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All previous versions of Microsoft Excel until Excel 2007 have been criticized by statisticians for several reasons, including the accuracy of statistical functions, the properties of the random number generator, the quality of statistical add-ins, the weakness of the Solver for nonlinear regression, and the data graphical representation. Until recently Microsoft did not make an attempt to fix all the errors in Excel and was still marketing a product that contained known errors. We provide an update of these studies given the recent release of Excel 2010 and we have added OpenOffice.org Calc 3.3 and Gnumeric 1.10.16 to the analysis, for the purpose of comparison. The conclusion is that the stream of papers, mainly in Computational Statistics and Data Analysis, has started to pay off: Microsoft has partially improved the statistical aspects of Excel, essentially the statistical functions and the random number generator.

The purpose of this paper is to discuss several fundamental issues in the theory of time-dependent spectra for univariate and multivariate non-stationary processes. The general framework is provided by Priestley's evolutionary spectral theory which is based on a family of stochastic integral representations. A particular spectral density function can be obtained from the WoldCramer decomposition, as illustrated by several examples. It is shown why the coherence is time invariant in the evolutionary theory and how the theory can be generalized so that the coherence becomes time dependent. Statistical estimation of the spectrum is also considered. An improved upper bound for the bias due to non-stationarity is obtained which does not rely on the characteristic width of the process. The results obtained in the paper are illustrated using time series simulated from an evolving bivariate autoregressive moving-average process of order (1, 1) with a highly time-varying coherence.

This paper is about vector autoregressive-moving average (VARMA) models with time-dependent coefficients to represent non-stationary time series. Contrary to other papers in the univariate case, the coefficients depend on time but not on the series' length n. Under appropriate assumptions, it is shown that a Gaussian quasi-maximum likelihood estimator is almost surely consistent and asymptotically normal. The theoretical results are illustrated by means of two examples of bivariate processes. It is shown that the assumptions underlying the theoretical results apply. In the second example the innovations are marginally heteroscedastic with a correlation ranging from −0.8 to 0.8. In the 1 Preprint version of a paper that will appear in Scandinavian Journal of Statistics (2017) two examples, the asymptotic information matrix is obtained in the Gaussian case. Finally, the finite-sample behavior is checked via a Monte Carlo simulation study for n from 25 to 400. The results confirm the validity of the asymptotic properties even for short series and the asymptotic information matrix deduced from the theory.

This article has three objectives: (a) to describe the method of automatic ARIMA modeling (AAM), with and without intervention analysis, that has been used in the analysis; (b) to comment on the results; and (c) to comment on the M3 Competition in general. Starting with a computer program for fitting an ARIMA model and a methodology for building univariate ARIMA models, an expert system has been built, while trying to avoid the pitfalls of most existing software packages. A software package called Time Series Expert TSE-AX is used to build a univariate ARIMA model with or without an intervention analysis. The characteristics of TSE-AX are summarized and, more especially, its automatic ARIMA modeling method. The motivation to take part to the M3-Competition is also outlined. The methodology is described mainly in three technical appendices: (A) choice of differences and of a transformation, use of intervention analysis; (B) available specification procedures; (C) adequacy, model checking and new specification. The problems raised by outliers are discussed, in particular how close they are from the forecast origin. Several series that are difficult to deal with from that point of view are mentioned and one of them is shown. In the last section, we comment on contextual information, the idea of an e-M Competition, prediction intervals and the possible use of other forecasting methods within Time Series Expert.

Recursive estimation methods for time series models usually make use of recurrences for the vector of parameters, the model error and its derivatives with respect to the parameters, plus a recurrence for the Hessian of the model error. An alternative method is proposed in the case of an autoregressive-moving average model, where the Hessian is not updated but is replaced, at each time, by the inverse of the Fisher information matrix evaluated at the current parameter. The asymptotic properties, consistency and asymptotic normality, of the new estimator are obtained. Monte Carlo experiments indicate that the estimates may converge faster to the true values of the parameters than when the Hessian is updated. The paper is illustrated by an example on forecasting the speed of wind.

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