Sio-Iong Ao

Applied Time Series Analysis

There are many reasons to analyze the time series data, for example, to understand the underlying generating mechanism better, to achieve optimal control of the system, or to obtain better forecasting of future values. Applied time series analysis consists of empirical models for analyzing time series in order to extract meaningful statistics and other properties of the time series data. Time series models have various forms and represent different stochastic processes. Time series analysis model is usually classified as either time domain model or frequency domain model. Time domain models include the auto-correlation and cross-correlation analysis. In a time domain model, mathematical functions are usually used to study the data with respect to time. The three broad classes for modeling the variations of time series process are the autoregressive models, the integrated models, and the moving average models. The autoregressive integrated moving average models are the general class of these models for forecasting a time series that can be stationarized by transformations such as differencing. In a frequency domain model, the analysis of mathematical functions or signals is conducted with respect to frequency rather than time. Mathematical models can be used to convert the time series data between the time and frequency domains. The parameters and features in the frequency domain can be used as inputs for the mathematical models like discrimination analysis and improved results can be obtained.

Real-Word Application III: Developing Innovative Computing Algorithms for Astronomical Time Series

With the advances of the technologies for the sky surveys, massive amount of survey data become available. It would be very helpful for the automatic and semi-automatic methods in the classifications/detections of the astrophysical objects. In fact, for surveys of millions of objects, it may not be possible to detect the desired objects by expert inspection alone. Quasars are interesting astrophysical objects that have been recently discovered more comprehensively from the sky surveys. Automatic and semi-automatic methods have been proposed for the detection of the quasars from the massive data produced by the modern sky surveys. In this chapter, the first section describes about the existing automatic and semi-automatic methods for the comprehensive search of quasars. Secondly, some innovative computing algorithms are described about how to classify the light curves of the quasars against light curves of the other stars.

Real-Word Application I: Developing Innovative Computing Algorithms for Business Time Series

Traditionally, business time series forecasting has been dominated by linear methods, which are easy to implement. They are also easy to understand and interpret. However, the business forecasting is a very difficult task, because the processes can behave more like a random walk process and may be time varying. The linear models have serious limitation with problems of nonlinear relationships. It may be unsatisfactory to approximate the linear models for these nonlinear relationships. In business organizations, forecasting is one of the most important activities that form the basis for strategic and operational decision (Zhang 2004). The importance and complexity of the business time series forecasting problem paves way for the importance of innovative computing paradigms. With the progress of the globalization, the effects from other markets may affect markets in other regions. The interdisciplinary innovative computing techniques can be applied to understand, model and design systems for business forecasting.

Advances in Innovative Computing Paradigms

In this chapter, it is the brief introduction to the innovative computing paradigms, the advances in the technology and the outline of the recent works of the innovative computing projects. There are different techniques to extract information from various kinds of datasets. In Section 3.1, it is about the research advances in computing algorithms and databases, covering topics like knowledge extraction, data mining algorithms, quantum computing, and DNA computing. In Section 3.2, the focus is on the advances in integration of hardware, systems and networks. Topics like innovative hardware system, graphics processing units, visual exploration, network interoperability, and code optimization are discussed. Section 3.3 is about the advances in Internet and grid computing. Updates about distributed computation, large-scale collaborations over the Internet, pooling of computer resources, and knowledge metadata systems are presented. The advances in visualization, design and communication are described in Section 3.4. Section 3.5 is about the advances of innovative computing for time series problems, like retrieval, automatic classification, clustering, and automatic monitoring of time series. In the last section, it is illustrated how to build an innovative computing algorithm for some simulated time series. Then, in the next three chapters, innovative computer algorithms are built for some real time series data in business, biology and physics.