2.2.5 Parameters calibration

In our time-varying Cox model, the calibration of parameters involves the following steps:

• Model fitting: The parameters are estimated by fitting the Cox model to the data. The model uses maximum partial likelihood estimation. The partial likelihood function is constructed based on the observed survival times and the risk sets, which include the individual firms still at risk at each observed event time.

• Optimisation: The fitting process involves maximising the partial likelihood function to estimate the model parameters (betas). This is done using the optimisation Efron method. It uses a more refined approximation to the partial likelihood function than the Breslow method. It calculates the partial likelihood by taking the permutations of the tied observations into account, providing a more precise estimate.

• Iterative process: The optimisation process is iterative and continues until convergence is achieved, which means the likelihood function stabilises, showing minimal change between iterations.