Fractional Differenced Modelling to Bursty Impulsive Noise in Low-Voltage PLC Networks: Long-Term Memory Process

Fractional differencing is a tool for modelling time series which have long-range dependence or long-term memory. That is, a time series in which the correlation between distant observations, however small, is not negligible. The bursty impulsive noise present in the low-voltage Power line communication (PLC) system has been found to be a time series with long-term memory. Fractionally differenced autoregressive moving average (FARMA) models are formed by allowing the differencing parameter
$d$
in the familiar Box-Jenkins autoregressive integrated moving average (ARIMA)
$(p, d, q)$
models to take fractional real values. As such, they enable the simultaneous modelling of the long-term and short-term memory behavior of a time series observations. This paper discusses the usefulness of fractional differencing to bursty PLC impulsive noise time series modelling. The parameters of the proposed FARMA model is estimated and diagnostically checked and validated through sample measurement data acquired from the University of KwaZulu-Natal.