Forecasting the in situ properties of coronal mass ejections (CMEs) from remote images is expected to strongly enhance predictions of space weather, and is of general interest for studying the interaction of CMEs with planetary environments. We study the feasibility of using a single heliospheric imager (HI) instrument, imaging the solar wind density from the Sun to 1 AU, for connecting remote images to in situ observations of CMEs. We compare the predictions of speed and arrival time for 22 CMEs (in 2008-2012) to the corresponding interplanetary coronal mass ejection (ICME) parameters at in situ observatories (STEREO PLASTIC/IMPACT, Wind SWE/MFI). The list consists of front- and backsided, slow and fast CMEs (up to $2700 \: km \: s^{-1}$). We track the CMEs to $34.9 ± 7.1$ degrees elongation from the Sun with J-maps constructed using the SATPLOT tool, resulting in prediction lead times of $-26.4 ± 15.3$ hours. The geometrical models we use assume different CME front shapes (Fixed-$Φ$, Harmonic Mean, Self-Similar Expansion), and constant CME speed and direction. We find no significant superiority in the predictive capability of any of the three methods. The absolute difference between predicted and observed ICME arrival times is $8.1 ± 6.3$ hours ($rms$ value of 10.9h). Speeds are consistent to within $284 ± 288 \: km \: s^{-1}$. Empirical corrections to the predictions enhance their performance for the arrival times to $6.1 ± 5.0$ hours ($rms$ value of 7.9h), and for the speeds to $53 ± 50 \: km \: s^{-1}$. These results are important for Solar Orbiter and a space weather mission positioned away from the Sun-Earth line. ; Comment: 19 pages, 13 figures, accepted for publication in the Astrophysical Journal