  We introduce a class of semiparametric time series models by assuming a
quasi-likelihood approach driven by a latent factor process. More specifically,
given the latent process, we only specify the conditional mean and variance of
the time series and enjoy a quasi-likelihood function for estimating parameters
related to the mean. This proposed methodology has three remarkable features:
(i) no parametric form is assumed for the conditional distribution of the time
series given the latent process; (ii) able for modelling non-negative, count,
bounded/binary and real-valued time series; (iii) dispersion parameter is not
assumed to be known. Further, we obtain explicit expressions for the marginal
moments and for the autocorrelation function of the time series process so that
a method of moments can be employed for estimating the dispersion parameter and
also parameters related to the latent process. Simulated results aiming to
check the proposed estimation procedure are presented. Real data analysis on
unemployment rate and precipitation time series illustrate the potencial for
practice of our methodology.
