Models of dependence in stock exchange quotations in the example of quotes of copper and stock of KGHM Polska Miedź SA

Abstract

This paper describes the structure and testing of econometric models of dependence in copper quotes and quotes of KGHM Polska Miedź SA stock on the basis of 6-month data from the London Metal Exchange (LME) and from the Warsaw Stock Exchange (WSE). The reasons for application of such models come from the high correlations between copper quotes in LME in US dollars (x) and KGHM quotes in Polish Zloty (s) in WSE (about 0.96), which confirms the natural hypothesis of the dependency of these values. The linear, power and exponential models are tested in the paper. This choice came from the naturalness of the linear model, the possibility of reduction of the power model and of the expo- nential model to the linear with variable replacement, frequent practical verifiability and lack of theoretical grounds for application of other models. The obtained linear model comes in the form: y = 0,0303_{x -}120,4991, whereas the alternative power model is: = 8.1816-10^_e X¹'⁸³⁷⁸. The exponential model and the linear, power and exponential models which take into consideration “one day delay” proved to be worse. Contrary to the expectations of the author, taking into consideration exchange rate fluctuations in Dollar against Zloty and conversion of copper prices into Zloty at the current rate did not improve the data for the model, as the corresponding correlation ratio (about 0.94) is slightly lower than in the original version. Therefore, the design of the corresponding models proved to be useless. These types of models may be used in predicting one value on the basis of forecast quotes of another. In the described case, the model may be the basis for predicting the quotes of KGHM Polska Miedź SA on the basis of the predicted quotes of copper.