arXiv 26 May 2025 · Econometrics
arXiv:2505.20508 · PDF · DOI · OpenAlex · Extracted main text
We study the Functional PCA (FPCA) forecasting method in application to functions of intraday returns on Bitcoin. We show that improved interval forecasts of future return functions are obtained when the conditional heteroscedasticity of return functions is taken into account. The Karhunen-Loeve (KL) dynamic factor model is introduced to bridge the functional and discrete time dynamic models. It offers a convenient framework for functional time series analysis. For intraday forecasting, we introduce a new algorithm based on the FPCA applied by rolling, which can be used for any data observed continuously 24/7. The proposed FPCA forecasting methods are applied to return functions computed from data sampled hourly and at 15-minute intervals. Next, the functional forecasts evaluated at discrete points in time are compared with the forecasts based on other methods, including machine learning and a traditional ARMA model. The proposed FPCA-based methods perform well in terms of forecast accuracy and outperform competitors in terms of directional (sign) of return forecasts at fixed points in time.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Aue, A., Norinho, D. D., and Hörmann, S (2015) "On the Prediction of Stationary Functional Time Series" | 1.000 | 22 | 3 | 100% |
| 2 | Shang, H. L. and Kearney, F (2022) "Dynamic Functional Time-series Forecasts of Foreign Exchange Implied Volatility Surfaces" | 1.000 | 14 | 3 | 100% |
| 3 | Shang, H. L (2020) "Dynamic Principal Component Regression for Forecasting Functional Time Series in A Group Structure" | 1.000 | 12 | 3 | 100% |
| 4 | Gradojevic, N., Kukolj, D., Adcock, R., and Djakovic, V (2023) "Forecasting Bitcoin with Technical Analysis: A not-so-random forest?" | 1.000 | 5 | 3 | 100% |
| 5 | Kokoszka, P., Rice, G., and Shang, H. L (2017) "Inference for the Autocovariance of a Functional Time Series Under Conditional Heteroscedasticity" | 0.737 | 3 | 2 | 100% |
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| 7 | Aguilera, A. M., Ocaña, F. A., and Valderrama, M. J (1997) "An Approximated Principal Component Prediction Model for Continuous-Time Stochastic Processes" | 0.644 | 2 | 2 | 100% |
| 8 | Gneiting, T. and Raftery, A. E (2007) "Strictly Proper Scoring Rules, Prediction, and Estimation" | 0.511 | 2 | 1 | 100% |
| 9 | Horvath, L. and Kokoszka, P. P (2012) Inference for functional data with applications | 0.511 | 2 | 1 | 100% |
| 10 | Bosq, D (2000) Linear Processes in Function Spaces | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 27 scored citations.