In this paper, we study the memory properties of transformations of linear processes. Dittmann and Granger (J Econ 110:113–133, 2002 ) studied the polynomial transformations of Gaussian FARIMA(0,  d , 0) processes by applying the orthonormality of the Hermite polynomials under the measure for the standard normal distribution. Nevertheless, the orthogonality does not hold for transformations of non-Gaussian linear processes. Instead, we use the decomposition developed by Ho and Hsing (Ann Stat 24:992–1024, 1996 ; Ann Probab 25:1636–1669, 1997 ) to study the memory properties of nonlinear transformations of linear processes, which include the FARIMA( p ,  d ,  q ) processes, and obtain consistent results as in the Gaussian case. In particular, for stationary processes, the transformations of short-memory time series still have short-memory and the transformation of long-memory time series may have different weaker memory parameters which depend on the power rank of the transformation. On the other hand, the memory properties of transformations of non-stationary time series may not depend on the power ranks of the transformations. This study has application in econometrics and financial data analysis when the time series observations have non-Gaussian heavy tails. As an example, the memory properties of call option processes at different strike prices are discussed in details.