Empirical modelling and model selection for forecasting inflation in a non-stationary world
Selection and forecasting are integral to econometric modelling and this thesis addresses both issues, with an application to UK inflation. Two automatic model selection algorithms, PcGets and RETINA, are evaluated on time-series and cross-section data. PcGets aims to select an undominated, congruent model of the phenomena of interest, whereas RETINA selects a parsimonious set of regressors that have predictive ability. Monte Carlo simulation results assess the null and non-null rejection frequencies of the algorithms in the presence of nonlinear functions. Both algorithms have the same properties as those for linear models under orthogonality, but collinearity increases null rejection frequencies and reduces non-null rejection frequencies. Simple operational rules that ‘double de-mean’ all functions are proposed to mitigate that problem. A nonlinear model selection strategy is proposed, that commences with a new test for nonlinearity, specifies the general model using polynomial functions as approximations, and undertakes a general-to-specific reduction using a multi-stage procedure. Nonlinearity poses a number of problems, including collinearity generated by nonlinear transformations, extreme observations leading to non-normal (fat-tailed) distributions, and often more variables than observations from general expansions approximating the nonlinearity, yet one must avoid excess retention of irrelevant variables. Solutions to all of these problems are proposed. A successful algorithm requires the synthesis of all of these developments to be implemented, as exclusion of one component of the algorithm can lead to severely erroneous conclusions. A model of inflation is built in which many determinants of inflation play a role in its explanation. The single cause explanation of inflation is refuted, along with a generic business cycle explanation. As forecast failure is prevalent, with naive devices often outperforming econometric models, a forecast competition is undertaken for UK annual and quarterly inflation, in which equilibrium correction models are compared to various forecasting rules. Robust forecasting devices prove useful in forecasting macroeconomic time-series, and they often outperform econometric models, both when there are structural breaks in the data and when the underlying process appears to be stable but with breaks in the explanatory variables. Increasing the information set does lead to improvements in forecasting performance suggesting that disaggregation can yield benefits. It is observed that much of the forecast error in the structural models is driven by the deterministic terms. Breaks in the mean of the cointegrating vector or the growth rate of the system will cause forecast ‘failure’, and results show how sensitive forecasts are to errors in these terms.