The Basics of Financial Econometrics: Tools, Concepts, and Asset Management Applications

APPENDIX C

Inferential Statistics

In Appendix A, we provided the basics of descriptive statistics. Our focus in this appendix is on inferential statistics, covering the three major topics of point estimators, confidence intervals, and hypothesis testing.

POINT ESTIMATORS

Since it is generally infeasible or simply too involved to analyze an entire population in order to obtain full certainty as to the true environment, we need to rely on a small sample to retrieve information about the population parameters. To obtain insight about the true but unknown parameter value, we draw a sample from which we compute statistics or estimates for the parameter.

In this section, we will learn about samples, statistics, and estimators. In particular, we present the linear estimator, explain quality criteria (such as the bias, mean squared error, and standard error) and the large-sample criteria. In the context of large-sample criteria, we present the idea behind consistency, for which we need the definition of convergence in probability and the law of large numbers. As another large-sample criterion, we introduce the unbiased efficiency, explaining the best linear unbiased estimator or, alternatively, the minimum-variance linear unbiased estimator.

Sample, Statistic, and Estimator

The probability distributions typically used in financial econometrics depend on one or more parameters. Here we will refer to simply the parameter θ, which will have one or several components, such as the parameters ...