Book contents
- Frontmatter
- Contents
- Acknowledgments
- List of Contributors
- Introduction
- 1 The ET Interview: Professor Clive Granger
- PART ONE SPECTRAL ANALYSIS
- PART TWO SEASONALITY
- PART THREE NONLINEARITY
- PART FOUR METHODOLOGY
- PART FIVE FORECASTING
- 17 Estimating the Probability of Flooding on a Tidal River
- 18 Prediction with a Generalized Cost of Error Function
- 19 Some Comments on the Evaluation of Economic Forecasts
- 20 The Combination of Forecasts
- 21 Invited Review: Combining Forecasts – Twenty Years Later
- 22 The Combination of Forecasts Using Changing Weights
- 23 Forecasting Transformed Series
- 24 Forecasting White Noise
- 25 Can We Improve the Perceived Quality of Economic Forecasts?
- 26 Short-Run Forecasts of Electricity Loads and Peaks
- Index
18 - Prediction with a Generalized Cost of Error Function
Published online by Cambridge University Press: 06 July 2010
- Frontmatter
- Contents
- Acknowledgments
- List of Contributors
- Introduction
- 1 The ET Interview: Professor Clive Granger
- PART ONE SPECTRAL ANALYSIS
- PART TWO SEASONALITY
- PART THREE NONLINEARITY
- PART FOUR METHODOLOGY
- PART FIVE FORECASTING
- 17 Estimating the Probability of Flooding on a Tidal River
- 18 Prediction with a Generalized Cost of Error Function
- 19 Some Comments on the Evaluation of Economic Forecasts
- 20 The Combination of Forecasts
- 21 Invited Review: Combining Forecasts – Twenty Years Later
- 22 The Combination of Forecasts Using Changing Weights
- 23 Forecasting Transformed Series
- 24 Forecasting White Noise
- 25 Can We Improve the Perceived Quality of Economic Forecasts?
- 26 Short-Run Forecasts of Electricity Loads and Peaks
- Index
Summary
Classical prediction theory limits itself to quadratic cost functions, and hence least-square predictors. However, the cost functions that arise in practice in economics and management situations are not likely to be quadratic in form, and frequently will be non-symmetric. It is the object of this paper to throw light on prediction in such situations and to suggest some practical implications. It is suggested that a useful, although suboptimal, manner of taking into account generalized cost functions is to add a constant bias term to the predictor. Two theorems are proved showing that under fairly general conditions the bias term can be taken to be zero when one uses a symmetric cost function. If the cost function is a non-symmetric linear function, an expression for the bias can be simply obtained.
INTRODUCTION
Suppose that one predicts some stochastic process and that it is subsequently found that an error of size x has been made. With such an error one can usually determine the cost of having made the error and the amount of this cost will usually increase as the magnitude of the error increases. Let g(x) represent the cost of error function. In both the classical theory of statistical prediction and in practice, this function is usually taken to be of the form g(x) = cx2, so that least-squares predictors are considered. However, in the fields of economics and management an assumption that the cost of error function is proportional to x2 is not particularly realistic.
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- Information
- Essays in EconometricsCollected Papers of Clive W. J. Granger, pp. 366 - 374Publisher: Cambridge University PressPrint publication year: 2001
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