Applied Time Series Analysis and Innovative Computing

"Chapter 1 Introduction (p. 1-2)

Abstract This book is organized as follows. In first two sections of this chapter, it is the brief introduction to the applied time series analysis and the advances in innovative computing paradigms. In the third section, we describe briefly about the three real-world applications of innovative computing paradigms for time series problems. The contributions of these algorithms to the time series analysis are also described briefly in that section and in more details in their respective chapters. In Chap. 2, we describe about the applied time series analysis generally. Time series analysis models including time domain models and frequency domain models are covered. In Chap. 3, we describe about the recent advances in innovative computing paradigms.

Topics like computing algorithms and databases, integration of hardware, systems and networks, Internet and grid computing, and visualization, design and communication, will be covered. The advances of innovative computing for time series problems are also discussed, and an example of building of an innovative computing algorithm for some simulated time series is illustrated. In Chap. 4, we present the real-world application of innovative computing paradigms for time series problems.

The interdisciplinary innovative computing techniques are applied to understand, model and design systems for business forecasting. In Chap. 5, the second real-world application is for the analysis of the biological time series. Recurrent Elman neural networks and support vector machines have been outlined for temporal modeling of microarray continuous time series data sets. In Chap. 6, we present the last real-world application for the astronomical time series. It is to explore if some innovative computing algorithms can automatically classify the light curves of the quasars against the very similar light curves of the other stars.

1.1 Applied Time Series Analysis

1.1.1 Basic Definitions

A time series can be regarded as any series of measurements taken at different times. Different from other common data analysis problems, time series data have a natural temporal ordering. Examples of time series are the daily stock prices, daily temperature, temporal gene expression values, and temporal light intensity of astronomical objects etc. 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 usually take advantage of the fact that observations close together in time are generally more closely related than observations further apart.

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. Time series forecasting is about the employment of time series model to forecast future events based on past events. The forecasting methods have been applied in various domains, like for example, business forecasting (Ao 2003b–e, 2006, 2007b) and genomic analysis (Ao et al. 2004, Ao 2006, 2007a).

1.1.2 Basic Applied Time Series Models

Time series models have various forms and represent different stochastic processes. Different from a deterministic process, in a stochastic process, there is some indeterminacy in its future evolution described by probability distributions. 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 (AR) models, the integrated (I) models, and the moving average (MA) models. They all depend linearly on previous time series data points (Box and Jenkins 1976). The autoregressive fractionally integrated moving average (ARFIMA) model is the generalization of these three classes."