Non-Parametric Test for the Existence of the Common Deterministic Cycle The Case of the Selected European Countries

Abstract

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.