This article aims at constructing a new method for testing the statistical significance of seasonal fluctuations for non-stationary processes. The constructed test is based on a method of subsampling and on the spectral theory of Almost Periodically Correlated (APC) time series. In the article we consider an equation of a nonstationary process, containing a component which includes seasonal fluctuations and business cycle fluctuations, both described by an almost periodic function. We build subsampling test justifying the significance of frequencies obtained from the Fourier representation of the unconditional expectation of the process. The empirical usefulness of the constructed test is examined for selected macroeconomic data. The article studies survey indicators of economic climate in industry, retail trade and consumption for European countries.
We discuss the notion of the financial cycle making a clear indication that the thorough study of its empirical properties in case of developing economies is still missing. We focus on the observed series of credit and equity and make formal statistical inference about the properties of the cycles in case of Polish economy. The non-standard subsampling procedure and discrete spectral characteristics of almost periodically correlated time series are applied to make formal statistical inference about the cycle. We compare the results with those obtained for UK and USA. We extract the cyclical component and confront empirical properties of the financial cycle for small open economy with those established so far in case of developed economies.
The economic activity indicators in Poland during the years 1995‒2011 exhibit various cyclical patterns. Employing the Christiano – Fitzgerald band-pass filter and unobserved components model it is shown that the cyclical processes of Polish economic activity are driven by overlapping higher frequency fluctuations (3‒4 years) and longer cycles of 8.5 years. The cyclical fluctuations of construction, transportation and trade are dissimilar to gross value added. Economic activity in transportation leads and in construction lags the fluctuations of gross value added. Cyclical fluctuations of gross value added seem to be determined by industry and construction. Manufacturing, especially capital and intermediate goods fluctuations are responsible for the variation of industry. The production of non-durable consumer goods, energy and production of electric power are relatively the most desynchronized compared to industry. Production of electric power leads industrial production. Capital goods, intermediate goods and energy cycle phases are asymmetric – the slowdown lasts shorter and has higher amplitude compared to expansion. During the last crisis occurred the intensified variation of economic activity in Poland.