A Note on Some Simple Time Series Estimates
C. A. McGilchrist, S. H. Huxham · Technometrics · 1972
The dependence structure of a stationary time series {Xt } is usually discussed in terms of the observed variables Xt . Let F(x) be the common marginal c.d.f. of the Xt We propose a model involving only the transformed series {Zt }, where Zt = F(Xt ). The conditional distribution of Zt given Z t–1, Z t–2, … is expressed in terms of Zt , Z t1, … and parameters β1, β2, …. The case where Zt depends only on Z t–1 is considered in detail. Estimators for the β's are found, and an example using a normal Markov process is given.