A Spectral Estimation of Discrete Harmonizable Process

In this paper, we develop the non-parametric spectral analysis for non-stationary discrete-time stochastic processes. This development will be investigated by using the multi-tapering and averaging technique. In particular, we obtain an estimator for the spectral density function of a harmonizable time series. This estimator is constructed by dividing the available time series into a number of overlapped and non-overlapped segments and then a multi-tapering technique is applied for each segment. Also, we obtain an estimator for the auto-covariance function and another estimator for the spectral distribution function of these processes, based on the spectral density estimator. Statistical properties of these estimators are investigated, including the asymptotic behaviour of the bias and covariance

Thienoisoindigo-Based Semiconductor Nanowires Assembled with 2-Bromobenzaldehyde via Both Halogen and Chalcogen Bonding

We fabricated nanowires of a conjugated oligomer and applied them to organic field-effect transistors (OFETs). The supramolecular assemblies of a thienoisoindigo-based small molecular organic semiconductor (TIIG-Bz) were prepared by co-precipitation with 2-bromobenzaldehyde (2-BBA) via a combination of halogen bonding (XB) between the bromide in 2-BBA and electron-donor groups in TIIG-Bz, and chalcogen bonding (CB) between the aldehyde in 2-BBA and sulfur in TIIG-Bz. It was found that 2-BBA could be incorporated into the conjugated planes of TIIG-Bz via XB and CB pairs, thereby increasing the pi - pi stacking area between the conjugated planes. As a result, the driving force for one-dimensional growth of the supramolecular assemblies via pi - pi stacking was significantly enhanced. TIIG-Bz/2-BBA nanowires were used to fabricate OFETs, showing significantly enhanced charge transfer mobility compared to OFETs based on pure TIIG-Bz thin films and nanowires, which demonstrates the benefit of nanowire fabrication using 2-BB

Bispectral Density Estimation of Continuous Time Series with Missed Observations

In this paper, we study the estimation of the bispectral density function of a strictly stationary r-vector valued continuous time series. The case of interest is when some of observations are mising due to some random failure. Bispectral density function is devoleped in case of L−joint segments of observations. The modified biperiodogram is defined and smoothed to estimate the bispectral density matrix. The theoriotical properties of the proposed estimator are explored

Bispectral Density Estimation of Continuous Time Series with Missed Observations

In this paper, we study the estimation of the bispectral density function of a strictly stationary r-vector valued continuous time series. The case of interest is when some of observations are mising due to some random failure. Bispectral density function is devoleped in case of L−joint segments of observations. The modified biperiodogram is defined and smoothed to estimate the bispectral density matrix. The theoriotical properties of the proposed estimator are explored

Higher Order Moments, Cumulants, Spectral and Bispectral Density Functions of the ZTPINAR(1) Process

In this paper, the higher order moments, cumulants, spectral, bispectral and normalized bispectral density functions of zero truncated Poisson first-order integer-valued autoregressive (ZTPINAR(1)) model are calculated. We estimated the spectrum, bispectrum and normalized bispectrum using the smoothed periodogram method with different lag windows. Finally, we used the bispectral density function and normalized bispectral density function in order for studying the linearity of integer valued time series models

Some Asymptotic Properties of a Kernel Bispectum Estimate with Different Multitapers

Assume X1,X2,…,XN are realizations of N observations from a real-valued discrete parameter third-order stationary process Xt,t=0±1,±2,…, with bispectrum fXXX(λ1,λ2) where “−π≤λ1,λ2≤π”. Based on the previous assumption, L different multitapered biperiodograms IXXX(mt)j(λ1,λ2);j=1,2,…,L on overlapped segments (Xt(j);1≤t<N) can be constructed. Further, the mean and variance of the average of these different multitapered biperiodograms can be expressed as asymptotic expressions. According to different bispectral windows/kernels (Wβ(j)(α1,α2), where “−π⩽α1,α2⩽π” andβ is the bandwidth) and IXXX(mt)j(λ1,λ2), the bispectrum fXXX(λ1,λ2) can be estimated. The asymptotic expressions of the first- and second-ordered moments as well as the integrated relative mean squared error (IMSE) of this estimate are derived. Finally, some estimation results based on numerically generated data from the selected process “DCGINAR(1)” are presented and discussed in detail