Page 79 - Invited Paper Session (IPS) - Volume 1

IPS61 Rituparna S. et al.

Granger causality in yield curves of different
markets
Rituparna Sen
Applied Statistics Division. Indian Statistical Institute, India

Abstract
We develop time series analysis of functional data observed discretely,
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 modeling the principal
component scores as vector ARMA process. We justify the method by showing
that an underlying ARMAH structure of the curves leads to a VARMA structure
on the principal component scores. We derive asymptotic properties of the
estimators, fits and forecast. 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 apply the
method to the yield curves of USA and India. We compare our forecasts to the
parametric model of Diebold and Li (2006). We then use the method of
Granger causality on the VARMA of Principal components scores for the two
markets to test if one market drives the other.

Keywords
Functional Principal Component; Vector ARMA; Prediction; Asymptotics;
Granger causality

1. Introduction
Functional data analysis (see Ramsay and Silverman (2005) for an overview) is an
extension of multivariate data analysis to functional data where each observation is a
n
curve, rather than a vector in R . An important feature of FDA is its ability to handle
dependencies within each observation, especially smoothness, ordering and
neighborhood. Actual observations can be at discrete and irregular points within the
curve. The first step of FDA is to replace these actual observations by a simple
functional representation. Spline-based approximation is the most commonly used
method. Kernel or wavelet-based approximations are also used.
An important tool of functional data analysis (FDA) is functional principal
component analysis (FPCA, see Castro et al. (1986); Rice and Silverman (1991)).
Functional processes can be characterized by their mean function and the
eigenfunctions of the autocovariance operator. This is a consequence of the
Karhunen-Loève representation of the functional process. The components of this
representation can be estimated. Individual trajectories are then represented by

68 | I S I W S C 2 0 1 9