will

be estimated using the nonparametric approach. Application of the model is applied to

mortality data of Norway, Canada and Japan. In the end of this thesis, mortality model

forecasting performance of hierarchical credibility approach is compared with Lee-Carter

model based on the values of AMAPE (Average of Mean Absolute Percentage Error) and

RR (Reduction Ratio). In accordance with the prediction results from this writing, the

hierarchical credibility approach yields better performance than the Lee-Carter model in

forecasting multi-population mortality."