No abstract

Much time series analysis can be performed by using readily available regression packages. In this paper it is shown that several frequency domain estimation algorithms for commonly used time series models may be recast as (possibly iterative) least squares regressions. This approach is exemplified by the fitting of (i) ARMA models (ii) the model described by Bloomfield (1973) and (iii) a model of Kolmogorov (1941) for the spectrum of turbulence in a fluid.

We show how the concept of hidden Markov model may be accommodated in a setting involving multiple sequences of observations. The resulting class of models allows for both interrelationships between different sequences and serial dependence within sequences. Missing values in the observation sequences may be handled in a straightforward manner. We also examine a group of methods, based upon the observed Fisher Information matrix, for estimating the covariance matrix of the parameter estimates. We illustrate the methods with both real and simulated data sets. RESUMENous montrons comment le concept du modtle de Markov cachC peut Stre accommodi a un environnement impliquant des sequences multiples d'observations. La classe de modkles en resultant permet des inter-relations entre differentes skquences et la dCpendance en serie au sein des sequences. Nous soulignons que les valeurs manquantes dans les sequences d'observations peuvent itre manipulkes de faqon simple. Nous examinons Cgalement un groupe de methodes fond6 sur la matrice d'information de Fisher observie, afin d'estimer la matrice de covariance des estimations de paramhtres. Nous illustrons les mithodes avec des ensembles de donntes rielles et simulies.

The transient electromagnetic (TEM) method is used extensively for mineral exploration and other applications such as geothermal soundings, oil exploration, groundwater pollution, soil salinity and geological mapping. Sferics pulses produced by lightning strokes propagating in the ionosphere-earth waveguide cavity induce noise in a bandwidth of a few Hz to tens of kHz. The usual method of stacking and calculating the mean of a given stack cannot effectively reduce the spike-like noise induced by high-amplitude sferics pulses. To reduce this type of noise, a number of different ways of stacking data were investigated and compared. Noise data were stacked by using robust estimators such as the median, trimmed mean, and a range of M-estimators. Since storage of all the samples of a given stack can take up a prohibitively large amount of microprocessor memory, recursive algorithms for the M-estimators and their standard error were developed for the realtime reduction of sferics pulses. The recursive algorithms have been demonstrated to work effectively on windowed data, and thus the memory normally required to obtain the mean is sufficient for calculation of the Mestimate.

Summary In this paper, a new test of the hypothesis that all the correlations between a set of variables are zero is proposed. It is based on the asymptotic behaviour of the largest of the observed correlation coefficients. Here “asymptotic” refers to the size of the correlation matrix considered. Simulations show that the critical levels, calculated using the asymptotic theory, are conservative but quite accurate, even for small correlation matrices.