A data set of weekly milk yield records was used to compare different test day models for their ability to interpolate and extrapolate missing milk yields. The criteria to compare the models were 1) the (co)variance structure modeled compared with the observed (co)variance structure in the data and 2) mean square error of predictions of missing ovservations (MSEP), which compared the predicted value of a missing record to the known value of the record. The test day models used were LEG(m), which are Legendre polynomials with an order of fit of m, and EXP, which is an exponential lactation function. When fitting the LEG(m) models, criteria 1) and 2) generally improved with an increasing order of fit as expected. The model EXP, which contains three random regression coefficients, was between LEG(1) and LEG(2), which contain two and three coefficients, respectively. The improvement of the criteria with m in LEG(m) became negligible after LEG(5). Thus, a 5th order Legendre polynomial yields a good fit with a minimum number of parameters. Also, the correlation structure of milk yields among days in milk modeled by LEG(5) resembled the correlation structure that was observed in the data. However, the modeled variances at the end of lactation were larger than those observed in the data except when LEG(0) was used. Legendre polynomials with a fit less than five yielded correlation structures that clearly deviated from the observed correlations, especially in the case of LEG(0). Overall, LEG(5) is preferred to develop a genetic TDM for breeding value estimation.