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.
The aim of the article is to construct an asymptotically consistent test, based on a subsampling approach, to verify hypothesis about existence of the individual or common deterministic cycle in coordinates of multivariate macroeconomic time series. By the deterministic cycle we mean the periodic or almost periodic fluctuations in the mean function in cyclical fluctuations. To construct test we formulate a multivariate non-parametric model containing the business cycle component in the unconditional mean function. The construction relies on the Fourier representation of the unconditional expectation of the multivariate Almost Periodically Correlated time series and is related to fixed deterministic cycle presented in the literature. The analysis of the existence of common deterministic business cycles for selected European countries is presented based on monthly industrial production indexes. Our main findings from the empirical part is that the deterministic cycle can be strongly supported by the data and therefore should not be automatically neglected during analysis without justification.
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.