THEORETICAL PREDICTABILITY AND SAMPLE PREDICTABILITY OF LONG-MEMORY TIME SERIES

摘要

The theoretical predictability (TP, calculated based on the known model) and sample predictability (SP, measured based on the multi-step forecast errors of sample data) of autoregressive (AR) processes and fractionally integrated autoregressive moving average (ARFIMA) processes are investigated. The results show that, while the long-memory ARFIMA processes show very high TP, and significantly higher than the AR(1) processes with equivalent autoregressive coefficients at lag 1, the SP of ARFIMA processes is much lower than the TP of the ARFIMA process, especially when the ARFIMA process has a high value of fractional differencing parameter (e.g, d ≥ 0.4) as well as a high autoregressive coefficient (e.g., Φ≥ 0.5) in its AR component. The results imply the difficulty and the uncertainty in measuring the predictability for a given real-world time series.