Some properties of the RGEKS index for scanner data Martin Ribe Statistics Sweden Presentation at Scanner Data Workshop in Stockholm, June 2012

The RGEKS index formula Index with base period 0 , current period T > 13, computed from (e.g.) Fisher index P Introduced by L. Ivancic, W.E. Diewert & K.J. Fox (J. Econometrics 2011), and J. de Haan & H.A. v.d. Grient (J. Econometrics 2011) To eliminate drift occurring in high-frequency chaining of usual indices, even Fisher index, on volatile data © SCB, M. Ribe, 2012-06-05

The RGEKS index link The link is the geometric mean of 13 indices from t – 1 to t , each of which is formed by chain-linking via a period s (t – 12 ≤ s ≤ t) s t – 1 t © SCB, M. Ribe, 2012-06-05

RGEKS re-written (for time-reversible P) as chaining of 4 links between periods: 0  12 12  (1, 13) (1, 13)  (T – 12, T) (T – 12, T)  T Shows that RGEKS is somewhat like a moving average © SCB, M. Ribe, 2012-06-05

Scenario 1 Period p1 p2 q1 q2 ... t – 4 100 10 t – 3 30 t – 2 20 t – 1 Outcome: Every 4 periods chained Fisher falls by 29% and RGEKS by 2.6% © SCB, M. Ribe, 2012-06-05

Scenario 2 – data Period p1 p2 q1 q2 t = 1,..., 24 100 × 1.0025t 100 25, ... That is, one product with 0.25% price rise per period, one with constant price Sudden shift in purchases © SCB, M. Ribe, 2012-06-05

Scenario 2 – outcome © SCB, M. Ribe, 2012-06-05

Volatility in volumes The figures are the highest ratios in the Product Groups, between largest and second largest monthly volume in 2010 for each EAN © SCB, M. Ribe, 2012-06-05

Questions for attention Is the drift attenuation of RGEKS safely effective enough for scanner data? How much is really gained by frequently updated weighting, when RGEKS does not follow fast fluctuations? What about risk of unnatural effects due to failure of RGEKS on the identity test? © SCB, M. Ribe, 2012-06-05