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Temporal Aggregation of Stationary And Nonstationary Discrete‐Time Processes
Author(s) -
Tsai Henghsiu,
Chan K. S.
Publication year - 2005
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2005.00430.x
Subject(s) - autocorrelation , mathematics , autoregressive fractionally integrated moving average , autoregressive model , stationary process , discrete time and continuous time , statistical physics , function (biology) , infinity , partial autocorrelation function , limiting , statistics , econometrics , mathematical analysis , long memory , time series , autoregressive integrated moving average , volatility (finance) , physics , evolutionary biology , biology , mechanical engineering , engineering
. We study the autocorrelation structure and the spectral density function of aggregates from a discrete‐time process. The underlying discrete‐time process is assumed to be a stationary AutoRegressive Fractionally Integrated Moving‐Average (ARFIMA) process, after suitable number of differencing if necessary. We derive closed‐form expressions for the limiting autocorrelation function and the normalized spectral density of the aggregates, as the extent of aggregation increases to infinity. These results are then used to assess the loss of forecasting efficiency due to aggregation.