The functional autoregressive process has become a useful tool in the analysis of functional time series data. It is defined by the equation , in which the observations Xn and errors [epsilon]n are curves, and is an operator. To ensure meaningful inference and prediction based on this model, it...

Principal component analysis has become a fundamental tool of functional data analysis. It represents the functional data as "X"_"i"("t")&equals;"μ"("t")&plus;Σ_{1≤"l"&infin ;}"η"_"i", "l"&plus; "v"_"l"("t "), where "μ" is the common mean, "v"_"l" are the eigenfunctions of the covariance operator and the...</sub>

, both methods have correct asymptotic size and detect a change with probability approaching unity. The methods are illustrated and compared in a small simulation study. Copyright Royal Economic Society 2006

We develop procedures for testing for changes in the mean of multivariatem-dependent stationary processes. Several test statistics are considered and corresponding limit theorems are derived. These include functional and Darling-Erdos type limit theorems. The tests are shown to be consistent...

The unconditional variance of various GARCH-type models is a function h(theta) of the parameter vector theta which is estimated by theta. For most models used in practice, closed-form expressions of h(.) have been found. On the contrary, the unconditional variance can be estimated by the sample...