Functional Autoregression for Sparsely Sampled Data

References

• Aue, A., Norinho, D. D., and Hörmann, S. (2015), “On the Prediction of Stationary Functional Time Series,” Journal of the American Statistical Association, 110, 378–392.
   Web of Science ®Google Scholar
• Behseta, S., Kass, R. E., and Wallstrom, G. L. (2005), “Hierarchical Models for Assessing Variability Among Functions,” Biometrika, 92, 419–434.
   Web of Science ®Google Scholar
• Besse, P. C., Cardot, H., and Stephenson, D. B. (2000), “Autoregressive Forecasting of Some Functional Climatic Variations,” Scandinavian Journal of Statistics, 27, 673–687.
   Web of Science ®Google Scholar
• Bolder, D., Johnson, G., and Metzler, A. (2004), An Empirical Analysis of the Canadian Term Structure of Zero-Coupon Interest Rates, Ontario, Canada: Bank of Canada.
   Google Scholar
• Bosq, D. (2000), Linear Processes in Function Spaces: Theory and Applications (Vol. 149), Berlin: Springer Science & Business Media.
   Google Scholar
• Cardot, H., Ferraty, F., and Sarda, P. (1999), “Functional Linear Model,” Statistics & Probability Letters, 45, 11–22.
   Web of Science ®Google Scholar
• Chen, Y., and Li, B. (2015), “An Adaptive Functional Autoregressive Forecast Model to Predict Electricity Price Curves,” Journal of Business & Economic Statistics. doi:10.1080/07350015.2015.1092976.
   Web of Science ®Google Scholar
• Crainiceanu, C., Ruppert, D., and Wand, M. P. (2005), “Bayesian Analysis for Penalized Spline Regression Using WinBUGS,” Journal of Statistical Software, 14, 1–24.
   Web of Science ®Google Scholar
• Cressie, N., and Wikle, C. K. (2011), Statistics for Spatio-Temporal Data, New York: Wiley.
   Google Scholar
• Damon, J., and Guillas, S. (2002), “The Inclusion of Exogenous Variables in Functional Autoregressive Ozone Forecasting,” Environmetrics, 13, 759–774.
   Web of Science ®Google Scholar
• ———– (2005), “Estimation and Simulation of Autoregressive Hilbertian Processes With Exogenous Variables,” Statistical Inference for Stochastic Processes, 8, 185–204.
   Google Scholar
• Didericksen, D., Kokoszka, P., and Zhang, X. (2012), “Empirical Properties of Forecasts With the Functional Autoregressive Model,” Computational Statistics, 27, 285–298.
   Web of Science ®Google Scholar
• Diebold, F. X., and Li, C. (2006), “Forecasting the Term Structure of Government Bond Yields,” Journal of Econometrics, 130, 337–364.
   Web of Science ®Google Scholar
• Diebold, F. X., Rudebusch, G. D., and Aruoba, B. S. (2006), “The Macroeconomy and the Yield Curve: A Dynamic Latent Factor Approach,” Journal of Econometrics, 131, 309–338.
   Web of Science ®Google Scholar
• Durbin, J., and Koopman, S. J. (2002), “A Simple and Efficient Simulation Smoother for State Space Time Series Analysis,” Biometrika, 89, 603–616.
   Web of Science ®Google Scholar
• Earls, C., and Hooker, G. (2014), “Bayesian Covariance Estimation and Inference in Latent Gaussian Process Models,” Statistical Methodology, 18, 79–100.
   Web of Science ®Google Scholar
• Fernandez, C., and Steel, M. F. (2000), “Bayesian Regression Analysis With Scale Mixtures of Normals,” Econometric Theory, 16, 80–101.
   Web of Science ®Google Scholar
• Gelman, A. (2006), “Prior Distributions for Variance Parameters in Hierarchical Models” ( comment on article by Browne and Draper), Bayesian Analysis, 1, 515–534.
   Web of Science ®Google Scholar
• Hays, S., Shen, H., and Huang, J. Z. (2012), “Functional Dynamic Factor Models With Application to Yield Curve Forecasting,” The Annals of Applied Statistics, 6, 870–894.
   Web of Science ®Google Scholar
• Horváth, L., and Kokoszka, P. (2012), Inference for Functional Data With Applications (Vol. 200), Berlin: Springer Science & Business Media.
   Google Scholar
• Hyndman, R. J., and Khandakar, Y. (2008), “Automatic Time Series Forecasting: The Forecast Package for R,” Journal of Statistical Software, 27, 1–22.
   Web of Science ®Google Scholar
• Hyndman, R. J., and Ullah, M. S. (2007), “Robust Forecasting of Mortality and Fertility Rates: A Functional Data Approach,” Computational Statistics & Data Analysis, 51, 4942–4956.
   Web of Science ®Google Scholar
• Kargin, V., and Onatski, A. (2008), “Curve Forecasting by Functional Autoregression,” Journal of Multivariate Analysis, 99, 2508–2526.
   Web of Science ®Google Scholar
• Kaufman, C. G., Sain, S. R., et al. (2010), “Bayesian Functional ANOVA Modeling Using Gaussian Process Prior Distributions,” Bayesian Analysis, 5, 123–149.
   Web of Science ®Google Scholar
• Kim, S., Shephard, N., and Chib, S. (1998), “Stochastic Volatility: Likelihood Inference and Comparison With ARCH Models,” The Review of Economic Studies, 65, 361–393.
   Web of Science ®Google Scholar
• Kokoszka, P. (2012), “Dependent Functional Data,” ISRN Probability and Statistics, Article ID 958254, doi:0.5402/2012/958254.
   Google Scholar
• Kokoszka, P., and Reimherr, M. (2013), “Determining the Order of the Functional Autoregressive Model,” Journal of Time Series Analysis, 34, 116–129.
   Web of Science ®Google Scholar
• Korobilis, D. (2013), “VAR Forecasting Using Bayesian Variable Selection,” Journal of Applied Econometrics, 28, 204–230.
   Web of Science ®Google Scholar
• Kowal, D. R., Matteson, D. S., and Ruppert, D. (2016), “A Bayesian Multivariate Functional Dynamic Linear Model,” Journal of the American Statistical Association, doi:1080/01621459.2016.1165104
   Web of Science ®Google Scholar
• Kuo, L., and Mallick, B. (1998), “Variable Selection for Regression Models,” Sankhyā: The Indian Journal of Statistics, Series B, 65–81.
   Google Scholar
• Laurini, M. P. (2014), “Dynamic Functional Data Analysis With Non-Parametric State Space Models,” Journal of Applied Statistics, 41, 142–163.
   Web of Science ®Google Scholar
• Matérn, B. (2013), Spatial Variation (Vol. 36), New York: Springer Science & Business Media.
   Google Scholar
• Neal, R. M. (1999), “Regression and Classification Using Gaussian Process Priors,” Bayesian Statistics, 6, 475–501.
   Google Scholar
• Nelson, C. R., and Siegel, A. F. (1987), “Parsimonious Modeling of Yield Curves,” Journal of Business, 60, 473.
   Web of Science ®Google Scholar
• Ramsay, J. O. (2006), Functional Data Analysis, New York: Online Library.
   Google Scholar
• Ramsay, J. O., Wickham, H., Graves, S., and Hooker, G. (2014), fda: Functional Data Analysis, R package version 2.4.4.
   Google Scholar
• Rasmussen, C. E., and Williams, C. K. (2006), Gaussian Processes for Machine Learning, Cambridge, MA: The MIT Press.
   Google Scholar
• Shi, J. Q., and Choi, T. (2011), Gaussian Process Regression Analysis for Functional Data, Boca Raton, FL: CRC Press.
   Google Scholar
• Wand, M., and Ormerod, J. (2008), “On Semiparametric Regression With O’Sullivan Penalized Splines,” Australian & New Zealand Journal of Statistics, 50, 179–198.
   Web of Science ®Google Scholar
• West, M., and Harrison, J. (1997), Bayesian Forecasting and Dynamic Models, Berlin: Springer.
   Google Scholar
• Wood, S. N. (2003), “Thin Plate Regression Splines,” Journal of the Royal Statistical Society, Series B, 65, 95–114.
   Google Scholar
• Yao, F., Müller, H.-G., and Wang, J.-L. (2005), “Functional Data Analysis for Sparse Longitudinal Data,” Journal of the American Statistical Association, 100, 577–590.
   Web of Science ®Google Scholar