Theory of copulas and Archimeadean copulas

In this case, the Gaussian Copula is used to connect the data that correlates with the time and with other data sets. Most often, practitioners rely only on the linear correlation to describe the degree of dependence between two or more variables; an approach that can lead to quite misleading conclusions as this measure is only capable of capturing linear relationships. Correlation doesn't mean causation, prediction using Copula is built on three things that the marginal distribution function, the kernel function, and the function of the Copula. Gaussian Copula involves the covariance matrix are approximated by using kernel functions. Kernel acts as the correlation between the approach of the data values that have the same characteristics. In this case, the characteristics used is the time. The advantage of the kernel function is able to calculate the correlation between random variables that have a realization using data characteristics. The advantage of using the kernel based Copula able to capture the dependencies between data and process data that have the same characteristics with time. Another benefit is that it allows a sequence of random variables have a joint distribution function so that the conditional probability of the prediction can be calculated. 1. PENDAHULUAN Karakteristik umum harga saham adalah memiliki tingkat ketidakpastian. Ketidakpastian ini dalam hal pergerakan harga saham dalam jangka pendek, ataupun dalam jangka panjang. Karakteristik ini tidak disukai oleh para investor karena menimbulkan risiko pada investasi mereka. Ketidakpastian ini juga tidak dapat dihindari dalam investasi. Untuk menghadapi ketidakpastian pergerakan harga, yang dapat dilakukan oleh investor adalah mengurangi ketidakpastian tersebut. Salah satu alat (tools) untuk mengurangi ketidakpastian adalah dengan melakukan prediksi (forecasting) harga saham. Proses prediksi harga saham terbagi menjadi dua kelompok. Kelompok pertama adalah pihak yang mempercayai bahwa terdapat suatu cara untuk memprediksi harga saham. Kelompok kedua adalah pihak yang berkeyakinan bahwa pasar adalah efisien, dan apabila ada informasi baru yang diperoleh, pasar akan menyerapnya dan mengkoreksi dirinya sendiri. Kelompok kedua ini percaya bahwa harga saham tidak dapat diprediksi. Hal inilah yang disebut teori Efficient Market Hypothesis (EMH) seperti yang disebutkan oleh Gryc (2006). Kelompok ini beranggapan bahwa pasar saham mengikuti pola random

In this research, we present a nonparametric approach for the estimation of a copula density using different kernel density methods. Different functions were used: Gaussian, Gumbel, Clayton, and Frank copula, and through various simulation experiments we generated the standard bivariate normal distribution at samples sizes (50, 100, 250 and 500), in both high and low dependency. Different kernel methods were used to estimate the probability density function of the copula with marginal of this bivariate distribution: Mirror-Reflection (MR), Beta Kernel (BK) and transformation kernel (KD) method, then a comparison was carried out between the three methods with all the experiments using the integrated mean squared error. Furthermore, some charts were used to support this comparison such as copula contours to spread the correlation before and after estimations. The simulation results show preference of the transformation kernel estimators (KDE) among all the estimation methods, which also proved that copulas are highly flexible models for high dependency especially of the Gaussian type.