Three essays on time-varying parameters and time series networks

This thesis is composed of three essays on time-varying parameters and time series networks where each essay deals with specific aspects thereof. The thesis starts with proposing a 2SLS based test for a threshold in models with endogenous regressors in Chapter 2. Many economic models are formulated in this way, for example output growth or unemployment rates in different states of the economy. Therefore, it is necessary to have tools available which are capable of indicating whether such effects exist in the data or not. Chapter 3 proposes, to my best knowledge, the first estimator for the inverse of the long-run covariance matrix of a linear, potentially heteroskedastic stochastic process under unknown sparsity constraints. That is, the econometrician does not know which entries of the inverse are equal to zero and which not. Such situations naturally arise, for example, when modelling partial correlation networks based on time series data. Finally, in Chapter 4 this thesis empirically investigates how robust two commonly applied network measures, the From- and the To-degree, are to the exclusion of central nodes in financial volatility networks. This question is motivated by the current empirical literature which excludes certain nodes such as Lehman Brothers from their analysis.