A predictive model for the daily exchange rate of the EUR USD using markov chain and cointegration techniques

الملخص EN

This paper adds to the literature of the exchange rates, some practical points which will be of great importance for financial markets and especially for the stock market.

Firstly, the daily alternation of High and Low on the exchange rates ofEUR/USD follows a uniform distribution and hence if someone bets on this alternation then he puts himself in a position of maximum uncertainty.

Secondly, buying and selling always represent the care for the speculators seeking the right time to open or close their operations.

Any decision deprived of necessary information of the exchange rate (market prices) and especially their volatility, leads to a high risk and the probability of failure of such a speculator is highly elevated.

The four variables Open, High, Low and Close are stationary in first difference.

Since the variables High and Low determine completely the daily extent of the exchange rate EUR/USD, one focused on their evolution taking into account the volatility resulting from an ARCH effect.

For these two variables, one performs a measurement of risk using the family of ARCH models such as ARCH-M, EARCH symmetric and asymmetric and GJR-EARCH asymmetric.

Thirdly, one presents an analysis of cointegration regression for the four systems of variables (High, Open), (Low, Open) and (High, Low, Open) and (High, Low, Open, Close).

Therefore, the Open variable is very informative for those four systems because its value is known at the opening of the market, so it could be served as an endogenous and exogenous variable.

Finally, one predicts prices and volatility of the high and Low using the (ECM) models associated to the two first systems and one shows that the ex-post forecasts reveal an excellent performance