** Transit areas were determined using short-cadence data by the method of narrow trapezoids. Typically, for 870.01, the number of trapezoids/transit was ~ 175; for 870.02, that number was ~ 200. The height of each trapezoid was conveniently defined by Exofast's OOT normalized flux and it's best-fit transit model curve; the widths were the sequential pairs of adjacent recorded-flux-times.
For literature references, including Tc#, Tc, and major TTV tabulations, see my "Summary" webpage. In particular, Xie, 2013 reported TTVs thru Q13 of 236 and 234 days for 870.01 and 870.02, respectively, but made no mention of the anomalous FAP of 870.02.
2 Sep 2014; updated 8 Sep 2014.
To see if this variability could be responsible for the very high FAP noted in the Lomb-Scargle periodogram (LSP) of 870.02, a series of LSPs were run using TTV-xy-data-inputs for which 3, then 6, then 9, etc., highest-standard-deviation-data-points had been removed from the initial number of  data points prior to running each LSP. The results are summarized in Table 1. Not only did removal of the highest-standard-deviation-data-points lead to a much more credible FAP for the ~ 228 day P_ttv caused by 870.01, it also exposed the credible presence of an additional planetary object in the system causing a weaker P_ttv of ~ 144 days.
Another measure of the lack of quiescence of transiting-planet host stars is the variation observed in (short-cadence data) transit shapes and (corresponding) transit areas. Thus, for 870.01, the average calculated** transit area was 101.7 ± 30.4 (days•norm.flux•10^6); for 870.02, the value was 107.4 ± 30.5 (days•norm.flux•10^6). These observed sizable variations are arrayed in Figures C. and D. Note that the variations are sufficient to blur differences that would normally be expected between non-overlapping (blue symbols) and overlapping (red symbols) transits.
TTVs are derived from Q0-Q17 Kepler data. x-axes: “Observed Tc” (Mid-Transit Time): EXOFAST’s best-fits from Normalized PDCSAP_FLUX Kepler light flux vs. time (BJD_tdb - 2454900) data. y-axes: “(O-C)”: difference between Observed Tc and the Calculated Tc from the graphically obtained linear ephemeris.
Figure: KOI-870.01, P = 5.91 days [Plot avg. error bars = ± 5.59 min.]
TTV_minimum: 95.28 ± 13.15 days, Amp_ttv_minimum: -7.54 ± 1.54 min.
TTV_maximum: 210.09 ± 13.44 days, Amp_ttv_maximum: 8.00 ± 1.54 min.
TTV_minimum: 324.89 ± 13.94 days, Amp_ttv_minimum: -7.54 ± 1.54 min.
TTV_maximum: 439.70 ± 14.62 days, Amp_ttv_maximum: 8.00 ± 1.54 min.
TTV_minimum: 554.51 ± 15.47 days, Amp_ttv_minimum: -7.54 ± 1.54 min.
TTV_maximum: 669.31 ± 16.45 days, Amp_ttv_maximum: 8.00 ± 1.54 min.
TTV_minimum: 784.12 ± 17.54 days, Amp_ttv_minimum: -7.54 ± 1.54 min.
TTV_maximum: 898.93 ± 18.73 days, Amp_ttv_maximum: 8.00 ± 1.54 min.
TTV_minimum: 1013.73 ± 19.99 days, Amp_ttv_minimum: -7.54 ± 1.54 min.
TTV_maximum: 1128.54 ± 21.31 days, Amp_ttv_maximum: 8.00 ± 1.54 min.
TTV_minimum: 1243.35 ± 22.69 days, Amp_ttv_minimum: -7.54 ± 1.54 min.
TTV_maximum: 1358.16 ± 24.11 days, Amp_ttv_maximum: 8.00 ± 1.54 min.
TTV_minimum: 1472.96 ± 25.57 days, Amp_ttv_minimum: -7.54 ± 1.54 min.
Linear ephemeris (this work): Tc = 8.98581314(Tc#) + 108.68578811
KOI-807 shows continuous and very large variation in light flux; Figure A. shows Kepler's long-cadence data for Q1-Q17. By far, the most prominent separation between flux minima, within neighboring patterns of increasing and/or decreasing minima, was 18.00 ± 0.71 days…most probably caused by relatively long-lasting star spots circling the star…implying that value as the star's rotation rate. The expanded ~18-day-period region of an LSP [Time vs. Stellar Flux Minima] is shown in Figure B. The broadened peaks, centered at 18.55 days (FAP: 1.064 x 10^-6) and 17.98 days (FAP: 1.297 x 10^-4) are consistent with expected expansion, contraction, and movement of starspots; and two such peaks, as seen (Figure B.), is consistent with two different starspot patterns at different latitudes.
The two known planets, 871.01 and 871.02, in this system have a period ratio of 1.5198, very close to a MMR of 3:2; correspondingly, their TTVs are exquisitely anti-correlated (see figures below). The amplitudes of the two TTVs is about the same at ~ 15.5 minutes suggesting similar masses for the two planets. [Furthermore, since their radii are very similar (NASA Exoplanet Archive (NEA): 2.17:2.02), they should have very smiler densities.] Interestingly, a normally non-credible value for the FAP of 870.02 was obtained from its [TTV xy-data] Lomb-Scargle periodogram of 0.501, while that of 870.01 is, indeed, quite credible at 0.0001402. The cause of 870.02's high FAP is probably related to the apparent large number and, perhaps, variable character of the host star's starspots* that 870.02 crosses during transits (perhaps especially compared the chord followed by 870.01) and the resulting variation of transit shapes and areas (see Addendum below).