On projection methods for functional time series forecasting

• URL: http://arxiv.org/abs/2105.04399v1
• Date: Mon, 10 May 2021 14:24:38 GMT
• Title: On projection methods for functional time series forecasting
• Authors: Antonio El\'ias (1) and Ra\'ul Jim\'enez (2) and Hanlin Shang (3) ((1) OASYS group, Department of Applied Mathematics, Universidad de M\'alaga, M\'alaga, Spain, (2) Department of Statistics, Universidad Carlos III de Madrid, Madrid, Spain, (3) Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, Australia)
• Abstract summary: Two nonparametric methods are presented for forecasting functional time series (FTS) We address both one-step-ahead forecasting and dynamic updating. The methods are applied to simulated data, daily electricity demand, and NOx emissions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Two nonparametric methods are presented for forecasting functional time series (FTS). The FTS we observe is a curve at a discrete-time point. We address both one-step-ahead forecasting and dynamic updating. Dynamic updating is a forward prediction of the unobserved segment of the most recent curve. Among the two proposed methods, the first one is a straightforward adaptation to FTS of the $k$-nearest neighbors methods for univariate time series forecasting. The second one is based on a selection of curves, termed \emph{the curve envelope}, that aims to be representative in shape and magnitude of the most recent functional observation, either a whole curve or the observed part of a partially observed curve. In a similar fashion to $k$-nearest neighbors and other projection methods successfully used for time series forecasting, we ``project'' the $k$-nearest neighbors and the curves in the envelope for forecasting. In doing so, we keep track of the next period evolution of the curves. The methods are applied to simulated data, daily electricity demand, and NOx emissions and provide competitive results with and often superior to several benchmark predictions. The approach offers a model-free alternative to statistical methods based on FTS modeling to study the cyclic or seasonal behavior of many FTS.

Related papers

• von Mises Quasi-Processes for Bayesian Circular Regression [57.88921637944379]
  We explore a family of expressive and interpretable distributions over circle-valued random functions. The resulting probability model has connections with continuous spin models in statistical physics. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Markov Chain Monte Carlo sampling.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Only the Curve Shape Matters: Training Foundation Models for Zero-Shot Multivariate Time Series Forecasting through Next Curve Shape Prediction [6.166295570030646]
  We present General Time Transformer (GTT), an encoder-only style foundation model for zero-shot multivariate time series forecasting. GTT is pretrained on a large dataset of 200M high-quality time series samples spanning diverse domains.
  arXiv  Detail & Related papers  (2024-02-12T11:04:14Z)
• Conformal Prediction Bands for Two-Dimensional Functional Time Series [0.0]
  Time evolving surfaces can be modeled as two-dimensional Functional time series, exploiting the tools of Functional data analysis. The main focus revolves around Conformal Prediction, a versatile non-parametric paradigm used to quantify uncertainty in prediction problems. A probabilistic forecasting scheme for two-dimensional functional time series is presented, while providing an extension of Functional Autoregressive Processes of order one to this setting.
  arXiv  Detail & Related papers  (2022-07-27T17:23:14Z)
• Time varying regression with hidden linear dynamics [74.9914602730208]
  We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates.
  arXiv  Detail & Related papers  (2021-12-29T23:37:06Z)
• Back2Future: Leveraging Backfill Dynamics for Improving Real-time Predictions in Future [73.03458424369657]
  In real-time forecasting in public health, data collection is a non-trivial and demanding task. 'Backfill' phenomenon and its effect on model performance has been barely studied in the prior literature. We formulate a novel problem and neural framework Back2Future that aims to refine a given model's predictions in real-time.
  arXiv  Detail & Related papers  (2021-06-08T14:48:20Z)
• Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting [98.57851612518758]
  Probabilistic time series forecasting involves estimating the distribution of future based on its history. We propose a deep state space model for probabilistic time series forecasting whereby the non-linear emission model and transition model are parameterized by networks. We show in experiments that our model produces accurate and sharp probabilistic forecasts.
  arXiv  Detail & Related papers  (2021-01-31T06:49:33Z)
• Remaining Useful Life Estimation Under Uncertainty with Causal GraphNets [0.0]
  A novel approach for the construction and training of time series models is presented. The proposed method is appropriate for constructing predictive models for non-stationary time series.
  arXiv  Detail & Related papers  (2020-11-23T21:28:03Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)
• Deep Distributional Time Series Models and the Probabilistic Forecasting of Intraday Electricity Prices [0.0]
  We propose two approaches to constructing deep time series probabilistic models. The first is where the output layer of the ESN has disturbances and a shrinkage prior for additional regularization. The second approach employs the implicit copula of an ESN with Gaussian disturbances, which is a deep copula process on the feature space.
  arXiv  Detail & Related papers  (2020-10-05T08:02:29Z)
• Stochastic Optimization for Performative Prediction [31.876692592395777]
  We study the difference between merely updating model parameters and deploying the new model. We prove rates of convergence for both greedily deploying models after each update and for taking several updates before redeploying. They illustrate how depending on the strength of performative effects, there exists a regime where either approach outperforms the other.
  arXiv  Detail & Related papers  (2020-06-12T00:31:16Z)
• A Multi-Channel Neural Graphical Event Model with Negative Evidence [76.51278722190607]
  Event datasets are sequences of events of various types occurring irregularly over the time-line. We propose a non-parametric deep neural network approach in order to estimate the underlying intensity functions.
  arXiv  Detail & Related papers  (2020-02-21T23:10:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.