The Nonlinear Intraday Pattern of Futures Market Exchange Rates: An Application of Neural Network Models

This paper applies a neural network model to intraday data of exchange rate futures between January 1990 and July 1992. We use the neural network model and the "lag selection method" to explore the intraday patterns of futures market exchange rates. The approach is particularly useful in detecting the possible nonlinear intraday patterns in the futures. We also conduct forecast performance tests on these intraday patterns. We use four futures-market exchange-rate data series provided by the Chicago Mercantile Exchange: the British Pound, the Japanese yen, the Deutsch Mark, and the Swiss Franc. These data are examined at 15-minute and one-hour intervals. The growth rate of the data is treated as a unit-variate time series and feedforward neural network models are fitted to the data. The independent variables in the neural network are the lags of the dependent variable. There are two parts to the empirical estimation. First, hourly data are divided into two parts, one for in-sample estimation and one for out-of-sample forecast. There are seven data points each day. The candidates for the independent variables are the first fifty lags. The "lag selection method" picks significant lags from them. The simplest means for picking lags is trying each individually. Examining the patterns of the significant lags across seven days, we decide if there are nonlinear data patterns. If the significant lags appear in a multiple of seven, there is an implied daily pattern. Otherwise, there is an irregular pattern. After the significant lags are identified, different combinations are used in the final forecasting model. For the out-of-sample forecast, we compare one-step ahead forecast performances from a neural network model, a linear least-squares regression model, and a random walk model. The forecast performance tests are determine if the derived intraday pattern is a profitable trading rule. Then, we apply the above procedure to 15-minute interval data in the middle of the day and the squares of the growth rate. Previous research shows that intraday patterns are related to the open and/or the close of the day. If no daily pattern is observed for the 15-minute interval data, the results support previous findings. The square of the growth rate is a measure of volatility. Applying the procedure to the squares of the growth rate helps us understand the intraday patterns of volatility. Several researches found intraday patterns in financial series. Most of those findings are based on linear models. This paper proposes to find nonlinear intraday patterns in the futures market and to test any profitability arising from these intraday patterns. We find that there are nonlinear intraday patterns. However, the results from forecast performance tests show that these patterns cannot generate a profitable trading rule.