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A review of flow field forecasting: A high‐dimensional forecasting procedure

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Abstract Forecasting, especially high‐dimensional forecasting, is becoming more and more sought after, particularly as computing resources increase in both size and speed. Flow field forecasting is a general purpose regression‐based forecasting method that has recently been expanded to high‐dimensional settings. In this article, we provide an overview of the flow field forecasting methodology, with a particular emphasis on environments where the number of candidate predictor variables is large, potentially larger than the number of observations. This article is categorized under: Statistical Models > Time Series Models Statistical Learning and Exploratory Methods of the Data Sciences > Classification and Regression Trees Statistical and Graphical Methods of Data Analysis > Data Reduction, Smoothing, and Filtering
Past histories h1, h2 and their respective associated changes d1, d2. These associations are used to interpolate the change d* associated with the current history h*. The histories in the top panel have consecutive components. The histories in the bottom panel have nonconsecutive components
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Iterating to forecast horizon. The double arrows indicate interpolation done by Gaussian process regression (GPR)
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Using Gaussian process regression (GPR), the time series is interpolated between the observed levels (i.e., black dots). The 95% error bands show that the further away you are from the actual data, the higher the error
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Statistical and Graphical Methods of Data Analysis > Data Reduction, Smoothing, and Filtering
Statistical Learning and Exploratory Methods of the Data Sciences > Classification and Regression Trees (CART)
Statistical Models > Time Series Models

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