http://www.statsoft.com/textbook/time-series-analysis/

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How To Identify Patterns in Time Series Data: Time Series Analysis

In the following topics, we will first review techniques used to identify patterns in time series data (such as smoothing and curve fitting techniques and autocorrelations), then we will introduce a general class of models that can be used to represent time series data and generate predictions (autoregressive and moving average models). Finally, we will review some simple but commonly used modeling and forecasting techniques based on linear regression. For more information see the topics below.

• General Introduction
• Two Main Goals
• Identifying Patterns in Time Series Data
  • Systematic pattern and random noise
  • Two general aspects of time series patterns
  • Trend Analysis
  • Analysis of Seasonality
• ARIMA (Box & Jenkins) and Autocorrelations
  • General Introduction
  • Two Common Processes
  • ARIMA Methodology
  • Identification Phase
  • Parameter Estimation
  • Evaluation of the Model
• Interrupted Time Series
• Exponential Smoothing
  • General Introduction
  • Simple Exponential Smoothing
  • Choosing the Best Value for Parameter a (alpha)
  • Indices of Lack of Fit (Error)
  • Seasonal and Non-seasonal Models With or Without Trend
• Seasonal Decomposition (Census I)
  • General Introduction
  • Computations
• X-11 Census method II seasonal adjustment
  • Seasonal Adjustment: Basic Ideas and Terms
  • The Census II Method
  • Results Tables Computed by the X-11 Method
  • Specific Description of all Results Tables Computed by the X-11 Method
• Distributed Lags Analysis
  • General Purpose
  • General Model
  • Almon Distributed Lag
• Single Spectrum (Fourier) Analysis
• Cross-spectrum Analysis
  • General Introduction
  • Basic Notation and Principles
  • Results for Each Variable
  • The Cross-periodogram, Cross-density, Quadrature-density, and Cross-amplitude
  • Squared Coherency, Gain, and Phase Shift
  • How the Example Data were Created
• Spectrum Analysis - Basic Notations and Principles
  • Frequency and Period
  • The General Structural Model
  • A Simple Example
  • Periodogram
  • The Problem of Leakage
  • Padding the Time Series
  • Tapering
  • Data Windows and Spectral Density Estimates
  • Preparing the Data for Analysis
  • Results when no Periodicity in the Series Exists
• Fast Fourier Transformations
  • General Introduction
  • Computation of FFT in Time Series