tokens: Nonlinear regression is the best model, according to SIC. The break period varies between 2.35 log P 2.55 days at different wavelengths for all statistical methods. The F-test suggests that the variances of the quadratic and two-slope models are statistically similar. Further, the variances of a quadratic model and a linear relation for P 400 days are also similar in most cases. Therefore, we adopt a break period of 300 days () as the optimal period at which the change in the slope of PL and PLC relations occurs for O-rich Miras. The break period possibly shifts to longer periods (∼350 days, days) at NIR wavelengths. NIR PLRs are discussed in detail in Section 5 . Table 4 Results of the Statistical Tests to Find a Kink in the O-rich Mira PL and PLC Relations in the LMC Note. SIC: Schwarz Information Criterion used to estimate the break period in a two-slope model. RW: Random walk, TM: The Testimator, FT: F-test p ( f ): Probability of acceptance of the null hypothesis that the variance of a quadratic and a linear relation for P 400 days are equal. 4. Stability of Maximum Light for Miras 4.1. Photometric Variability at Max-light Optical photometry provides clear evidence that Miras display significantly smaller scatter in the PLRs at max-light than at mean-light. The pulsation properties and brightness variations of Miras are not strictly periodic and vary from cycle-to-cycle. Therefore, it is important to investigate the stability of max-light over different pulsation cycles. However, apart from OGLE I -band time-series observations, there is a lack of continuous photometry for Miras in the LMC, and even OGLE data do not necessarily cover the epochs of max-light during all pulsation cycles. High-precision photometry and subhour cadence from Kepler can be extremely useful to test the stability of max-light over different pulsation cycles. Bányai et al. ( 2013 ) analyzed variability in M giants from Kepler and identified a dozen long-period Mira-like variables. We estimate the scatter in the max-light magnitudes and median magnitudes for Miras over different pulsation cycles. For OGLE Miras, the sample is restricted to those stars for which GPR predicts max-light magnitudes with a precision better than three times their median uncertainty, and the time coverage is equivalent to the period of each Mira. The top panel of Figure 9 displays the comparison of the scatter in the median- and max-light magnitudes for OGLE and Kepler Mira candidates. When the scatter in both sets of magnitudes is smaller than 0.4 mag, max-light magnitudes seem to be more stable for most O-rich Miras. C-rich Miras often exhibit long-term trends and thus display large scatter both at median- and max-light. The bottom panel of Figure 9 presents the variation in min-light magnitudes versus the scatter in median magnitudes. For a majority of the stars, min-light magnitudes display significantly larger scatter than median magnitudes over multiple pulsation cycles. The
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