Time series of functional data
نویسنده
چکیده
We develop time series analysis of functional data, treating the whole curve as a random realization from a distribution on functions that evolve over time. The method consists of principal components analysis of functional data and subsequently modelling the principal component scores as vector ARMA process. We carry out the estimation of VARMA parameters using the equivalent state space representation. We derive asymptotic properties of the estimators and the fits. We apply the method to two different data sets. For term structures of interest rates, this provides a unified framework for studying the time and maturity components of interest rates under one set-up with few parametric assumptions. We compare our forecasts to the parametric Diebold and Li (2006) model. Secondly, we apply this approach to hourly spot prices of electricity and obtain fits and forecasts that are better than those existing in the electricity literature. Dr. Rituparna Sen is a PhD in Statistics from University Chicago and post-graduate student in Statistics of Stanford University having done her masters from ISI Kolkata. She has an illustrious academic background winning numerous awards such as the Gold Medal from her alma mater the Indian Statistical Institute Kolkata. Her research interests lies in application of statistics to finance including convergence of stochastic processes, Inference for diffusions, Bayesian filtering, asymptotic inference, likelihood estimation, functional data analysis, hidden Markov models in Statistics and discontinuous asset price, stochastic volatility, optimal derivative pricing and hedging in incomplete market, covolatility for asynchronous data, volatility in the presence of microstructure noise in finance. Dr. Sreejata Banerjee Associate Professor Union Bank Chair for Excellence in Banking Seminar Coordinator Madras School of Economics
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