Computation of estimates in segmented regression and a liquidity effect model

Weighted least squares (WLS) estimation in segmented regression with multiple change points is considered. A computationally efficient algorithm for calculating the WLS estimate of a single change point is derived. Then, iterative methods of approximating the global solution of the multiple change-point problem based on estimating change points one-at-a-time are discussed. It is shown that these results can also be applied to a liquidity effect model in finance with multiple change points. The liquidity effect model we consider is a generalization of one proposed by Çetin et al. [2006. Pricing options in an extended Black Scholes economy with illiquidity: theory and empirical evidence. Rev. Financial Stud. 19, 493–529], allowing that the magnitude of liquidity effect depends on the size of a trade. Two data sets are used to illustrate these methods.