Asymptotic Properties of Quasi-Maximum Likelihood Estimators for ARMA Models with Time-Dependent Coefficients

For about thirty years, time series models with time-dependent coefficients have sometimes been considered as an alternative to models with constant coefficients or non-linear models. Analysis based on models with time-dependent models has long suffered from the absence of an asymptotic theory except in very special cases. The purpose of this paper is to provide such a theory without using a locally stationary spectral representation and time rescaling. We consider autoregressive-moving average (ARMA) models with time-dependent coefficients and a heteroscedastic innovation process. The coefficients and the innovation variance are deterministic functions of time which depend on a finite number of parameters. These parameters are estimated by maximising the Gaussian likelihood function. Deriving conditions for consistency and asymptotic normality and obtaining the asymptotic covariance matrix are done using some assumptions on the functions of time in order to attenuate non-stationarity, mild assumptions for the distribution of the innovations, and also a kind of mixing condition. Theorems from the theory of martingales and mixtingales are used. Some simulation results are given and both theoretical and practical examples are treated. Received 2004; Final version 23 December 2004     

Mixed insoluble acidic salts of tetravalent metals

Solid amorphous Zr-, Ti- and Zr_xTi_(1–x) phosphates (where x=0.10, 0.33, 0.66, and 0.90) in various sodium forms were contacted with an excess of solid oxalic acid dihydrate to its molten state for a given time. The oxalic acid was removed by extraction and the residue was washed with redistilled water. As a result of this, crystalline forms of Zr-, Ti-, and Zr_xTi_(1–x) phosphates were obtained. Using various sodium forms of the initial samples, higher rate of crystallisation resulted than that found in case of hydrogen forms of initial samples.     

Controlled Dispersion and Setting of Cellulose Nanofibril - Carboxymethyl Cellulose Pastes

Cellulose - This work investigated the redispersion and setting behavior of highly loaded (~?18 wt.% solids in water) pastes of cellulose nanofibrils (CNFs) with carboxymethyl cellulose...     

Mechanical enhancement of cellulose nanofibril (CNF) films through the addition of water-soluble polymers

Cellulose - In this work, water-soluble polymers were screened through solution casting and polyvinyl alcohol (PVA) and poly(2-ethyl-2-oxazoline) (PEOX) were found as reinforcement agents for...     

Conversion of solid amorphous mixed zirconium-titanium phosphates into crystalline from by molten oxalic acid

Solid amorphous mixed zirconium-titanium phosphates, with general formula Zr_xTi_/1–x//HPO₄/₂.n H₂O/ where x=0.1–1, and n=3–5/, are mixed with an excess of solid oxalic acid dihydrate and digested in molten oxalic acid. Then oxalic acid is removed by extraction and the residue washed with dilute /O.OlM/ HCl solution and bidistilled water. As a result of this method, crystalline mixed zirconium-titanium phosphate is formed.     

Analyses of scanning electrochemical microscopy and electrochemical impedance spectroscopy in direct methanol fuel cells: permeability resistance and proton conductivity of polyaniline modified membrane

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