Hippocampus is a brain region that is important for the encoding and retrieval of episodic memories. The spiking activity of hippocampal place cells depends strongly on spatial location in an environment. Their position-dependent firing rate is usually modeled as a parametric function of 2-D or 3-D space. Yet, no study to date has optimized such functions using a rigorous statistical model selection procedure. Here, we model the position-dependent firing rate of hippocampal place cells using two different series expansion models and determine the optimal model type and order. Our results indicate that the optimal order is much higher than those used in earlier studies. We have observed that the models of some cells are reminiscent of the firing patterns of grid cells. These findings are important for elucidating the origins of place cell activity, for accurate assessments of the amount of position information encoded in this activity, and for the inference of position using neural decoding algorithms.