Fisher's test of periodicity in time series and Siegel's version of this test for compound periodicities are investigated in the paper. An improvement increasing the power of the test is suggested and demonstrated by means of numerical simulations.

Let $\left\{W_t\right\}=\left\{{(X_{t^{\text{'}}}^{\text{'}},Y_t^{\text{'}})}^{\text{'}}\right\}$ be vector ARMA $(m,n)$ processes. Denote by ${\widehat{X}}_t\left(a\right)$ the predictor of $X_t$ based on $X_{t-a},X_{t-a-1},...$ and by ${\widehat{X}}_t(a,b)$ the predictor of $X_t$ based on $X_{t-a},X_{t-a-1},...,Y_{t-b},Y_{t-b-1},...$. The accuracy of the predictors is measured by ${\Delta }_X\left(a\right)=\text{E}[X_t-{\widehat{X}}_t\left(a\right)]{[X_t-{\widehat{X}}_t\left(a\right)]}^{\text{'}}$ and ${\Delta }_X(a,b)=\text{E}[X_t-{\widehat{X}}_t(a,b)]{[X_t-{\widehat{X}}_t(a,b)]}^{\text{'}}$. A general sufficient condition for the equality ${\Delta }_X\left(a\right)={\Delta }_X(a,a)]$ is given in the paper and it is shown that the equality ${\Delta }_X\left(1\right)={\Delta }_X(1,1)]$ implies ${\Delta }_X\left(a\right)={\Delta }_X(a,a)]$ for all natural numbers $a$.

Se estudia el problema de inversión en un mercado en donde las rentabilidades aleatorias de los títulos satisfacen una relación temporal con rentabilidades anteriores y las interrelaciones vendrán dadas a través de unos índices, uno común a todos los títulos y otro específico del sector en que pueda incluirse cada título.

For data generated by stationary Markov chains there are considered estimates of chain parameters minimizing $\phi$–divergences between theoretical and empirical distributions of states. Consistency and asymptotic normality are established and the asymptotic covariance matrices are evaluated. Testing of hypotheses about the stationary distributions based on $\phi$–divergences between the estimated and empirical distributions is considered as well. Asymptotic distributions of $\phi$–divergence test statistics are...

For a binary stationary time series define ${\sigma }_n$ to be the number of consecutive ones up to the first zero encountered after time $n$, and consider the problem of estimating the conditional distribution and conditional expectation of ${\sigma }_n$ after one has observed the first $n$ outputs. We present a sequence of stopping times and universal estimators for these quantities which are pointwise consistent for all ergodic binary stationary processes. In case the process is a renewal process with zero the renewal state...

A random process (field) with given parametrized mean and covariance function is observed at a finite number of chosen design points. The information about its parameters is measured via the Fisher information matrix (for normally distributed observations) or using information functionals depending on that matrix. Conditions are stated, under which the contribution of one design point to this information is zero. Explicit expressions are obtained for the amount of information coming from a selected...

Financial investors often face an urgent need to predict the future. Accurate forecasting may allow investors to be aware of changes in financial markets in the future, so that they can reduce the risk of investment. In this paper, we present an intelligent computing paradigm, called the Complex Neuro-Fuzzy System (CNFS), applied to the problem of financial time series forecasting. The CNFS is an adaptive system, which is designed using Complex Fuzzy Sets (CFSs) whose membership functions are complex-valued...

It is proved that Hannan's procedure for statistical test of periodicity in the case of time series with dependent observations can be combined with Siegel's improvement of the classical Fischer's test of periodicity. Simulations performed in the paper show that this combination can increase the power of Hannan's test when at least two periodicities are present in the time series with dependent observations.