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 the forecast performance tests on these intraday patterns.

Four futures market exchange rate data provided by Chicago Mercantile Exchange on the British pound, Japanese yen, Deutsche mark, and Swiss franc are used in the paper. The data of each exchange rate 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 of empirical estimation.

First, the hourly data are divided into two parts, one for the in-sample estimation and the other for the out-of-sample forecast. There are seven data points each day. The candidates for the independent variables are the first lag up to 50 lags. These lags are across a period of seven trading days. The procedure of the "lag selection method" is to pick significant lags from these 50 lags. The simplest way to pick the lags is to try each lag individually. By examining the patterns of these significant lags across seven days, we can decide if there are nonlinear patterns in the data. If the significant lags appear in the multiple of seven, this implies that there is a daily pattern. Otherwise, there is an irregular pattern. After these significant lags are identified, different combinations of the lags are used in constructing the final forecasting model.

For the out-of-sample forecast, we compare one-step ahead forecast performances from the neural network model, linear least squared regression model, and the random walk model. The forecast performance tests are used to determine if the derived intraday pattern is a profitable trading rule.

Second, 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 the intraday patterns are related to the open and/or the close of the day. If there is no daily pattern observed for these 15-minute interval data, the results will support previous findings. The square of the growth rate is a measure of the volatility. Applying the procedure to the squares of the growth rate help us to understand the intraday patterns of volatility.

Several researches found intraday patterns in financial series. Most of those findings are based on the analysis of a linear model. This paper proposed to find nonlinear intraday patterns in the futures market and to test the profitability from these intraday patterns. We found that there are nonlinear intraday patterns. However, the results from forecast performance tests show that these patterns cannot generate a profitable trading rule.