Forecasting semi-stationary processes and statistical arbitrage

If a financial derivative can be traded consecutively and its terminal payoffs can be adjusted as the sum of a bounded process and a stationary process,then we can use the moving average of the historical payoffs to forecast and the corresponding errors form a generalised mean reversion process.Thus we can price the financial derivatives by its moving average.One can even possibly get statistical arbitrage from certain derivative pricing.Weparticularly discuss the example of European call options.We show that there is a possibility to get statistical arbitrage from Black-Scholes’s option price.

AN INFORMATIC APPROACH TO A LONG MEMORY STATIONARY PROCESS

Long memory is an important phenomenon that arises sometimes in the analysis of time series or spatial data.Most of the definitions concerning the long memory of a stationary process are based on the second-order properties of the process.The mutual information between the past and future I_(p−f) of a stationary process represents the information stored in the history of the process which can be used to predict the future.We suggest that a stationary process can be referred to as long memory if its I_(p−f) is infinite.For a stationary process with finite block entropy,I_(p−f) is equal to the excess entropy,which is the summation of redundancies that relate the convergence rate of the conditional(differential)entropy to the entropy rate.Since the definitions of the I_(p−f) and the excess entropy of a stationary process require a very weak moment condition on the distribution of the process,it can be applied to processes whose distributions are without a bounded second moment.A significant property of I_(p−f) is that it is invariant under one-to-one transformation;this enables us to know the I_(p−f) of a stationary process from other processes.For a stationary Gaussian process,the long memory in the sense of mutual information is more strict than that in the sense of covariance.We demonstrate that the I_(p−f) of fractional Gaussian noise is infinite if and only if the Hurst parameter is H∈(1/2,1).

The Classification to Stationary Process of Tidal Motion Observed at the Time of Kuroshio’s Meandering

The tide level displays information about the state of the sea current and the tidal motion. The tide level of the southern coast of Japan Island is affected strongly by Kuroshio Current flowing in the western part of North Pacific Ocean. When Kuroshio takes the straight path and flow along the Japan Islands, the tide level increases, and it is calculated from two tide level data observed at Kushimoto and Uragami in the southern part of Kii Peninsula. In contrast, the tide level decreases at the time when Kuroshio leaves from the Japan Islands. In this paper, the hourly tidal data are analyzed using the Autocorrelation Function (ACF) and the Mutual Information (MI) and the phase trajectories at first. We classify the results into 5 types of tidal motion. Each categorized type is investigated and characterized precisely using the mean tide level and the unit root test (ADF test) next. The frequency of the type having unstable tidal motion increases when the Kuroshio Current is non-meandering or in a transition state or the tide level is high, and the type shows a non-stationary process. On the other hand, when the Kuroshio Current meanders, the tidal motion tends to take a periodical and stable state and the motion is a stationary process. Though it is not frequent, we also discover a type of stationary and irregular tidal motion.

Limit theorems for supremum of Gaussian processes over a random interval

Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.

A NOTE ON SAMPLE PATH PROPERTIES OF l^p-VALUED GAUSSIAN PROCESSES

The a.s. sample path properties for l p valued Gaussian processes with stationary increments under some more general conditions are established.

Sampling Geostatistical Structures in Extremal Framework

Geostatistics of extreme values makes it possible to model the asymptotic behavior of random phenomena that depend on time or space. In this paper, we propose new models of the extremal coefficient of a stationary random field where the cumulative distribution is associated with a multivariate copula. More precisely, some models of extensions of the extremogram and these derivatives are built in a spatial framework. Moreover, both these two geostatistical tools are modeled using the extremal variogram which characterizes the asymptotic stochastic behavior of the phenomena.

Approximation of weak sense stationary stochastic processes from local averages

We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.

The Limit Theorems for Maxima of Stationary Gaussian Processes with Random Index

Let {X（t）, t ≥ 0} be a standard（zero-mean, unit-variance） stationary Gaussian process with correlation function r（·） and continuous sample paths. In this paper, we consider the maxima M（T） = max{X（t）, t∈ [0, T ]} with random index TT, where TT /T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of M（TT） exists under some additional conditions related to the correlation function r（·）.

CONSTRUCTION OF POLYNOMIAL MATRIX USING BLOCK COEFFICIENT MATRIX REPRESENTATION AUTO-REGRESSIVE MOVING AVERAGE MODEL FOR ACTIVELY CONTROLLED STRUCTURES

The polynomial matrix using the block coefficient matrix representation auto-regressive moving average(referred to as the PM-ARMA)model is constructed in this paper for actively controlled multi-degree-of-freedom(MDOF)structures with time-delay through equivalently transforming the preliminary state space realization into the new state space realization.The PM-ARMA model is a more general formulation with respect to the polynomial using the coefficient representation auto-regressive moving average(ARMA)model due to its capability to cope with actively controlled structures with any given structural degrees of freedom and any chosen number of sensors and actuators.(The sensors and actuators are required to maintain the identical number.)under any dimensional stationary stochastic excitation.

Shift ergodicity for stationary Markov processes

In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple proof of the conclusion that every stationary Markov process is a generalized convex combination of stationary ergodic Markov processes. A direct consequence is that a stationary distribution of a Markov process is extremal if and only if the corresponding stationary Markov process is time ergodic and every stationary distribution is a generalized convex combination of such extremal ones. We then consider space ergodicity for spin flip particle systems. We prove space shift ergodicity and mixing for certain extremal invariant measures for a class of spin systems, in which most of the typical models, such as the Voter Models and the Contact Models, are included. As a consequence of these results we see that for such systems, under each of those extremal invariant measures, the space and time means of an observable coincide, an important phenomenon in statistical physics. Our results provide partial answers to certain interesting problems in spin systems.

BOOTSTRAP MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETER IN SPECTRAL DENSITY OF STATIONARY PROCESSES

This paper is concerned with the estimation of parameters in spectral density of a stationary process. A new estimate of the parameter is proposed by using the bootstrap method. We call it the bootstrap maximum likelihood estimate (BMLE). In this paper, under suitable regularity conditions, the BMLE is shown to be consistent and asymptotically normal.

Asymptotic analysis of a nonlinear stochastic eco-epidemiological system with feedback control

This paper proposes a new stochastic eco-epidemiological model with nonlinear incidence rate and feedback controls.First,we prove that the stochastic system has a unique global positive solution.Second,by constructing a series of appropriate stochastic Lyapunov functions,the asymptotic behaviors around the equilibria of deterministic model are obtained,and we demonstrate that the stochastic system exists a stationary Markov process.Third,the conditions for persistence in the mean and extinction of the stochastic system are established.Finally,we carry out some numerical simulations with respect to different stochastic parameters to verify our analytical results.The obtained results indicate that the stochastic perturbations and feedback controls have crucial effects on the survivability of system.

Nonparametric estimation for stationary and strongly mixing processes on Riemannian manifolds

In this paper,nonparametric estimation for a stationary strongly mixing and manifoldvalued process(X_(j))is considered.In this non-Euclidean and not necessarily i.i.d setting,we propose kernel density estimators of the joint probability density function,of the conditional probability density functions and of the conditional expectations of functionals of X_(j)given the past behavior of the process.We prove the strong consistency of these estimators under sufficient conditions,and we illustrate their performance through simulation studies and real data analysis.

SOME FUNCTIONAL LIMIT THEOREMS FOR THE INFINITE SERIES OF OU PROCESSES

This paper obtains functional modulus of continuity and Strassen's functional LIL of theinfinite series of independent Ornstein-Uhlenbeck processes, which also imply the Levy's exactmodulus of continuity and LIL of this process respectively.

BANDWIDTH SELECTION IN NONPARAMETRIC SPECTRAL DENSITY ESTIMATION OF THE STATIONARY GAUSSIAN PROCESS

We propose a method for estimating mean squared error and bandwidth in the windowedspectral density estimation of a stationary Gaussian process, and also provide a method forestimating the second order derivative of the spectral density function. The asymptotic propertiesand the convergence rates of the estimators are given.

Asymptotic Results for Random Processes

In this paper we establish asymptotic results and a generalized uniform law of the iterated logarithm （LIL） for the increments of a strictly stationary random process, whose results are proved by separating linearly positive quadrant dependent （LPQD） random process and linearly negative quadrant dependent （LNQD） one, respectively.

ASYMPTOTIC BEHAVIOR OF BOOTSTRAP SPECTRAL WINDOW ESTIMATION

This paper is concerned with the nonparametric spectral density estimation of a stationary Gaussian process. A new estimator of the spectral density is proposed by the bootstrap method. The asymptotic behavior of the estimate has been studied. The consistency and asymptotic normality of the estimate are given.

Stochastic Volatility Model and Technical Analysis of Stock Price

In the stock market, some popular technical analysis indicators （e.g. Bollinger Bands, RSI, ROC, ...） are widely used by traders. They use the daily （hourly, weekly, ...） stock prices as samples of certain statistics and use the observed relative frequency to show the validity of those well-known indicators. However, those samples are not independent, so the classical sample survey theory does not apply. In earlier research, we discussed the law of large numbers related to those observations when one assumes Black-Scholes＇ stock price model. In this paper, we extend the above results to the more popular stochastic volatility model.

A Note on Moments of Dividends

We reconsider a formula for arbitrary moments of expected discounted dividend payments in a spectrally negative Lévy risk model that was obtained in Renaud and Zhou （2007, [4]） and in Kyprianou and Palmowski （2007, [3]） and extend the result to stationary Markov processes that are skip-free upwards.

Influence of a non-rotating shoulder on heat generation,microstructure and mechanical properties of dissimilar AA2024/AA7050 FSW joints

Friction stir welding （FSW） and stationary shoulder friction stir welding （SSFSW） were carried out for the butt joining of dissimilar AA2024-T3 and AA7050-T7651 aluminium alloys with thicknesses of 2 mm. A comparison between the two processes was performed by varying the welding speed while keeping the rotational speed constant, Through the analysis of the force and torque produced during welding and a simple analytical model, it was possible to show that in SSFSW there is more effective coupling with the tool and the heat produced is more efficiently distributed. This process decreases both the welding area and the diffusion at the interface of the two alloys compared with FSW. The minimum microhardness occurred at the advancing side （AS） at the interface between the thermo-mechanically affected zone （TMAZ） and the stir zone （SZ） in both processes, although the decrease was more gradual in SSFSW. This interface is also where all specimens failed for both welding technologies. An increase in tensile strength was measured in SSFSW compared with standard FSW. Furthermore, it was possible to establish the mechanical performance of the material in the fracture zone using digital image correlation.