Time Series with unbounded peaks in the spectrum are surprisingly common in many data analytic situations. In this talk we will look at modeling such processes, and the relationship between those models and fractal geometry originally identified by Mandlebrot. The models obtained from this can be challenging to work with at a theoretical level, but there are a number of methods of estimating the parameters (like the fractal dimension) and then forecasting the series. This talk will present details of these models and explain how they can be used both to understand the underlying process better and to obtain better (long range) forecasts. Our seminars are customarily followed with drinks on our balcony or at the Rose from around 5:15. About the Speakers: Shelton Peiris is A/Professor at the School of Mathematics and Statistics who primarily researches time series modelling. Richard and Helen are PhD students of his.