We review and simultaneously introduce a convenient statistical concept for the mathematical representation of the Statistical Activity Cost Theory (SACT) introduced by Willett (1987 and 1988). Further, we discuss, and present a critique of, a variety of statistical models with respect to long...

Most MCMC users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. Potentially useful diagnostics may be borrowed from diverse areas such as time series. One such method is phase randomisation. The aim of this paper is to describe this...

Of much interest in financial econometrics is the recovery of joint distributional behaviour of collections of contemporaneous financial time series, e.g., two related commodity price series, or two asset returns series. An approach to model their joint behaviour is to use copulas. Essentially,...

Motivated by the problem of setting prediction intervals in time series analysis, we suggest two new methods for conditional distribution estimation. The first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density...

We study a generalised version of the logistic map of the unit interval $(0,1)$, in which the point $x$ is taken to $1-|2x-1|^nu$. Here, $nu 0$ is a parameter of the map, which has received attention only when $nu =1$ and 2. We obtain the invariant density when $nu = frac12$, and derive...

In order to develop statistical tests for the Lyapunov exponents of deterministic dynamical systems, we develop bootstrap tests based on empirical likelihood for percentiles and expectiles of strictly stationary processes. The percentiles and expectiles are estimated in terms of asymmetric least...

The efficient market hypothesis states that an efficient market immediately incorporates all available information into the price of the traded entity. It is well established that the stock market is not an efficient market as it consists of numerous traders with differing strategies and...

One critical factor in open pit mining projects is the estimation of the recoverable reserves. The reason for this is that at the valuation stage there is a lack of information about future metal prices and production costs. Consequently, the estimation of the recoverable reserves needs to be...

The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series. This is because the bispectrum is the Fourier transform of the third-order moment. An advantage of the bispectrum is that its estimator comprises terms...

In this paper, we consider additive stochastic nonparametric regression models. By approximating the nonparametric components by a class of orthogonal series and using a generalized cross-validation criterion, an adaptive and simultaneous estimation procedure for the nonparametric components is...