Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Kandethody M. Ramachandran, Ph.D.

Committee Member

Yuncheng You, Ph.D.

Committee Member

Gangaram S. Ladde, Ph.D.

Committee Member

Manoug Manougian, Ph.D.


ARIMA, Foreign Exchange Trading, k-Nearest Neighbor Algorithm, Mahalanobis Distance, Multi-step ahead Time Series Forecasting


Foreign exchange (FX) rate forecasting has been a challenging area of study in the past. Various linear and nonlinear methods have been used to forecast FX rates. As the currency data are nonlinear and highly correlated, forecasting through nonlinear dynamical systems is becoming more relevant. The nearest neighbor (NN) algorithm is one of the most commonly used nonlinear pattern recognition and forecasting methods that outperforms the available linear forecasting methods for the high frequency foreign exchange data. The basic idea behind the NN is to capture the local behavior of the data by selecting the instances having similar dynamic behavior. The most relevant k number of histories to the present dynamical structure are the only past values used to predict the future. Due to this reason, NN algorithm is also known as the k-nearest neighbor algorithm (k-NN). Here k represents the number of chosen neighbors.

In the k-nearest neighbor forecasting procedure, similar instances are captured through a distance function. Since the forecasts completely depend on the chosen nearest neighbors, the distance plays a key role in the k-NN algorithm. By choosing an appropriate distance, we can improve the performance of the algorithm significantly. The most commonly used distance for k-NN forecasting in the past was the Euclidean distance. Due to possible correlation among vectors at different time frames, distances based on deterministic vectors, such as Euclidean, are not very appropriate when applying for foreign exchange data. Since Mahalanobis distance captures the correlations, we suggest using this distance in the selection of neighbors.

In the present study, we used five different foreign currencies, which are among the most traded currencies, to compare the performances of the k-NN algorithm with traditional Euclidean and Absolute distances to performances with the proposed Mahalanobis distance. The performances were compared in two ways: (i) forecast accuracy and (ii) transforming their forecasts in to a more effective technical trading rule. The results were obtained with real FX trading data, and the results showed that the method introduced in this work outperforms the other popular methods.

Furthermore, we conducted a thorough investigation of optimal parameter choice with different distance measures. We adopted the concept of distance based weighting to the NN and compared the performances with traditional unweighted NN algorithm based forecasting.

Time series forecasting methods, such as Auto regressive integrated moving average process (ARIMA), are widely used in many ares of time series as a forecasting technique. We compared the performances of proposed Mahalanobis distance based k-NN forecasting procedure with the traditional general ARIM- based forecasting algorithm. In this case the forecasts were also transformed into a technical trading strategy to create buy and sell signals. The two methods were evaluated for their forecasting accuracy and trading performances.

Multi-step ahead forecasting is an important aspect of time series forecasting. Even though many researchers claim that the k-Nearest Neighbor forecasting procedure outperforms the linear forecasting methods for financial time series data, and the available work in the literature supports this claim with one step ahead forecasting. One of our goals in this work was to improve FX trading with multi-step ahead forecasting. A popular multi-step ahead forecasting strategy was adopted in our work to obtain more than one day ahead forecasts. We performed a comparative study on the performance of single step ahead trading strategy and multi-step ahead trading strategy by using five foreign currency data with Mahalanobis distance based k-nearest neighbor algorithm.