Insights into the appropriate level of disaggregation for efficient time series model forecasting

Abstract

This paper provides a potentially valuable insight on how to assess if the forecasts from an autoregressive moving average model based on aggregated data could be substantially improved through disaggregation. It is argued that, theoretically, the absence of moving average (MA) terms indicates that no forecasting efficiency improvements can be achieved through disaggregation. In practice, it is found that there is a strong correlation between the statistical significance of the MA component in the aggregate model and the magnitude of the forecast mean square error (MSE) decreases that can be achieved through disaggregation. That is, if a model includes significant MA terms, the forecast MSE improvements that may be gained from disaggregation could be substantial. Otherwise, they are more likely to be relatively small or non-existent.

Keywords:

• data aggregation
• efficient forecasting

Notes

1. Since, by definition, y_q(t) (the left hand side of Eq. (7)) equals (the sum of the left hand sides of Eqs. (4)–(6) divided by three), the right hand side of Eq. (7) should be the sum of the right hand sides of Eqs. (4)–(6) divided by three. Then is it also recognized that , thus , which accounts for in Eq. (7)).

2. Specifically, , where the various assumed sets of values for ρ₁, ρ₂ and ρ₃ are provided in Table 1 and z_m(t) is a draw from a normally, independently and identically distributed random variable with mean zero and unit variance. The initial values of y_m(t−3), y_m(t−6) and y_m(t−9) are set to 0 and thus, the first 1000 simulated values for y_m(t) are discarded.

3. Using the Ljung–Box test with 36 lagged quarterly residual correlations.