Comment on 'Second-Order Statistical Structure of Geomagnetic Field Reversals' by P. S. Naidu

In a recent paper, Naidu [1975] has proposed that the reversal intervals of the geomagnetic field for the period 0-76 m.y. are not independent. In fact, the author has fitted a first order autoregressive moving average model to the data published by Heirtzler et al. [1968]. This conclusion, if true, is of importance because it suggests that the mechanism governing the reversals of the geomagnetic dynamo possesses a memory

Evidence and Ideology in Macroeconomics: The Case of Investment Cycles

The paper reports the principal findings of a long term research project on the description and explanation of business cycles. The research strongly confirmed the older view that business cycles have large systematic components that take the form of investment cycles. These quasi-periodic movements can be represented as low order, stochastic, dynamic processes with complex eigenvalues. Specifically, there is a fixed investment cycle of about 8 years and an inventory cycle of about 4 years. Maximum entropy spectral analysis was employed for the description of the cycles and continuous time econometrics for the explanatory models. The central explanatory mechanism is the second order accelerator, which incorporates adjustment costs both in relation to the capital stock and the rate of investment. By means of parametric resonance it was possible to show, both theoretically and empirically how cycles aggregate from the micro to the macro level. The same mathematical tool was also used to explain the international convergence of cycles. I argue that the theory of investment cycles was abandoned for ideological, not for evidential reasons. Methodological issues are also discussed

Time series modelling and maximum entropy

This paper briefly reviews the principles of maximum entropy spectral analysis and the closely related problem of autoregressive time series modelling. The important aspect of model identification is discussed with particular emphasis on the representation of harmonic processes with noise in terms of autoregressive moving-average models. It is shown that this representation leads to a spectral estimator proposed by Pisarenko in 1973

IEEE transactions on acoustics, speech, and signal processing

p. 1680-1686The standard methods of performing discrete convolution, that is, directly in the time domain or by means of the fast Fourier transform in the frequency domain, implicitly assume that the signals to be convolved are zero outside the observation intervals. Often this assumption produces undesirable end effects which are particularly severe when the signals are short in duration. This paper presents an approach to discrete convolution which obviates the zero assumption. The method is structurally similar to the Burg method [l], which estimates the autocorrelation coefficients of a series in a manner which does not require a predefinition of the behavior of the signal outside of the known interval. The basic principle of the present approach is that each term of the convolution is recursively determined from previous terms in a manner consistent with the optimal modeling of one signal into the other. The recursion uses forward and backward modeling together with the Morf et al. [2] algorithm for computation of the prediction error filter. The method is illustrated by application to the computation of the analytic signal and the derivative