# Time Series and Statistics by John Eatwell

By John Eatwell

This is often an excerpt from the 4-volume dictionary of economics, a reference publication which goals to outline the topic of economics this present day. 1300 topic entries within the whole paintings hide the huge topics of financial conception. This extract concentrates on time sequence and information.

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Extra resources for Time Series and Statistics

Sample text

Some measure of central tendency relating to the posterior pdf, say the mean, modal value or median might be used as a point estimate. However, if the posterior pdf is asymmetric, these measures of central tendency will differ and the problem of choice among them remains. When a loss function, L( lJ, 0), is available, this problem can be solved by choosing the value of 0 that minimizes expected loss and such a value is the Bayesian point estimate. Explicitly, the problem to be solved in Bayesian point estimation is min EL( lJ, 0) with respect to 0, or min 6 f 8 L(lJ,O)p(lJ/D)dlJ.

A distinctive feature of Bayesian inference procedures is that they permit investigators to use both sample and prior information in a logically consistent manner in making inferences. This is important since prior information is widely used by Bayesian and non-Bayesian workers in making inferences. Bayes' Theorem, sometimes referred to as the Principle of Inverse Probability, serves as a fundamental learning model in the Bayesian approach. Initial or prior information is combined with current sample information by use of Bayes' Theorem to produce a 'post-data' or 'posterior distribution' that incorporates both prior and sample information.

G. Raiffa and Schlaifer (1961) for further discussion of natural conjugate prior distributions. Another property of Bayes' Theorem that is quite useful and appealing is that it can be applied sequentially to data sets with results that are identical to what is obtained by an application to an entire data set. 10). 10). 2), marginal and conditional posterior pdfs are of interest. Let 8 be partitioned as 40 Bayesian inference 6' = (6;,6;) and suppose that interest centres on 6 1 • For example 6 2 may be a vector of nuisance parameters that are of little interest to an investigator.