TY - JOUR
T1 - Temporal aggregation of seasonally near-integrated processes
AU - Barrio Castro, Tomás del
AU - Rodrigues, Paulo M.M.
AU - Robert Taylor, A. M.
N1 - el Barrio Castro acknowledges financial support from the projectsECO2014-58991-C3-3-R and ECO2017-83255-C3-2-P (Agencia Estatal de Investigación Ministerio de Ciencia,Inovación y Universidades)
PY - 2019/11
Y1 - 2019/11
N2 - We investigate the implications that temporally aggregating, either by average sampling or systematic (skip) sampling, a seasonal process has on the integration properties of the resulting series at both the zero and seasonal frequencies. Our results extend the existing literature in three ways. First, they demonstrate the implications of temporal aggregation for a general seasonally integrated process with S seasons. Second, rather than only considering the aggregation of seasonal processes with exact unit roots at some or all of the zero and seasonal frequencies, we consider the case where these roots are local-to-unity such that the original series is near-integrated at some or all of the zero and seasonal frequencies. These results show, among other things, that systematic sampling, although not average sampling, can impact on the non-seasonal unit root properties of the data; for example, even where an exact zero frequency unit root holds in the original data it need not necessarily hold in the systematically sampled data. Moreover, the systematically sampled data could be near-integrated at the zero frequency even where the original data is not. Third, the implications of aggregation on the deterministic kernel of the series are explored.-142.
AB - We investigate the implications that temporally aggregating, either by average sampling or systematic (skip) sampling, a seasonal process has on the integration properties of the resulting series at both the zero and seasonal frequencies. Our results extend the existing literature in three ways. First, they demonstrate the implications of temporal aggregation for a general seasonally integrated process with S seasons. Second, rather than only considering the aggregation of seasonal processes with exact unit roots at some or all of the zero and seasonal frequencies, we consider the case where these roots are local-to-unity such that the original series is near-integrated at some or all of the zero and seasonal frequencies. These results show, among other things, that systematic sampling, although not average sampling, can impact on the non-seasonal unit root properties of the data; for example, even where an exact zero frequency unit root holds in the original data it need not necessarily hold in the systematically sampled data. Moreover, the systematically sampled data could be near-integrated at the zero frequency even where the original data is not. Third, the implications of aggregation on the deterministic kernel of the series are explored.-142.
KW - Aggregation
KW - Average sampling
KW - Demodulation
KW - Seasonal (near-) unit roots
KW - Systematic sampling
UR - http://www.scopus.com/inward/record.url?scp=85062372322&partnerID=8YFLogxK
U2 - 10.1111/jtsa.12453
DO - 10.1111/jtsa.12453
M3 - Article
AN - SCOPUS:85062372322
SN - 0143-9782
VL - 40
SP - 872
EP - 886
JO - Journal Of Time Series Analysis
JF - Journal Of Time Series Analysis
IS - 6
ER -