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Context. Classical T Tauri stars (cTTs) are pre-main sequence stars surrounded by an accretion disk. They host a strong magnetic field, and both magnetospheric accretion and ejection processes develop as the young magnetic star interacts with its disk. Studying this interaction is a major goal toward understanding the properties of young stars and their evolution. Aims. The goal of this study is to investigate the accretion process in the young stellar system HQ Tau, an intermediate-mass T Tauri star (1.9 M$_{\odot}$). Methods. The time variability of the system is investigated both photometrically, using Kepler-K2 and complementary light curves, and from a high-resolution spectropolarimetric time series obtained with ESPaDOnS at CFHT. Results. The quasi-sinusoidal Kepler-K2 light curve exhibits a period of 2.424 d, which we ascribe to the rotational period of the star. The radial velocity of the system shows the same periodicity, as expected from the modulation of the photospheric line profiles by surface spots. A similar period is found in the red wing of several emission lines (e.g., HI, CaII, NaI), due to the appearance of inverse P Cygni components, indicative of accretion funnel flows. Signatures of outflows are also seen in the line profiles, some being periodic, others transient. The polarimetric analysis indicates a complex, moderately strong magnetic field which is possibly sufficient to truncate the inner disk close to the corotation radius, r$_{cor}$ $\sim$3.5 R$_{\star}$. Additionally, we report HQ Tau to be a spectroscopic binary candidate whose orbit remains to be determined. Conclusions. The results of this study expand upon those previously reported for low-mass T Tauri stars, as they indicate that the magnetospheric accretion process may still operate in intermediate-mass pre-main sequence stars, such as HQ Tau.