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| Lascsáková M. |
| THE INFLUENCE OF USING THE DIFFERENT NUMERICAL METHODS TO FORECAST THE ALUMINIUM PRICES BY MEANS OF TWO INITIAL VALUES |
Abstract
Observing trends and forecasting movements of the metal prices is still a current problem. In the mathematical models forecasting the prices on the commodity exchanges the statistical methods are usually used [1], [5]. They need to process a large number of the historical market data. The amount of the needed market data can sometimes be a problem. In such cases other mathematical methods are required.
The paper deals with deriving the numerical model based on the numerical solution of the Cauchy initial problem for the 1st order ordinary differential equations to prognose the prices of aluminium on the London Metal Exchange. We came out of the monthly averages of the daily closing aluminium prices "Cash Seller&Settlement price" in the period from December 2002 to June 2006.
When forecasting monthly average prices, we compare the accuracy of the prognoses acquired by the two chosen numerical methods. In the paper the method of exponential forecasting and the embedded Runge-Kutta formulae of the 5th order to the 6th order are used. The method of exponential forecasting was derived in [4]. In this paper its forecasting success is observed in comparison with the well-known numerical method (the embedded Runge-Kutta formulae of the 5th order to the 6th order [2], [3]). Two types of forecasting are created according to the way of calculating the prognosis by means of the two known previous values, daily forecasting and monthly forecasting. The advantages of the numerical methods during different movements of the aluminium prices are analysed.
Comparing the prognoses obtained by means of the chosen numerical methods and the aluminium stock exchanges we have found out that there are either no diferences in forecasting by using the chosen numerical methods (daily forecasting) or, if there are any, they are little (monthly forecasting). By monthly forecasting, using the method of exponential forecasting we obtain usually higher values of the prognoses than by using the embedded Runge-Kutta formulae of the 5th order to the 6th order. Based on this knowledge, forecasting by using the method of exponential forecasting is usually more advantageous in the stable increasing trend if the increase of the price raises its intensity, during the slighter decline of the prices and in the period of the change from the decreasing trend to the increasing one. On the other hand, the embedded Runge-Kutta formulae of the 5th order to the 6th order gives usually more accurate prognoses in the rapid decreasing trend, in the case of the decreasing intensity of the increase in the prices and in the increasing trend with the decline of the prognosed price.
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| Keywords: forecasting|numerical modelling|ordinary differential equation| |
| No 3 (2008), p. 381-389 |
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| Ivanišin P., Hirjak M. |
| BLAST FURNACE SLAG, PROCESSING AND UTILIZATION |
| Keywords: blast furnace slag|processing of slag|granulated blast furnace slag|blast furnace gravel and blast furnace pumice|utilization of blast furnace slag| |
| No 3 (2008), p. 414-418 |
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