Round table Long Series: Connection and Methodological Changes Craig McLaren (Office for National Statistics, UK) Rio de Janerio, th August 2006

Office for National Statistics 2 Introduction Thank you for inviting me here today Dealing with methodological change from a time series perspective is a challenging issue Users should have continuity of time series Common issue across National Statistics Institutes Talk about previous experiences and issues

Office for National Statistics 3 Issues covered in slides Smoothing in methodological change Description of a generalised backcasting tool under development at ABS Multivariate approach for short time spans Lessons learnt from previous exercises Upcoming issues at ONS and ABS

Office for National Statistics 4 Dealing with methodological change? Want to remove the effect of methodological change E.g. Change to estimation method, classification structures Improves the quality of data by increasing consistency and coherence across time Should not remove effect of real world change Appropriate to still reflect this in the time series Two approaches Edit unit records: typically used for Population data Alter final estimates: typically used for Economic data Consider monthly and quarterly time series with altering the final estimates

Office for National Statistics 5 Motivation: Example Level-shift caused by methodological change Want to raise level of early part of series

Office for National Statistics 6 Motivation: Example of seasonally adjusted before and after backcasting

Office for National Statistics 7 Appropriate backcasting Knowledge required Whether or not to backcast Estimation and significance of impact Estimate a suitable backcasting length How far back does the change in series exist? Was the change constant or gradual? Determine if change is definitional or not Measure the difference between the old and new series For example: conduct parallel sample, do parallel estimation Quality control Assessing the magnitude of revisions

Office for National Statistics 8 Parallel estimation Different scenarios Different scenarios Multiple time point overlap One time point overlap Can even have no overlap: use forecasting Recompile historical data under new definition High quality but expensive How far back to go? New data points Model historical data and evaluate impact by intervention analysis Smoothing back based on the impact assessment

Office for National Statistics 9 Parallel estimation Measuring impact Impact can have different components Trend break: more parallel estimates, more accuracy Seasonal break: need at least a year + one period of parallel estimates Usually assume no seasonal break Multiplicative relationship: impact = 100*average(O new / O old ) Additive relationship: impact = average(O new - O old )

Office for National Statistics 10 Parallel estimation Significance of impact Need to assess quality of impact estimate Is impact significantly different from zero? Need relative standard error for (O new - O old ) Should assess if statistically significant difference Options for different levels Aggregation level at which impacts are significant determines backcast process Quality assurance given for this level and upwards Lower level series adopt impact of higher level series

Office for National Statistics 11 Aggregation structures Directly backcast series Lowest-level directly seasonally adjusted series Indirectly backcast series All other series formed by aggregation 1-D2-D

Office for National Statistics 12 Backcast objective Objective function for ABS backcasting Maintain the historical seasonally adjusted movement Minimise methodological change effect to ensure the continuity of a time series Need to avoid misinterpretation of a measurement change as a real world change Aim: bound revisions to movements and maintain stable seasonal factors Alternative objective functions equally valid

Office for National Statistics 13 Shape of backcast factors Directly backcast series Multiplicative: exponential shape: O bt = O t * xt/N Additive: linear shape: O bt = O t + tx Index series only: infinite shape: O bt = O t * x Indirectly backcast series Follow aggregation structure No particular shape

Office for National Statistics 14 Shape of backcast factors (continued) real data: exponential shape comparison

Office for National Statistics 15 Shape of backcast factors Finite versus infinite length Infinite length: multiply whole series by constant For directly backcast series: no revisions For indirectly backcast series: small revisions Good for index series Usually bound length for conceptual reasons New definition inappropriate long ago: e.g. new technology Nonsensical to increase an old estimate too much Risk management

Office for National Statistics 16 Quality measure Assess absolute change to the period to period movement in the seasonally adjusted estimates due to backcasting Delta = In general Either percentage or quantity change Multiplicatively seasonally adjusted: percentage Additively seasonally adjusted: quantity

Office for National Statistics 17 Quality measure Delta and the absolute differences, pre- vs post- backcasting ==> quality measure seasonally adjusted %-movements

Office for National Statistics 18 Quality measure Delta (continued) Maximum percentage change of movements in seasonally adjusted estimates pre and post backcast over a series Used as quality measure delta maximum (user specified) Effectively a bound on revisions in seasonally adjusted movements Compare maximum delta to delta maximum Can be normalised to allow comparisons between series

Office for National Statistics 19 Quality measure Length of backcast Governed by choice of how much tolerance in the change to movements pre and post backcast Smaller tolerance (delta) => longer backcast (typically) delta maximum selection Choose this so the backcast doesn't adversely affect published values For example, at most one significant figure in published movements In practice one common length for entire group of time series

Office for National Statistics 20 want delta < threshold backcast shape and length N Backcasting process

Office for National Statistics 21 Generalised backcasting tool Australian Bureau of Statistics Consistent ABS approach to backcasting Standard shapes to smooth in impacts Consistent diagnostics Consistent language Client areas can perform backcasts without input from Time Series Analysis experts Streamlined process Directly updates stored original estimates Currently in development

Office for National Statistics 22 Generalised backcasting tool Process flow generalised backcasting facility collection of series impacts settings new backcast originals (overwriting old originals) clearance report diagnostics final length selection

Office for National Statistics 23 Example: Generalised backcasting tool

Office for National Statistics 24 Example: Generalised backcasting tool

Office for National Statistics 25 Example: Generalised backcasting tool Seasonally adjusted estimates

Office for National Statistics 26 Example: Generalised backcasting tool Change in seasonally adjusted movements

Office for National Statistics 27 Example: Generalised backcasting tool Clearance report

Office for National Statistics 28 Multivariate approach Dealing with methodological change Title: Estimation of seasonal factors for a short time span using multi-level modelling Number of overlap periods is typically short This solution was used to assist with transition between two surveys and the results were used within ABS National Accounts Joint work with Xichuan (Mark) Zhang, ABS

Office for National Statistics 29 Multivariate approach Assumptions New survey measures the same underlying activity as the old survey Trend movement is the same for different surveys but may be at a different trend level Seasonal factors are assumed to be different for different surveys Can use multilevel models if there is a hierarchical structure

Office for National Statistics 30 Multivariate approach Model Mixed model j : industry i : old and new k : state totals 1k... j

Office for National Statistics 31 Multivariate approach Final model  Assume a log additive model for the time series decomposition

Office for National Statistics 32 Multivariate approach Outline of steps 1. Run full model 2. Remove "trend" of each series 3. Estimate seasonal factors 4. Test if old and new surveys have same seasonal factors 5. Convert from model into X-11 framework

Office for National Statistics 33 Multivariate approach Example: real world application Two surveys 15 industries 8 states and Australia Data available: Four parallel quarter estimates over 2001

Office for National Statistics 34 Example: New and old original data for 2 different industries

Office for National Statistics 35 Example: Selected state results * seasonal factors are not significantly different between new and old survey

Office for National Statistics 36 Multivariate approach Comments A mixed model (random and fixed effects) with multi-level modelling allowed realistic seasonal factors to be estimated for a short time series Provided a framework More cases like this will occur in practice Further work by Carole Birrell and David Steel at University of Wollongong

Office for National Statistics 37 General points Previous lessons Quality assurance of the new estimation methodology Prepare users for revisions in time series estimates One overlap time point is simply not enough to make a good impact assessment because of rotation effects May required re-backcast once additional information available Variance of impact assessments were not available

Office for National Statistics 38 General points Previous lessons (continued) Managing statistical risk Classification and estimation methodology changing at same time versus consecutive change approach Different measurement methods: parallel estimates and parallel run Rehearsal of backcast environment in relation to regular production schedule Ensure additivity of estimates for shallow aggregation structure Decision on new estimates should be published e.g. if the new estimate is good enough for publication or only for impact measurement purpose

Office for National Statistics 39 Upcoming examples Office for National Statistics Industry classification changes Approximately once every 12 years Strong link to European needs Long agreement process Currently in planning stage for upcoming changes Broad time frame 2007 Adding new industry codes to business register 2008 Annual surveys selected on new codes 2009 Short-term surveys selected on new codes 2011 National Accounts first moves to new codes

Office for National Statistics 40 Upcoming examples Office for National Statistics (continued) Need to be able to re-construct results from old (2003) and new (2007) classifications Options available: Domain estimation Conversion matrices Parallel running for a limited period? Problems of compiling and publishing results on two bases simultaneously Constrain results

Office for National Statistics 41 Upcoming examples Australian Bureau of Statistics Range of issues New industry classification Generalised regression sample and estimation including using ABS Survey Facilities estimation approach Building Activity Survey turnover stratification changes … Developing tools to assist Generalised backcasting tool

Office for National Statistics 42 Upcoming examples Australian Bureau of Statistics (continued) Currently: creation of new frames and specification of backcasting facility 2006 to 2009: Transition phase with dual frames involving parallel estimation based on top-up samples September 2009 onwards: Implementation where sample design and estimation is based on new classification

Office for National Statistics 43 Upcoming examples Australian Bureau of Statistics (continued) Measuring the impact For quarterly subannual surveys: 5 overlap points For monthly subannual surveys: 13 overlap points Methodology Division will provide advice on the significance of the impact, i.e. is there any real impact? If no seasonal change then minimum of 3 overlap points  To calculate the trend factor for backcasting all new and old estimates are needed  (Trend New / Trend Old )=(1/5)Sum(Original New /Original Old ) t

Office for National Statistics 44 Some further information ONS MD contact: ABS MD contact: McLaren and Zhang (2003) Estimation of seasonal factors for a short time span using multi-level modelling with mixed effects, Working Paper No. 2003/1,