LongMemory.jl: Generating, Estimating, and Forecasting Long Memory Models in Julia

In time series analysis, the concept of Long Memory encompasses datasets including a strong dependency on past values.Hurst ( 1956) is one of the pioneering works on the subject from the field of Hydrology: while analyzing the flow of the Nile river, he noted that water reservoirs that do not account for its long-term dynamics were still at risk of overflowing.Long memory models are generally used in climate, finance, biology, economics, and many other fields.See Beran et al. (2013) for a textbook on the subject.We say that a stationary time series has long memory with parameter -1/2 < < 1/2 if it has an autocovariance function () that behaves as: