The main goal of this paper is to propose the probabilistic description of cyclical (business) fluctuations. We generalize a fixed deterministic cycle model by incorporating the time-varying amplitude. More specifically, we assume that the mean function of cyclical fluctuations depends on unknown frequencies (related to the lengths of the cyclical fluctuations) in a similar way to the almost periodic mean function in a fixed deterministic cycle, while the assumption concerning constant amplitude is relaxed. We assume that the amplitude associated with a given frequency is time-varying and is a spline function. Finally, using a Bayesian approach and under standard prior assumptions, we obtain the explicit marginal posterior distribution for the vector of frequency parameters. In our empirical analysis, we consider the monthly industrial production in most European countries. Based on the highest marginal data density value, we choose the best model to describe the considered growth cycle. In most cases, data support the model with a time-varying amplitude. In addition, the expectation of the posterior distribution of the deterministic cycle for the considered growth cycles has similar dynamics to cycles extracted by standard bandpass filtration methods.

Regarded primarily as a scandalist, Bruno Jasieński is also an innovator and ‘theoretician’ of the avant-garde. Then, so the argument, he converted to Communism and put his pen in the service of that ideology. He paid for it with the price of debasing his talent to the level of a socialist realist hack and, eventually, the price of his life when the regime he so avidly supported turned on him in the great purges of 1937–38. This article takes issue with the claim – which is part of the generally accepted narrative – that Jasieński ‘swerved gently to the left’ in 1923–1925. This article analyses the politics of young Bruno Jasieński's verse, i.e. the texts produced before 1921, the year of the publication of the first collection of his poems. In so far as his early poetic work contains nothing but praise of the Russian revolution and its ethos, his ideological evolution in the nineteen twenties should termed radicalization rather than a shift to the left.