1 Seasonal Adjustments: Causes of Revisions Øyvind Langsrud Statistics Norway

Seasonally adjustment based on X12-ARIMA Two-step procedure: regARIMA + trend and seasonal filters regARIMA –Seasonal ARIMA model with regression parameters –Holiday and trading day adjustment –Produce forecasts for use in the next step Important choices –Type of ARIMA model –Regression parameters: Holidays and trading days –How to handle outliers langsrud_pdf_movie.pdf

Revision The revision is caused by updated models and parameters Revision is a problem –Can be confusing –Not easy to communicate Choosing seasonal adjustment methodology can be viewed as a question of balancing –the requirement of optimal seasonal adjustment at each time point –against the requirement of minimal revisions. Can revision be reduced without reducing the quality of the adjustment?

Revision on log-scale A t = seasonally adjusted series. Y t = original series A t|t+h is the seasonal adjustment of Y t calculated from the series where Y t+h is the last observation OneMonthRevision t = ( log(A t|t+1 ) – log(A t|t ) ) *100%

regARIMA modeling: Comparison by out-of-sample forecasts Comparison of methods when model selection is involved is not straightforward –Standard model fit criteria do not take into account the selection process –Fair comparison by out-of-sample forecasts X-12-ARIMA make use forecasts

Relative forecasting error Y t+h|t is the forecast of Y t+h calculated from the series where Y t is the last observation Example: Y t+h|t =101, Y t+h =100 –100% * ( )/101 = % –100% * (log(101)-log(100)) = % –100% * ( )/100 = %

% opposite log- increase denominator based Other examples

% opposite log- increase denominator based Other examples

RMSE root mean square error

ARIMA model is held fixed  from a single analysis of the whole series by using the ARIMA model according to automdl. Outliers are held fixed  from the same single analysis as above. Trading days: six parameters  = maximum number of parameters. Eastern is handled as usual at Statistics Norway  up to three parameters. Base method:

ARIMA model is held fixed  from a single analysis of the whole series by using the ARIMA model according to automdl. Outliers are held fixed  from the same single analysis as above. Trading days: six parameters  = maximum number of parameters. Eastern is handled as usual at Statistics Norway  up to three parameters. Comparing methods by deviating from the base method

Automatic ARIMA model selection: automdl vs pickmdl automdl as default in X-12-ARIMA pickmdl selects ARIMA model from five candidates (0 1 1)(0 1 1) * (0 1 2)(0 1 1) X (2 1 0)(0 1 1) X (0 2 2)(0 1 1) X (2 1 2)(0 1 1) X

Automatic outlier detection: critical=4 vs critical=8 t-statistic limit Both additive outliers and level shifts Critical=4 is close to default in X-12-ARIMA Critical=8: outliers are extremely rare

Trading day: 6 parameters vs other choices 6 parameters = maximum number of parameters Other choices – Production index –Standard choice at Statistics Norway based on industrial knowledge –0, 1, 5 and 6 parameters Other choices – Index of household consumption of goods –1 parameter, weekdays vs Sundays/Saturdays

Moving holiday: Easter vs no Easter Method in Norway –Up to three parameters: Before Easter, Easter, After Easter –Selection based on model fit an t-tests History analysis –Exactly as today’s Norwegian procedure

Conclusion Automatic outlier detection and ARIMA model selection leads to revision problems –Problems can be reduced by using pickmdl and by increasing outlier detection limit –Better solutions by fixing outliers and models Holidays and trading days are less important –Norway’s procedure may be improved –More investigation will be performed

Findley DF (2005), "Some Recent Developments and Directions in Seasonal", JOURNAL OF OFFICIAL STATISTICS, Vol 21, 343–365 Findley DF, Monsell BC, Bell WR, Otto MC, and Chen BC (1998), "New capabilities and methods of the X-12-ARIMA seasonal-adjustment program", JOURNAL OF BUSINESS & ECONOMIC STATISTICS, Vol. 16, Roberts CG, Holan SH, Monsell B (2010), "Comparison of X-12-ARIMA Trading Day and Holiday Regressors with Country Specific Regressors", JOURNAL OF OFFICIAL STATISTICS, Vol 26, US Census Bureau (2011), "X-12-ARIMA Reference Manual", UK - The Office for National Statistics (2007), "Guide to Seasonal Adjustment with X-12-ARIMA **DRAFT**", analysis/guide-to-seasonal-adjustment.pdf Eurostat - Methodologies and working papers (2009) "Ess Guidelines on Seasonal Adjustment",

X12-ARIMA output series d11 = Y / e18, in our modelleing e18 = e10*d18 Y = Original series d11 = Final seasonally adjusted data ( A t ) e18 = Final adjustment ratios d10 = Final seasonal factors d18 = Combined holiday and trading day factors Can calculate revisions in e18, d10, d18 similar to d11 d11revision = - e18revision