Following the current IGS (International GNSS Service) convention, the precise satellite orbit and clock are archived with the standard ``SP3' format, which is disseminated on daily basis. Thus, the adjacent IGS precise orbit products display discontinuity at the junction of two successive days. The orbit discontinuity reflects the orbit errors due to orbit propagation errors, owing to the orbit dynamics mis-modeling. Most researches use the Day Boundary Discontinuity (DBD) for the assessment of orbit quality. In this paper, the long period DBD time series of the precise IGS orbit products are analyzed. The precise orbit products of five GNSS (Global Navigation Satellite System) Analysis Centers (AC), including GeoForschungsZentrum (GFZ), Center for Orbit Determination in Europe (COD), European Space Agency (ESA), Shanghai Astronomical Observatory (SHA), and Jet Propulsion Laboratory (JPL), are used to derive the orbit discontinuity time series covering the period from the year 2013 to 2017. Analysis of the time series shows that the mean three-dimensional DBD of GFZ, COD, ESA, SHA, and JPL are 7.79 cm, 1.51 cm, 7.77 cm, 11.75 cm, and 2.51 cm, respectively. The periodic characteristic of DBD shows significant signals at the frequency of 90 days, 120 days, and 340 days, which correspond to the long period ocean tides. The amplitude of these periods is about millimeters to 1 centimeter, indicating the current utmost precision of GNSS orbits. The fundamental period terms of 175 days and 352 days match the GPS draconitic year, corresponding to the re-visit cycle of GPS constellation. The analysis of orbit extrapolation errors of COD products verifies the influence of dynamic models, e.g. the earth radiation pressure model and the solar radiation pressure model, on the orbit discontinuity, where the periodical and systematic effects are derived.