There are three crucial mathematical system concepts in Finance, which are either being confused or misapplied - uncertainty, complexity and rank. First, the concept of epistemic uncertainty is sufficient for modeling and the concept of probability is unnecessary. This is illustrated by...

We consider mean-reverting stochastic processes and build a self- consistent model for forward price dynamics and their applications in power industries. This model with stochastic volatility of the forward price is built using the ideas and equations of stochastic differential geometry in order...

This paper provides some test cases, called circuits, for the evaluation of Gaussian likelihood maximization algorithms of the cointegrated vector autoregressive model. Both I(1) and I(2) models are considered. The performance of algorithms is compared first in terms of effectiveness, defined as...

This paper builds on Kočenda (2001) and extends it in two ways. First, two new intervals of the proximity parameter ε (over which the correlation integral is calculated) are specified. For these ε- ranges new critical values for various lengths of the data sets are introduced and through...

Wavelet analysis, although used extensively in disciplines such as signal processing, engineering, medical sciences, physics and astronomy, has not yet fully entered the economics discipline. In this discussion paper, wavelet analysis is introduced in an intuitive manner, and the existing...

This paper models the firm's production process as a system of simultaneous technologies for desirable and undesirable outputs. Desirable outputs are produced by transforming inputs via the conventional transformation function, whereas (consistent with the material balance condition) undesirable...

We study the finite-sample properties of tests for overidentifying restrictions in linear regression models with a single endogenous regressor and weak instruments. Under the assumption of Gaussian disturbances, we derive expressions for a variety of test statistics as functions of eight...

The paper begins with a figurative representation of the contrast between present-day and formal applied econometrics. An explication of the status of bridge principles in applied econometrics follows. To illustrate the concepts used in the explication, the paper presents a simultaneous-equation...

We investigate confidence intervals and inference for the instrumental variables model with weak instruments. Wald-based confidence intervals perform poorly in that the probability they reject the null is far greater than their nominal size. In the worst case, Wald-based confidence intervals...

In this paper, we develop methods of the determination of the rank of random matrix. Using the matrix perturbation theory to construct or find a suitable bases of the kernel (null space) of the matrix and to determine the limiting distribution of the estimator of the smallest singular values. We...