|Ph.D Student||Oren Anava|
|Subject||An Online Learning Approach to Time Series Prediction|
|Department||Department of Industrial Engineering and Management||Supervisor||Professor Hazan Elad|
|Full Thesis text|
Wouldn’t it be nice to be able to predict the future? to know the price of Apple shares before it is actually determined in the stock market? to catch a hard attack before it happens? to forecast the future price of housing in Israel? These tasks and more are all studied under the academic research field called time series analysis. This field was originated in the statistics community more than a century ago, and is still studied rather extensively in the present.
Essentially, the statistical approach to time series analysis consists of the following steps: (i) given a time series, fit a parametric model that captures it in the best way; (ii) estimate the model parameters using familiar statistical techniques; and (iii) use the model for inference (and rarely, also for prediction). While having many strong theoretical appeals, the statistical approach suffers from strict assumptions that are unlikely to hold in practice, and the following statement from [Thomson, 94] is sometimes quoted:
Experience with real-world data, however, soon convinces one that both stationarity and Gaussianity are fairy tales invented for the amusement of undergraduates.
This thesis offers a novel approach to time series analysis: an online learning approach. The main focus of this approach is prediction quality rather than inference, and it requires less stringent assumptions on the mechanism generating the time series. The goal of this thesis is to show that the new approach is more general than the traditional statistical approach, both in theory and in practice. Adaptations of the new approach to several of the most fundamental models and scenarios in time series analysis will be presented and analyzed.