We propose a number of volatility measures that are based on ensemble averaging instead of time averaging. These measures allow fast measurement of current volatility without relying on series of past data (realized volatility) of future expectations (implied volatility). The introduced...

Professional market participants have to deal with illiquid securities on a constant basis. For such securities traditional risk assessment techniques fail. This can lead to underestimated and distorted results for the entire investment portfolio, and ultimately to inadequate risk management. We...

In Nature’s Law, Elliott explained that the Fibonacci sequence provides a mathematical basis of the wave principle. In The Wave Principle of Human Social Behavior and The New Science of Socionomics, Prechter explained how Fibonacci sequence exists at all those instances where growth is the...

In order to have references for discussing mathematical menus in political science, I review the most common types of mathematical formulae used in physics and chemistry, as well as some mathematical advances in economics. Several issues appear relevant: variables should be well defined and...

Campbell and Shiller average 10 years of real S&P 500 earnings to construct its Cyclically Adjusted P/E ratio, or CAPE, which they then use to forecast its future 10-year returns. In essence, Campbell and Shiller kill two birds with one large stone - they use the 10-year average to reduce noise...

Filtering has had a profound impact as a device of perceiving information and deriving agent expectations in dynamic economic models. For an abstract economic system, this paper shows that the foundation of applying the filtering method corresponds to the existence of a conditional expectation...

Infra-monthly time series have increasingly appeared on the radar of official statistics in recent years, mostly as a consequence of a general digital transformation process and the outbreak of the COVID-19 pandemic in 2020. Many of those series are seasonal and thus in need for seasonal...

Infra-monthly economic time series have become increasingly popular in official statistics in recent years. This evolution has been largely fostered by official statistics’ digital transformation during the last decade. The COVID-19 pandemic outbreak in 2020 has added fuel to the fire as many...

The COVID-19 outbreak in 2020 has fostered in many countries the development of new weekly economic indices for the timely tracking of pandemic-related turmoils and other forms of rapid economic changes. Such indices often utilise information from daily and weekly economic time series that...