  Periodic autoregressive (PAR) time series with finite variance is considered
as one of the most common models of second-order cyclostationary processes.
However, in the real applications, the signals with periodic characteristics
may be disturbed by additional noise related to measurement device disturbances
or to other external sources. Thus, the known estimation techniques dedicated
for PAR models may be inefficient for such cases. When the variance of the
additive noise is relatively small, it can be ignored and the classical
estimation techniques can be applied. However, for extreme cases, the additive
noise can have a significant influence on the estimation results. In this
paper, we propose four estimation techniques for the noise-corrupted PAR models
with finite variance distributions. The methodology is based on Yule-Walker
equations utilizing the autocovariance function. It can be used for any type of
the finite variance additive noise. The presented simulation study clearly
indicates the efficiency of the proposed techniques, also for extreme case,
when the additive noise is a sum of the Gaussian additive noise and additive
outliers. The proposed estimation techniques are also applied for testing if
the data corresponds to noise-corrupted PAR model. This issue is strongly
related to the identification of informative component in the data in case when
the model is disturbed by additive non-informative noise. The power of the test
is studied for simulated data. Finally, the testing procedure is applied for
two real time series describing particulate matter concentration in the air.
