Time-varying trading day adjustment in SEASABS Lujuan Chen, - PowerPoint PPT Presentation

Time-varying trading day adjustment in SEASABS Lujuan Chen, Jonathan Campbell Australian Bureau of Statistics Views expressed are those of the authors and do not necessarily represent those of the ABS. Where quoted or used, they should be attributed clearly to the authors.

Outline • SEASABS • Estimation of Trading Day • Improvements in SeasABS – Modified Regression – Split Trading Day – Moving Trading Day – Example • Conclusion • Future work

SEASABS

Background – Seasonal Adjustment • Most official statistical agencies publish original and seasonally adjusted estimates    O seasonal trend irregular t    S T I t t t       - S s S s combined factor, seasonal factor t t i t , t t i    others including TD effect i t , i ˆ  S estimate to produce seasonally adjusted estimates ˆ    SA O / S T I t t t t t

Trading day An effect present in many time series due to 1. the difference of the number of days in each period is different 2. the different levels of activity associated with different days of the week; and 3. the changing composition of the days of the week in each period

Estimation of trading-day  X-11 regression method - Young, A. (1965) implemented in X-11 - Shiskin, J. (1967) 6        I 1 ( D D ) e , e ~ NID (0, ) t j jt 7 t t t  j 1  ARIMAX method - Hillmer, S. (1982) implemented as RegARIMA in X-12- ARIMA - Findley (1998) and Tramo - Maravell (1996) 6      log( O ) ( D D ) z , z ARIMA t j jt 7 t t t  j 1                   d s D s s B B (1 B ) (1 B ) (log O X ) B B e , e ~ NID (0, ) t t t  other methods including regression and state-space models

Static Trading Day in Retail 1.075 1.050 1.025 1.000 0.975 0.950 0.925 0.900 Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Non Leap Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon leap Feb Wed Thu Fri Sat Sun Mon Tue Feb Trading Day Tday * Irreg

Modified regression • Does it make sense for a day’s weight to be negative? • Many series are strictly non-negative • Option to constrain the regression so that daily weights are at least zero • Basic method used, improvement possible

Split Trading Day 1.4 1.2 1 0.8 0.6 0.4 0.2 0 M T W T F S S M T W T F S S M T W T F S S M T W T F S S • Sudden change in weekly cycle • Can be done with pre-specified weights static regression or moving regression • Not much used in practice

Time-varying trading day 1.4 1.2 1 0.8 0.6 0.4 0.2 0 M T W T F S S M T W T F S S M T W T F S S M T W T F S S • Standard regression on 7 year moving spans • Shorter spans at series ends • Negative daily weights not allowed • Smoothed using 3x3 moving average

Moving Trading Day in Retail 1.075 1.050 1.025 1.000 0.975 0.950 0.925 0.900 Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Non Leap Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon leap Feb Wed Thu Fri Sat Sun Mon Tue Feb Trading Day Tday * Irreg

Conclusion • Trading Day effects do change over time • SeasABS ’ methods allow factors to follow those changes • Without that, residual TD effects remain

Future work 1. Improved constrained regression for non- negative parameters 2. Investigation of filter choice for smoothing parameter estimates 3. Intra-Year moving trading day corrections 4. Use of spectral tests to identify trading day effects