Estimating the mean and its effects on Neyman smooth tests of normality for ARMA models

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Authors Pierre Duchesne, Pierre Lafaye de Micheaux, Joseph Tagne Tatsinkou
Journal/Conference Name Canadian Journal of Statistics
Paper Category
Paper Abstract Goodness-of-fit tests represent an important part of any model building strategy. In time series modelling, many test procedures concentrate on specifying the model structure. However it is also of interest to check distributional assumptions. In autoregressive moving-average (ARMA) time series models, available results based on the smooth test paradigm assume that the mean of the process is known. However in practical applications, the mean is unknown and it needs to be estimated. Under general assumptions on the estimation procedures, the asymptotic distributions of the smooth test statistics based on estimation of all the parameters, including the mean, are derived. Surprisingly it is found that mean estimation has an impact on the asymptotic behaviours. This finding is in sharp contrast with portmanteau test procedures, where the degrees of freedom of the approximate distributions remain unchanged whether the mean is estimated or not. The test statistic relies on the order of the family, and a data-driven choice of that parameter is discussed, giving a fully automatic testing procedure. Theoretical and empirical comparisons between the smooth test statistic assuming a known mean and the new test statistic are presented. Consistency is studied. In a simulation study, the effects of assuming incorrectly the mean being known are illustrated. An application using annual data on the productivity of potatoes (per acre) in Prince Edward Island for the time period 1957–2014 illustrates the procedure. The Canadian Journal of Statistics 44: 241–270; 2016 © 2016 Statistical Society of Canada
Date of publication 2016
Code Programming Language R

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