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In the paper we consider the problem of estimating parameters entering thedrift of a fractional Ornstein-Uhlenbeck type process in the non-ergodic case,when the underlying stochastic integral is of Young type. We consider thesampling scheme that the process is observed continuously on $[0,T]$ and$T\to\infty$. For known Hurst parameter $H\in(0.5, 1)$, i.e. the long rangedependent case, we construct a least-squares type estimator and establishstrong consistency. Furthermore, we prove a second order limit theorem whichprovides asymptotic normality for the parameters of the periodic function witha rate depending on $H$ and a non-central Cauchy limit result for the meanreverting parameter with exponential rate. For the special case that theperiodicity parameter is the weight of a periodic function, which integrates tozero over the period, we can even improve the rate to $\sqrt{T}$.

Inference for fractional Ornstein-Uhlenbeck type processes with periodic mean in the non-ergodic case