corresponds to the physical period of the star. Random errors correspond to the uncertainty in the centroid of each periodogram peak, these errors are typically assumed to be Gaussian. There are at least four factors which contribute to random uncertainties in the stellar rotation period inferred from starspots. These factors include:

1.  Noise in the photometry.

2.  Inadequacies in the model used to determine the period (e.g. the light curve is periodic but not sinusoidal).

3.  Spot evolution.

4.  Differential rotation.

In Paper II we conducted bootstrap simulations of the period detection for each star. This effectively determines the contribution of photometric noise to the period uncertainty. We redo these bootstrap simulations here for the multi-harmonic AoV period determinations.

To assess the uncertainty due to inadequacies in the model and due to spot evolution we conduct Monte Carlo simulations. We simulate light curves for 1000 spotted stars using the spot model due to @Dorren.87. For each simulation we place three spots with random angular sizes between $0.05$ and $0.5$ radians, random latitudes and random longitudes on the surface of a star, assign the star a random rotation period between $0.2$ and $20~{\rm days}$, and allow the spots to vary sinusoidally 