Patterns of mutations in the DNA of modern-day individuals have been shaped by the demographic history of our ancestors. Inferring the demographic history from these patterns is a challenging problem due to complex dependencies along the genome. Several recent methods have adopted McVean's sequentially Markovian coalescent (SMC') to model these dependencies. However, these methods involve simplifying assumptions that preclude the inference of rates of migration between populations. We have developed the first method to infer directional migration rates as a function of time. To do this, we employ sequential Monte Carlo (SMC) methods, also known as particle filters, to infer parameters in the SMC' model. To improve the sampling from the state space of SMC' we have developed a sophisticated sampling technique that shows better performance than the standard bootstrap filter. We apply our algorithm, SMC², to Neanderthal data and are able to infer the time and extent of migration from the Vindija Neanderthal population into Europeans. With the large volume of sequencing data being produced from diverse populations, both modern and ancient, there is high demand for methods to interrogate this data. SMC² provides a flexible algorithm, which can be modified to suit many data applications. For instance, we show that our method performs well when the phasing of the samples is unknown, which is often the case in practice. The long runtime of SMC² is the main limiting factor in the adoption of the method. We have started to explore ways to improve the runtime, by developing an adaptive online expectation maximisation (EM) procedure.