Non-normality and non-linearity in univariate standard models of inflation

The empirical evidences presented in a vast number of recent publications gave rise to debates in the literature regarding the problem of stationarity of inflation. Sometimes considered as a unit root process and sometimes as a stationary process, in most of the studies inflationary time series are modelled assuming normality and linearity. The present thesis relaxes the frequently used assumptions of linearity in price processes and normality in distribution of inflation, and suggests two ways of modelling inflationary data. Firstly, it is assumed that distribution of inflation is a stable Paretian distribution and, under this assumption, stationarity of inflation is examined applying an appropriate test. Secondly, price time series are modelled by treating them as a unit root bilinear process, which further leads to non-normality in distribution of inflation. A recently proposed test for presence of no-bilinearity is then applied. If bilinearity is detected, the bilinear coefficient is estimated by the Kalman filter method. Subsequently, the finite sample properties of this estimator are evaluated using Monte Carlo simulation experiments. A series of Monte Carlo simulations leads to calculating the r-statistic critical values for testing whether the estimated bilinear coefficients significantly differ from zero. The methodologies explained above are then applied to a large set of worldwide price and inflationary data for 107 different countries. Assuming that the distribution of inflation is a stable Paretian distribution 75% of the inflationary time series are classified as integrated of order zero. Under the assumption of normality of distribution of inflation this can be inferred for 11.11% of the inflationary time series. It has been also shown that 71.03% of the price time series exhibit unit root bilinearity. Analysis of the inflationary time series reveals the presence of bilinearity in 9.35% of them.