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Abstract:
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Faced with the (difficult) task of predicting high-frequency market movements, it is tempting to entertain the idea of incorporating information from the past behavior of the price process on multiple timescales. However, it is not always a priori clear what timescales are the most relevant in the sense of carrying the most predictive power. With this in mind, we propose a multi-scale autoregressive time series model, in which the quantity of interest (here: the high-frequency return) is explicitly modeled as linearly dependent on its own past averages over unknown time-spans, which we show how to estimate from the data. We show basic probabilistic properties of the model (including how it can mimic white-noise-like behavior), its estimation theory via change-point detection, as well as an application in a high-frequency forecasting exercise, which shows the potential of the new framework.
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