Judul: Analyze Volatility of Large Chilli and Cayenne  Pepper in Indonesia
Abstrak: Komoditas cabai di pasar Indonesia dikenal dalam berbagai jenis di antaranya cabai besar yang terdiri atas cabai merah besar dan cabai keriting serta cabai rawit yang terdiri atas cabai rawit hijau dan cabai rawit merah. Permintaan cabai besar dan cabai rawit memiliki sifat tidak elastis sehingga harganya cenderung volatile. Pola harga yang volatile menyebabkan komoditas cabai termasuk ke dalam kelompok volatile food. Penelitian ini ditujukan untuk mengetahui perbedaan baik pada pola harga cabai besar dan cabai rawit dan volatilitas pada kedua harga cabai tersebut. Metode yang digunakan adalah model ARIMA dan ARCH-GARCH. Hasil penelitian menunjukkan volatilitas yang terjadi pada kedua komoditas tersebut cenderung rendah dan harga cabai rawit memiliki volatilitas yang lebih tinggi dengan koefisien ARCH 0.833003 dibandingkan harga cabai besar yang memiliki koefisien ARCH 0.479061. Harga cabai besar dan cabai rawit memiliki volatilitas yang tinggi yaitu pada periode November sampai dengan Februari. Tingginya volatilitas disebabkan oleh cuaca yang ekstrem sehingga produksi cabai menurun sedangkan permintaan meningkat., The chili commodity in Indonesian market is known in various types, including large chilies consisting of red chilies and curly chilies and cayenne pepper consisting of green cayenne pepper and red cayenne pepper. The demand for large chilies and cayenne pepper is inelastic, so the price tends to be volatile. The volatile price pattern causes the chili commodity to be included in the volatile food category. This study is to determine the differences in both the price patterns of large chili and cayenne pepper and the volatility of the two chili prices. The method that used are ARIMA and ARCH-GARCH models. The results showed that the volatility that occurred in these two commodities tended to be low and the price of cayenne pepper had higher volatility with an ARCH coefficient of 0.833003 compared to the price of large chili which had an ARCH coefficient of 0.479061. The prices of large chilies and cayenne pepper are highly volatile on the November to February. The high volatility was caused by extreme weather so that chili production decreased while demand increased.
Keyword: ARCH-GARCH, ARIMA, Volatility, Cayenne Pepper, Large Chili

Judul: Analysis the Effect of Large Red Chili Prices and Green Cayenne Pepper Prices in Indonesia Using Vector Autoregressive Model
Abstrak: Berdasarkan Pusat Informasi Harga Pangan Strategis, cabai merupakan salah satu dari sepuluh komoditas yang memiliki kontribusi signifikan dalam pembentukan angka inflasi pada sektor bahan makanan di Indonesia. Oleh karena itu, cabai dapat dikatakan komoditas penting bagi perekonomian Indonesia. Harga komoditas cabai sering mengalami lonjakan harga dan fluktuatif. Oleh karena itu, analisis terhadap harga cabai dibutuhkan untuk membantu pengambilan kebijakan stabilisasi harga. Variabel pada penelitian ini adalah harga cabai merah besar dan harga cabai rawit hijau yang termasuk sebagai komoditas pangan strategis. Perkembangan harga cabai merah besar dan harga rawit hijau selama beberapa tahun membentuk data time series. Model Vector Autoregressive (VAR) adalah model peramalan data deret waktu multivariat. Model tersebut tidak hanya bergantung pada lag dari peubah itu sendiri tetapi juga dipengaruhi oleh lag peubah lainnya. Keunggulan Model Vector Autoregressive (VAR) adalah tidak perlu menentukan variabel bebas dan variabel terikat. Hasil penelitian menunjukkan model terbaik untuk menggambarkan harga cabai merah besar dan harga cabai rawit hijau adalah VAR(8). Nilai MAPE untuk harga cabai merah besar sebesar 8,59% dengan R^2 sebesar 80,00% dan untuk harga cabai rawit hijau sebesar 7.05% dengan R^2 sebesar 83,33%. Berdasarkan uji kausalitas Granger cabai merah besar dan cabai rawit hijau memiliki hubungan dua arah., According to the Information Center for Strategic Food Prices, chili is one of ten commodities that have a significant contribution to the inflation rate in the food sector in Indonesia. Therefore, chili can be said to be an important commodity for the Indonesian economy. Chili commodity prices often spike and fluctuate. Therefore, an analysis of chili prices is needed to assist price stabilization policymaking. The variables in this study are the prices of large red chilies and the prices of green cayenne peppers, which were included as strategic food commodities. The price of large red chili and the prices of green cayenne pepper over several years form a time series. The Vector Autoregressive (VAR) model is a multivariate time series data forecasting model. The model does not only depend on the lag of the variable itself but is also affected by the lag of other variables. The advantage of the Vector Autoregressive Model (VAR) is that there is no need to determine dependent and independent variables. The results showed that the best model to describe the price of large red chilies and green cayenne peppers was VAR(8). The MAPE value for the price of large red chili is 8.59% with R^2 of 80.00% and for the price of green cayenne pepper is 7.05% with R^2 of 83.33%. Based on the Granger causality test, the price of large red chilies and the price of green cayenne pepper have a two-way relationship.
Keyword: VAR, uji kausalitas Granger, Granger causality test

Judul: Hamiltonian formulation for linear waves motion in two layers fluid
Abstrak: The surface wave could be considered as a wave that separates two fluids, namely water and air. Based on this assumption, it is introduced the interfacial wave, a wave between two layers of fluid with different density. The formulation of interfacial waves motion begins with deriving the base equation of irrotational ideal fluid. Furthermore, according to irrotational fluid assumption, the base equation can be stated in velocity potential. In this derivation, the fluids domain is assumed to be restricted by rigid lid boundary conditions, both at the upper and lower limit. Therefore, the interfacial waves motion can be explained in a hamiltonian formulation. In the hamiltonian formulation, total energy is defined as the sum of kinetic and potential energy. The hamiltonian system is obtained from reduction of kinetic energy by using the Dirichlet Neumann Operator. The resulted kinetic energy equation is nonlinear. Therefore, this form is linearized by first part of the Taylor expansion. This linearization gives a dispersion relation of linear wave. Based on this dispersion relation, the phase speed of the linear wave depends on the density ratio of the two layers fluid.
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