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Many stochastic time series can be modelled by discrete random walks in whicha step of random sign but constant length $\delta x$ is performed after eachtime interval $\delta t$. In correlated discrete time random walks (CDTRWs),the probability $q$ for two successive steps having the same sign is unequal1/2. The resulting probability distribution $P(\Delta x,\Delta t)$ that adisplacement $\Delta x$ is observed after a lagtime $\Delta t$ is knownanalytically for arbitrary persistence parameters $q$. In this short note weshow how a CDTRW with parameters $[\delta t, \delta x, q]$ can be mapped ontoanother 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 walkshave the same displacement distributions $P(\Delta x,\Delta t)$ on long timescales. The nonlinear scaling functions $g(q,s)$ and $q^{\prime}(q,s)$ andderived explicitely. This scaling method can be used to model time seriesmeasured at discrete sample intervals $\delta t$ but actually corresponding tocontinuum processes with variations occuring on a much shorter time scale$\delta t/s$.

Scaling properties of correlated random walks