arXiv subjects

Michael Grabinski

Publications and source records attributed to Michael Grabinski.

3 recordsLinked to original sources

arXiv2025

Business Cycles explained by Instability

Business cycles (a periodic change of e.g. GDP over five to ten years) exist, but a proper explanation for it is still lacking. Here we extend the well-known NAIRU (non-accelerating inflation rate of unemployment) model, resulting in a set of differ-ential equations. However, the solution is marginal stable. Therefore we find a nat-ural sinusoidal oscillation of inflation and unemployment just as observed in busi-ness cycles. When speculation is present, the instability becomes more severe. So we present for the first time a mathematical explanation for business cycles. The steering of central banks by setting interest rates to keep inflation stable and low needs an overhaul. One has to distinguish between real monetary instability and the one caused naturally by business cycles.

econ.TH↗

arXiv2024

A new measure of risk using Fourier analysis

We use Fourier analysis to access risk in financial products. With it we analyze price changes of e.g. stocks. Via Fourier analysis we scrutinize quantitatively whether the frequency of change is higher than a change in (conserved) company value would allow. If it is the case, it would be a clear indicator of speculation and with it risk. The entire methods or better its application is fairly new. However, there were severe flaws in previous attempts; making the results (not the method) doubtful. We corrected all these mistakes by e.g. using Fourier transformation instead of discrete Fourier analysis. Our analysis is reliable in the entire frequency band, even for fre-quency of 1/1d or higher if the prices are noted accordingly. For the stocks scrutinized we found that the price of stocks changes disproportionally within one week which clearly indicates spec-ulation. It would be an interesting extension to apply the method to crypto currencies as these currencies have no conserved value which makes normal considerations of volatility difficult.

q-fin.ST↗

arXiv2021

Statistical significance revisited

Statistical significance measures the reliability of a result obtained from a random experiment. We investigate the number of repetitions needed for a statistical result to have a certain significance. In the first step, we consider binomially distributed variables in the example of medication testing with fixed placebo efficacy, asking how many experiments are needed in order to achieve a significance of 95 %. In the next step, we take the probability distribution of the placebo efficacy into account, which to the best of our knowledge has not been done so far. Depending on the specifics, we show that in order to obtain identical significance, it may be necessary to perform twice as many experiments than in a setting where the placebo distribution is neglected. We proceed by considering more general probability distributions and close with comments on some erroneous assumptions on probability distributions which lead, for instance, to a trivial explanation of the fat tail.

stat.ME↗