Econometric Forecasting and High-Frequency Data Analysis

The following sections are included:

• CONTENTS

• FOREWORD

• PREFACE

The following sections are included:

• Introduction
  • Motivation
  • Overview
    • A theoretical illustration
    • Example
    • Generalisations
    • Forecast evaluation

• Measuring and Reporting Forecast Uncertainty
  • Model-based measures of forecast uncertainty
    • The linear regression model
    • Estimation error in multi-step forecasts
    • Stochastic simulation in non-linear models
    • Loss functions
    • Model uncertainty
  • Empirical measures of forecast uncertainty
  • Reporting forecast uncertainty
    • Forecast intervals
    • Density forecasts
    • Graphical presentations
    • Additional examples
  • Forecast scenarios
  • Uncertainty and disagreement in survey forecasts

• Evaluating Interval and Density Forecasts
  • Likelihood ratio tests of interval forecasts
  • Chi-squared tests of interval forecasts
  • Extensions to density forecasts
  • The probability integral transformation
  • The inverse normal transformation
  • The Bank of England's inflation forecasts
  • Comparing density forecasts

• Conclusion

• References

The following sections are included:

• Introduction

• The Methodology of the Current Quarter Model (CQM)

• The Methodology of the Survey Corner

• Conclusion

• References

This chapter deals with seasonal time series in economics and it reviews models that can be used to forecast out-of-sample data. Some of the key properties of seasonal time series are reviewed, and various empirical examples are given for illustration. The potential limitations to seasonal adjustment are reviewed. The chapter further addresses a few basic models like the deterministic seasonality model and the airline model, and it shows what features of the data these models assume to have. Then, the chapter continues with more advanced models, like those concerning seasonal and periodic unit roots. Finally, there is a discussion of some recent advances, which mainly concern models which allow for links between seasonal variation and heteroskedasticity and non-linearity.

The following sections are included:

• Introduction

• Compound Autoregressive Processes and Affine Processes
  • The Gaussian Autoregressive Process
  • Definition of a Car Process
  • Marginal Distribution
  • Nonlinear Prediction Formulas
  • Compounding Interpretation
    • Integer Autoregressive Process
    • Nonnegative Continuous Variables
  • Continuous Time Affine Processes

• Autoregressive Gamma Process
  • Gamma Distribution
    • Centered Gamma Distribution
    • Noncentered Gamma Distribution
    • Change of scale
  • The Autoregressive Gamma Process
  • Nonlinear Prediction Formula
  • Link with the Cox, Ingersoll, Ross Process
  • Extensions
    • Autoregressive gamma process of order p

• Wishart Autoregressive Process
  • The Outer Product of a Gaussian VAR(1) Process
  • Extension to Stochastic Positive Definite Matrices
  • Conditional Moments
  • Continuous Time Analogue

• Structural Applications
  • Derivative Pricing
    • Affine Term Structures
    • Corporate Bonds
    • Stock Derivatives

• Concluding Remarks

• References

• Appendix 1
  • Prediction Formula

A condensed presentation of linear multivariate time series models, their identification and their use for forecasting is given. General stationary processes, ARMA and state space systems and linear dynamic factor models are described.