Nonparametric Finance

Chapter 5Time Series Analysis

Time series analysis can be used to analyze both a univariate time series and a vector time series. We are interested in estimating the dependence between consecutive observations. In a vector time series there is both cross-sectional dependence and time series dependence, which means that the components of the vector depend on each other at any given point of time, and the future values of the vectors depend on the past values of the vectors.

Model free time series analysis can estimate the joint distribution of

5.1

for some . The estimation could be done using nonparametric multivariate density estimation. A different model free approach models at the first step the distribution of parametrically, using density . At the second step, parameter is taken to be time dependent. This leads to a semiparametric time series analysis, because we combine a cross-sectional parametric model with a time varying estimation of the parameter. Time localized maximum likelihood ...