We aim at studying the causal link between the knotty jet structure in CARMA 7, a young Class 0 protostar in the Serpens South cluster, and episodic accretion in young protostellar disks. We used numerical hydrodynamics simulations to derive the protostellar accretion history in gravitationally unstable disks around solar-mass protostars. We compared the time spacing between luminosity bursts Deltatau_mod, caused by dense clumps spiralling on the protostar, with the differences of dynamical timescales between the knots Deltatau_obs in CARMA 7. We found that the time spacing between the bursts have a bi-modal distribution caused by isolated and clustered luminosity bursts. The former are characterized by long quiescent periods between the bursts with Deltatau_mod = a few * (10^3-10^4) yr, whereas the latter occur in small groups with time spacing between the bursts Deltatau_mod= a few * (10-10^2) yr. For the clustered bursts, the distribution of Deltatau_mod in our models can be fit reasonably well to the distribution of Deltatau_obs in the protostellar jet of CARMA 7, if a certain correction for the (yet unknown) inclination angle with respect to the line of sight is applied. The K-S test on the model and observational data sets suggests the best-fit values for the inclination angles of 55-80 deg., which become narrower (75-80 deg.) if only strong luminosity bursts are considered. The dynamical timescales of the knots in the jet of CARMA 7 are too short for a meaningful comparison with the long time spacings between isolated bursts in our models. The exact sequences of time spacings between the luminosity bursts in our models and knots in the jet of CARMA 7 were found difficult to match. (abridged)
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