2017/12/06 by Srinjoy Das, Das, Srinjoy, Dimitris N. Politis +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Statistical Methods and Inference #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.1712.02383
openalex publication_date 2017/12/06 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
The Model-free Prediction Principle of Politis (2015) has been successfully\napplied to general regression problems, as well as problems involving\nstationary time series. However, with long time series, e.g. annual temperature\nmeasurements spanning over 100 years or daily financial returns spanning\nseveral years, it may be unrealistic to assume stationarity throughout the span\nof the dataset. In the paper at hand, we show how Model-free Prediction can be\napplied to handle time series that are only locally stationary, i.e., they can\nbe assumed to be as stationary only over short time-windows. Surprisingly there\nis little literature on point prediction for general locally stationary time\nseries even in model-based setups and there is no literature on the\nconstruction of prediction intervals of locally stationary time series. We\nattempt to fill this gap here as well. Both one-step-ahead point predictors and\nprediction intervals are constructed, and the performance of model-free is\ncompared to model-based prediction using models that incorporate a trend and/or\nheteroscedasticity. Both aspects of the paper, model-free and model-based, are\nnovel in the context of time-series that are locally (but not globally)\nstationary. We also demonstrate the application of our Model-based and\nModel-free prediction methods to speleothem climate data which exhibits local\nstationarity and show that our best model-free point prediction results\noutperform that obtained with the RAMPFIT algorithm previously used for\nanalysis of this data.\n