Waveform Dictionaries as Applied to the Australian Exchange Rate

This paper proposes a new method, called waveform dictionaries, to analyze the trend of the exchange rate of the Australian dollar against other currencies. Four different currencies are explored. They are the U.S. dollar, the Japanese yen, the British pound and the euro. The exchange rates can be classified as non-stationary signals. The waveform dictionaries can reduce the complexity of these signals to produce some informative correlation features. These features are sparse in the time-frequency domain and thus can efficiently represent the characteristics of the signal. These features are then displayed in time-frequency (scale) maps. These maps provide possible insights into market behavior such as the dominant market reaction to news.