This project can be mainly divided into two sections. In the first section it attempts to model an irregularly spaced time series data where time scale is being measured with a measurement error. Modelling an irregularly spaced time series data alone is quite challenging as traditional time series techniques only capture equally/regularly spaced time series data. In addition to that, the measurement error in the time scale make it even more challenging to incorporate measurement error models and functional approaches to model the time series. Thus, this project is based on a Bayesian approach to model a flexible regression function when the time scale is being measured with a measurement error. The regression functions are modelled with regression P-splines and the exploration of posterior is carried out using a fully Bayesian method that uses Markov chain monte carlo (MCMC) techniques. In section two, we identify the relationship/dependency between two irregularly spaced time series data sets which were modelled using regression P-splines and a fully Bayesian method, using windowed moving correlations. The validity of the suggested methodology is then explored using two simulations. It is then applied on two irregularly spaced time series data sets each subjected to measurement errors in time scale to identify the dependency between them in terms of statistically significant correlations.
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