GARCH processes and the phenomenon of misleading and unambiguous signals

Abstract

In finance, it is quite usual to assume that a process behaves according to a previously specified target generalized autoregressive conditionally heteroscedastic process. The impact of rumors or other events on this process can be frequently described by an outlier responsible for a short‐lived shift in the process mean or by a sustained change in the process variance. This calls for the use of joint schemes for the process mean and variance. Since changes in the mean and in the variance require different actions from the traders/brokers, this paper provides an account on the probabilities of misleading and unambiguous signals of those joint schemes, thus adding insights on their out‐of‐control performance.

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

“…The last computational example is on a theoretical advantage of our mathematical model, that is, that the optimized stored energy (value function) and the optimal policy are concurrently obtained through solving the HJBQVIs only at once. This is a clear advantage over the widely used Monte Carlo stochastic‐type models that require generating a large number of sample paths …”

“…This is a clear advantage over the widely used Monte Carlo stochastic-type models that require generating a large number of sample paths. 75,76 An additional numerical computation is carried out here to demonstrate that the computed optimal policy is superior to policies with a fixed PV angle and, thus, without switching costs. We numerically verify that the optimal policy, which switches the panel angle depending on the cloud dynamics subject to the switching costs, truly outperforms the others.…”

Misleading signals in joint schemes for the mean vector and covariance matrix

“…Several additional works also addressed these two probabilities, namely, Morais and Pacheco, Reynolds and Stoumbos, Morais et al, and Ralha et al, for univariate normal i.i.d. output; Knoth et al, Ramos et al, Ramos, and Morais et al, for univariate stationary Gaussian processes; Sousa et al, for univariate GARCH processes; Ramos and Ramos et al, for bivariate normal i.i.d. output; and Ramos et al, for MVN i.i.d.…”

“…37 Since then, the PMS of types III and IV have been thoroughly discussed in several theses, namely, Morais, 40 Ramos, 34 and Sousa. 41 Several additional works also addressed these two probabilities, namely, Morais and Pacheco, 38 Reynolds and Stoumbos, 42 Morais et al, 43 and Ralha et al, 44 for univariate normal i.i.d. output; Knoth et al, 45 Ramos et al, 32 Ramos, 35 and Morais et al, 46 for univariate stationary Gaussian processes; Sousa et al, 47 for univariate GARCH processes; Ramos 35 and Ramos et al, 33,48 for bivariate normal i.i.d.…”