Table 1
Results of evidence-based model comparison.
| Model | Number of | No decisive | No decisive | No decisive | No decisive | Max |
| model parameters | evidence against | evidence against | evidence against | evidence against | evidence | |
| it at 3σ | it at 5σ | it at 7σ | it at 10σ | |||
|
|
||||||
| Constant | 1 | 0 | 0 | 0 | 0 | 0 |
| Constant plus noise | 2 | 59 | 64 | 73 | 94 | 4 |
| Sinusoid (flat prior in P) | 4 | 28 | 37 | 46 | 58 | 2 |
| Sinusoid (flat prior in log P) | 4 | 20 | 23 | 29 | 39 | 2 |
| Sinusoid (periodogram prior) | 4 | 27 | 30 | 39 | 50 | 4 |
| Two sinusoids (flat priors in P) | 7 | 33 | 36 | 45 | 60 | 7 |
| Sinusoid (flat prior in P) plus noise | 5 | 467 | 583 | 721 | 921 | 149 |
|
|
||||||
| Wiener process (random walk) | 2 | 2205 | 2724 | 3230 | 3949 | 11 |
| OU process (damped random walk) | 3 | 6023 | 6069 | 6093 | 6131 | 5047 |
| Gaussian CAR(2) process (φ1 = φ2 = 0.1) | 2 | 0 | 0 | 0 | 1 | 0 |
| Gaussian CAR(2) process (τ1 = τ2) | 3 | 1 | 2 | 2 | 3 | 0 |
| Gaussian CAR(2) process (τ1 ≠ τ2) | 4 | 5 | 5 | 5 | 5 | 5 |
| Cauchy CAR(1) process (φ = 1) | 2 | 81 | 108 | 172 | 361 | 36 |
| Symmetric stable CAR(1) process (φ = 1, β = 0) | 3 | 0 | 0 | 0 | 0 | 0 |
| Stable CAR(1) process (φ = 1) | 4 | 0 | 0 | 0 | 0 | 0 |
| Gaussian CARMA(1, 1) process | 4 | 0 | 0 | 0 | 0 | 0 |
|
|
||||||
| Constant + Gaussian ARCH(1) process | 3 | 236 | 268 | 306 | 355 | 69 |
| Sinusoid + Gaussian ARCH(1) process | 6 | 923 | 1208 | 1529 | 2096 | 155 |
| Gaussian CAR(1)-ARCH(1) process | 4 | 1884 | 2257 | 2639 | 3183 | 219 |
| Gaussian CAR(1)-GARCH(1, 1) process | 5 | 3542 | 3912 | 4285 | 4751 | 536 |
| Gaussian CARMA(1, 1)-GARCH(1, 1) process | 6 | 1533 | 2041 | 2593 | 3486 | 58 |
Notes.For each model under consideration we quote the number of model parameters, the number of QSO lightcurves where there is no decisive evidence against this model at a specified confidence level, and the number of QSO lightcurves where each model provides the highest evidence. The upper block of the table contains deterministic models. The middle block contains stochastic models with constant variance, while the lower block contains stochastic process with stochastic variance. (Periods of all sinusoids are between 1 and 10 000 days.) The last column adds up to the total of 6304 QSO lightcurves, the other columns do not.
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