Long Memory Differencing Parameter Estimation In Time Domain.

ABSTRACT

This thesis proposed a new method of estimation of the long memory differencing parameter (d) in Time domain which is a least squares estimator d of d based on regression of the autocorrelation function. The research work employed one simulated time series data set and three real life time series data that has long memory for the application of the proposed method. The time plot of the series showed that the series were stationary and the .autocorrelation of the series suggested the presence of long memory structure because of the long lasting autocorrelation function. Hurst exponent test confirmed the presence of long memory structure. Using the newly proposed method of estimation, the long memory differencing parameter (d) was estimated for varying values of lag length (K). The time series data were seen to follow a fractional white noise model ARFIMA(O, d, 0) when adequately differenced but could give an ARFIMA(p, d, q) model when either under-differenced or over-differenced. A comparative study of some of the existing methods of estimating the long memory differencing parameter was done. The research work revealed that once a long memory processes is adequately differenced, the differenced series becomes i.i.d random variable as shown by the ML estimator of d. A probe on the relationship between the long memory differencing parameter d and the lag length based on the proposed method showed that there exist a negative linear relationship between them.