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.
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