Abstract: When
the long-memory structure of time series is caused by the non-zero fractional
differencing parameter d, its short-memory counterpart corresponds to the
case In
this paper, the contiguity of those two processes is discussed. In other words,
it is investigated whether or not the transition between a long-memory process
and the short-memory counterpart is smooth when dis very close to zero. A rigorous proof is established to show that
contiguity in terms of autocovariance and autocorrelation functions holds when dtends to zero. Numerical results for fractionalprocesses
reveal how the rate of contiguity depends on the lag of the autocorrelation
function as well as the parameters of the short-memory counterpart.
Keywords and phrases: contiguity, rate of contiguity, fractional differencing, long-memory, autocovariance, autocorrelation, fractional ARIMA.
