Estimating the memory parameter for potentially non-linear and non-Gaussian time series with wavelets

The asymptotic theory for the memory-parameter estimator constructed from the log-regression with wavelets is incomplete for 1/$f$ processes that are not necessarily Gaussian or linear. Having a complete version of this theory is necessary because of the importance of non-Gaussian and non-linear long-memory models in describing financial time series. To bridge this gap, we prove that, under some mild assumptions, a newly designed memory estimator, named LRMW in this paper, is asymptotically consistent. The performances of LRMW in three simulated long-memory processes indicate the efficiency of this new estimator.

Markov-Switching Stochastic Processes in an Active Trading Algorithm in the Main Latin-American Stock Markets

In the present paper, we review the use of two-state, Generalized Auto Regressive Conditionally Heteroskedastic Markovian stochastic processes (MS-GARCH). These show the quantitative model of an active stock trading algorithm in the three main Latin-American stock markets (Brazil, Chile, and Mexico). By backtesting the performance of a U.S. dollar based investor, we found that the use of the Gaussian MS-GARCH leads, in the Brazilian market, to a better performance against a buy and hold strategy (BH). In addition, we found that the use of t-Student MS-ARCH models is preferable in the Chilean market. Lastly, in the Mexican case, we found that is better to use Gaussian time-fixed variance MS models. Their use leads to the best overall performance than the BH portfolio. Our results are of use for practitioners by the fact that MS-GARCH models could be part of quantitative and computer algorithms for active trading in these three stock markets.

A Gaussian Model for the Time Development of the Sars-Cov-2 Corona Pandemic Disease. Predictions for Germany Made on 30 March 2020

For Germany, it is predicted that the first wave of the corona pandemic disease reaches its maximum of new infections on 11 April 2020 − 3.4 + 5.4 days with 90% confidence. With a delay of about 7 days the maximum demand on breathing machines in hospitals occurs on 18 April 2020 − 3.4 + 5.4 days. The first pandemic wave ends in Germany end of May 2020. The predictions are based on the assumption of a Gaussian time evolution well justified by the central limit theorem of statistics. The width and the maximum time and thus the duration of this Gaussian distribution are determined from a statistical χ 2 -fit to the observed doubling times before 28 March 2020.

A Gaussian model for the time development of the Sars-Cov-2 corona pandemic disease. Predictions for Germany made on March 30, 2020

For Germany it is predicted that the first wave of the corona pandemic disease reaches its maximum of new infections on April 11th, 2020 days with 90 percent confidence. With a delay of about 7 days the maximum demand on breathing machines in hospitals occurs on April 18th, 2020 days. The first pandemic wave ends in Germany end of May 2020. The predictions are based on the assumption of a Gaussian time evolution well justified by the central limit theorem of statistics. The width and the maximum time and thus the duration of this Gaussian distribution are determined from a statistical χ2-fit to the observed doubling times before March 28, 2020.