  Many stochastic time series can be modelled by discrete random walks in which
a step of random sign but constant length $\delta x$ is performed after each
time interval $\delta t$. In correlated discrete time random walks (CDTRWs),
the probability $q$ for two successive steps having the same sign is unequal
1/2. The resulting probability distribution $P(\Delta x,\Delta t)$ that a
displacement $\Delta x$ is observed after a lagtime $\Delta t$ is known
analytically for arbitrary persistence parameters $q$. In this short note we
show how a CDTRW with parameters $[\delta t, \delta x, q]$ can be mapped onto
another CDTRW with rescaled parameters $[\delta t/s, \delta x\cdot g(q,s),
q^{\prime}(q,s)]$, for arbitrary scaling parameters $s$, so that both walks
have the same displacement distributions $P(\Delta x,\Delta t)$ on long time
scales. The nonlinear scaling functions $g(q,s)$ and $q^{\prime}(q,s)$ and
derived explicitely. This scaling method can be used to model time series
measured at discrete sample intervals $\delta t$ but actually corresponding to
continuum processes with variations occuring on a much shorter time scale
$\delta t/s$.
