Case Studies in Time Series Analysis

The following sections are included:

• Preface

• Contents

In this chapter, we shall introduce some basic ideas and models of time series which are very often used in applications. One of the most important concepts in time series is “stationary” even though observations recorded in practice are not always stationary. The reader may easily find that many techniques and theory for analyzing nonstationary data series are based on the theory and methods of stationary time series.

In this chapter, we want to introduce a class of stationary series which has been used in different fields of science, engineering, economics, medicine, etc., we generally call this class as ARMA model. The ARMA model is not only very much interested by the researchers in application fields, but also very much interested by the theoretical researchers since, ARMA model involves very deep mathematical ideas, e.g. Markovian extension theory, rational approximation problem, etc.

In this chapter, the theory and methods on prediction, filtering and spectral analysis of time series will be introduced, and mainly the series is to be stationary, such as AR or ARMA models.

The following sections are included:

• Problem Statement and Working Diagram of a Dynamic Marine Gravity Meter

• The First Test for Solving the Problem

• Design a new digital filter under Min-Max criterion

• The frequency rectification by filtering

• Practical checking in the prospecting field of the East Sea of China

The following sections are included:

• Problem statement

• Design the filter by maximum entropy modelling

• A practical filter design

The following sections are included:

• Introduction

• Spectral analysis of VEP records for dull and normal children

• Statistical Analysis for the detection of characteristics

• Physiological interpretation

• Appendix III Sampling Interval and Aliasing

The following sections are included:

• Introduction

• Principal component analysis in frequency domain and its application in AI analysis

• Practical checking

• Discussion

• Appendix IV

The following sections are included:

• Introduction

• Statistical analysis of LH release

• Practical rhythm analysis of LH release

• Discussion

The following sections are included:

• Introduction

• Statistical detection of weak ring signals from the noise background

• Discussion

The following sections are included:

• Introduction

• A new model fitting procedure for freight transportation prediction

• Forecasting for freight transportation of practical data

• Discussion

• Appendix VII
  • On the X-11 processing procedure
  • Simple exponential smoothing predictor
  • Program for fitting a spline function

The following sections are included:

• Introduction

• Constructing a prediction formula based on the hidden periodicities by the quantile method

• Comparison and discussion

• Appendix VIII
  • Quantile method for detecting the hidden periodicities
  • RMA forecasting method

In this section, the author wants to introduce some of the other cases study in time series analysis which had found very illustrative of applying the theory and methods for solving practical problems.

The following sections are included:

• Bibliography

• Subject Index