Generalized autoregressive moving average modeling of the Bellcore data

Generalized autoregressive moving average (GARMA) models are fitted to the Leland et al. (1994) Bellcore Ethernet trace data. We find the time series to have long memory. In addition, we find evidence for self-similarity, as was also found in earlier studies. Our GARMA analysis shows the time series m-aggregated at 0.01, 10, 100 and 1000 seconds to be non-stationary. However, the first differences of these series are found to be stationary by the same analysis, and are represented well by GARMA models. Unlike in earlier studies, our estimation methodology can be extended to forecast the time series. We present GARMA model forecasts for the first difference of the m-aggregated data at 100, and compare with ARIMA forecasts. The fitted GARMA(0,0) model forecast is very good and tracks both the level and pattern in the time series with a negligible 95% confidence interval of 0.02. The ARIMA(15,1,5) model can track neither the level nor the pattern, and has a 95% confidence interval of 0.86 (nearly the same magnitude of the time series data) for the same 1000 predicted points. The fitted GARMA(0,0) model utilizes 4 parameters versus 23 for the ARIMA(15,1,5) model. The autocorrelation and partial autocorrelation functions indicate a very large number of parameters for the ARIMA model. Based on the similarity of the spectra of the time series data m-aggregated at various levels, we can expect similar quality of forecasts for those series using the GARMA framework.