# Model-Free Prediction and Regression

## A Transformation-Based Approach to Inference

• Dimitris N. Politis
Book

Part of the Frontiers in Probability and the Statistical Sciences book series (FROPROSTAS)

1. Front Matter
Pages i-xvii
2. ### The Model-Free Prediction Principle

1. Front Matter
Pages 1-1
2. Dimitris N. Politis
Pages 3-11
3. Dimitris N. Politis
Pages 13-30
3. ### Independent Data: Regression

1. Front Matter
Pages 31-31
2. Dimitris N. Politis
Pages 33-56
3. Dimitris N. Politis
Pages 57-80
4. Dimitris N. Politis
Pages 81-93
4. ### Dependent Data: Time Series

1. Front Matter
Pages 95-95
2. Dimitris N. Politis
Pages 97-112
3. Dimitris N. Politis
Pages 113-139
4. Dimitris N. Politis
Pages 141-176
5. Dimitris N. Politis
Pages 177-195
5. ### Case Study: Model-Free Volatility Prediction for Financial Time Series

1. Front Matter
Pages 197-197
2. Dimitris N. Politis
Pages 199-236
6. Back Matter
Pages 237-246

### Introduction

The  Model-Free  Prediction Principle expounded upon in this monograph is based on the simple notion of transforming a complex dataset to one that is easier  to work with, e.g., i.i.d. or Gaussian. As such, it restores the emphasis on observable quantities, i.e., current and future data, as opposed to unobservable model parameters and estimates thereof, and yields optimal predictors in diverse settings such as regression and time series. Furthermore, the Model-Free Bootstrap takes us beyond point prediction in order to construct frequentist prediction intervals without resort to unrealistic assumptions such as normality.

Prediction has been traditionally approached via a model-based paradigm, i.e.,  (a) fit a model to the data at hand, and (b) use the fitted model to extrapolate/predict future data. Due to both mathematical and computational constraints, 20th century  statistical practice focused mostly on parametric models. Fortunately, with the advent of widely accessible powerful computing in the late 1970s, computer-intensive methods  such as    the bootstrap and cross-validation freed practitioners from the limitations of parametric models, and paved  the way towards the `big data' era of the 21st century. Nonetheless, there is a further step one may take, i.e.,  going beyond even nonparametric models; this is where the Model-Free Prediction Principle is useful.

Interestingly, being able to predict a response variable Y associated with a regressor variable  X taking on any possible value seems to inadvertently also achieve  the main goal of modeling, i.e., trying to describe how Y depends on X. Hence, as prediction can be  treated as a by-product of model-fitting, key estimation problems can be addressed as a by-product  of being able to perform prediction. In other words, a practitioner can use Model-Free  Prediction ideas in order to additionally obtain point estimates  and confidence intervals for relevant  parameters   leading to an alternative, transformation-based approach to statistical inference.

### Keywords

Independent and identically distributed Markov processes Modeling Prediction Regression Statistical interference Time series i.i.d.

#### Authors and affiliations

• Dimitris N. Politis
• 1
1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA

### Bibliographic information

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