Realtime filtering: using the multivariate DFA to monitor the US business cycle

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Real-time filtering using the multivariate DFA
to monitor the US business cycle

• Forecasting the NBER-dating of US-recessions

M. Wildi (2009), M. Wildi and J-E Sturm (2008)
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NBER-Datinghttp//www.nber.org/cycles.html

• History
• December 2007-
• Peak announced in December 2008
• March 2001-November 2001
• Trough ann. in July 2003
• July 1990-March 1991
• July 1981-November 1982
• January 1980-July 1980
• November 1973-March 1975
• December 1969-November 1970
• April 1960-February 1961
• NBER-dating substantially delayed (1 year)
• Faster dating?
• Prediction?

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FAQ http//www.nber.org/cycles.html

• Q Typically, how long after the beginning of a
  recession does the Business Cycle Dating
  Committee declare that a recession has started?
• A Anywhere from 6 to 18 months. The committee
  waits long enough so that the existence of a
  recession is not at all in doubt.

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Jeff Frankels Weblog Who needs the NBER
Committee anyway?  

• Everyone in the real world has known that the
  economy has been in a recession for some time   
  Ivy Tower Eggheads Finally Figure Out What
  Everybody Else Has Known All Along. The implicit
  critique is that the committee takes too long
  after the event typically almost a year to
  make its declaration.  
• One short answer is that our job is to be
  definitive, authoritative, but not fast.  We
  dont want to have to revise our dating...  We
  leave it to others  pundits, forecasters,
  consulting companies, financial newsletters, and
  so on to try to get there first.   We
  deliberately get there last.

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http//www.econbrowser.com/archives/2008/12/recess
ion_datin.html

• The typical Econbrowser reader might not be
  surprised at the NBER decision -- but some others
  will. From a May 2008 WSJ article
• "The data are pretty clear that we are not in a
  recession," Council of Economic Advisers Chairman
  Edward Lazear told a meeting of editors and
  reporters from the Wall Street Journal and Dow
  Jones Newswires.
• "I would be very surprised if the NBER, looking
  back at this period, would date this as a
  recession," Mr. Lazear said. There are even
  indications that revised first-quarter estimates
  would be slightly stronger than 0.6. "The
  optimists seem to have been closer to right on
  that than the pessimists," he said.
• Just to reiterate, that quote is from May 2008.

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Priorities real-time setting

• Fast and reliable recession alarms
• Data is noisy smoothing-filter
• Small real-time errors
• Priorities
• Emphasize the statistical efficiency
• Emphasize data revision aspects

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Established econometric tools

• J. Piger
• M. Chauvet
• CFNAI (StockWatson)
• ADS index

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Recession dating by J. PigerData available in
September 2008

• http//www.uoregon.edu/jpiger/us_recession_probs.
  htm

• Historical recession probabilities
• in the graph are smoothed (not real-time)

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Revisions Data available in Sep. 2008, Nov.
2008, Feb.2009
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2. Recession dating by M. Chauvet (data as to
Oct. 2008)

• http//faculty.ucr.edu/chauvet/prob1108.pdf

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Real-time and historical performances

• Real-time filter filtered probabilities are
  delayed
• Last recession is signaled first in Sep. 2008
• There are a few missings
• Additional revisions due to up-dating of data
• Smoothed probabilities are very accurate
• Recently (26.03.09), real-time estimates were no
  more available (only smoothed estimates)

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3. CFNAI (Chicago Fed National Activity Index)

• Stock and Watson (Journal of Monetary Economics
  1999).
• Factor common to all of the various inflation
  indicators ... the CFNAI provides a useful gauge
  on current and future economic activity and
  inflation in the United States.
• The 85 economic indicators production and
  income employment, unemployment, and hours
  personal consumption and housing and sales,
  orders, and inventories.
• The two most prominent examples of monthly
  coincident business cycle indicators, to which
  policy makers and other economic agents often
  refer, are the Chicago Fed National Activity
  Index4 (CFNAI) for the US and EuroCOIN for the
  euro area (Breitung/Eickmeier 2005).

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• Data up to February 2008

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• Data up to March 2008
• Revisions

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• Data up to March 2009

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Real-time performance

• Recession first discovered in March 2008
• False alarms 2003
• Threshold -0.7 possibly insufficiently tight
• Revisions (Feb. and Mar. 2008)
• Large data-set (85 time series)
• Publication lag one month

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4. Aruoba-Diebold-Scotti Business Conditions
Index
The ADS business conditions index is based on the
framework developed in Aruoba, S.B., Diebold,
F.X. and Scotti, C. (2009), "Real-Time
Measurement of Business Conditions," Journal
of Business and Economic Statistics
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ADS-Index since Jan. 2000
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ADS-Index (large) revisions
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Data and characterization of recessions

• Data as used by M. Chauvet
• A simple indicator
• Smoothing (band-pass filter)

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Description Data

• Lntc - total civilian employment
• Publication lag 1 month
• Lnip - industrial production
• Lag 1 month
• Lnm - manufacturing and trade sales
• Lag 2 months (series is delayed by one month in
  our filter design)
• Lnpa empl. on non-agric. Payroll
• Lag 1 month
• Lnpi pers. income less trans. paym.
• Lag 1 month
• The series are transformed as 100log(xt/xt-1)
• As to 26.03.2009, they go up to 200902 (200812
  for Lnm)

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Official NBER-characterization
http//www.nber.org/cycles.html

• a recession is a significant decline in
  economic activity spread across the economy,
  lasting more than a few months, normally visible
  in
• real GDP, real income, employment, industrial
  production, and wholesale-retail sales.

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Data
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Data as to 26.03.2009 ends in Feb09/Jan08 (after
Shift)
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Smoothing the series bandpass 6-32
quartersDATA AS TO JAN.09
Band-Passed Series (Band-Pass 1.5-8 years) and
NBER-datings
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Smoothing the series bandpass 6-32
quartersDATA AS TO MAR.09
Band-Passed Series (Band-Pass 1.5-8 years) and
NBER-datings
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Summary

• Levels of all band-passed series are low
• All series
• Deep troughs
• Conclusion (characterization)
• Compute aggregate
• Band-pass aggregate and look for deep troughs
• Equal-weights no revisions

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Recession rules fixed vs. adaptive rulesData up
to Jan09

• Historic rule anticipates recessions!!!
• No False alarms or missings

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Recession rules fixed vs. adaptive rulesData up
to Mar09

• Large revisions of the (univariate) CF-filter!

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Problems and a solution

• Problem
• Ideal band-pass filter is not real-time
  (symmetric filter)
• Univariate CF-filter performs poorly
• Data revisions
• Solution
• Compute an efficient real-time estimate of the
  band-passed filtered aggregate
• Our methodological contribution MDFA

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Real-time signalextraction

• DFA (univariate)
• MDFA (multivariate)

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Filter-dimensions

• Univariate methods Longitudinal Filtering
• L-Filtering
• Factor Models Transversal Filtering
• T-Filtering (target endogeneous)
• Multivariate Filtering
• L- and T-Filtering Simultaneously
• Complex Estimation Problem
• Cointegration
• Leads/lags
• Filter before aggr. or aggr. before filtering?

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Structure of the Estimation Problem

• One- and multi-step ahead forecasts

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Do the statistics fit the problem- structure
(intention of the user)?

• Target good one- and multi-step ahead
  forecasts

• Statistic
• Estimation one-step ahead MSE
• Identification Information criteria
• Diagnostics

• Traditional forecasting approaches are
  inefficient! (WS 2005, W2007, W2008)

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Real-Time Multivariate Filter

• Direct Filter Approach

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Efficiency (Theorem 4.1, Wildi2008,
Wildi/Sturm2008)

• The error term eT is smallest possible uniformly
• Efficiency!!! ? main methodological difference to
  all other real-time estimation procedures
• Customization match optimization criterion to
  problem-structure

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Optimal (Efficient) Criterion under Cointegration
(Rank1)

• Filter Restrictions are satisfied

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Short reminder

• If the filter error would vanish, then the
  corresponding rule would anticipate recessions
  without generating false alarms.
• Of course, the filter error cannot vanish. But it
  can be reduced when compared to standard
  approaches (forecasting)
• Efficiency ? methodological contribution in this
  particular (recession-dating) framework

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Performances DFA (Forecasting)

• TP-filters won NN3 (2007) and NN5 (2008)
  forecasting competitions (60 participants each
  time)
• IIF and University of Lancaster
• Monthly Macro- and Financial Data (111 time
  series) and daily financial data (111 time
  series)
• Outperformed winner and runner-up of the
  prestigious M3 competition
• X-12-ARIMA, Tramo
• Forecast-Pro, Autobox
• Exponential smoothing Simple, Holt, Damped
• Neural nets, artificial intelligence

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Performances DFA (Signal extraction)

• Business Survey Data (KOF, FED, 2005)
• X-12-ARIMA, Tramo/Seats
• MSE-gain 30
• Economic Sentiment Indicator (2006)
• Dainties
• TPs discovered 2-3 months earlier
• Output-gap US- and Euro-GDP (2008)
• CF
• turning-points anticipated by 1-2 quarters

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Empirical results
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Error nomenclature

• False alarm a recession is erroneously signaled
  in- between two consecutive recessions
• Missing the end of a recession is erroneously
  signaled during an on-going connected period of
  recession
• Delay the begin of a recession is not recognized
• In contrast to a missing, delays are
  connected periods of false signals at the
  beginning of a recession
• Lead the begin of a recession is anticipated
• In contrast to a false alarm, a lead is a
  connected period of alarms closely located
  before the begin of a recession (anticipation)
• Trade-off
• False alarms and anticipations (loosening the
  alarm-rule)
• missings and delays (tightening the alarm-rule)

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BEGIN of Recessions (vintage Feb 2008)

• Normal mean cannot be computed before Dec 1968
  (needs 10 years of data support)
• Lnm is shifted by 1 month so that publication lag
  of real-time indicator is one month

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BEGIN of Recessions (Mar. 2008)

• Normal mean cannot be computed before Dec 1968
  (needs 10 years of data support)
• Lnm is shifted by 1 month so that publication lag
  of real-time indicator is one month

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Performance (Feb 2008 vintage vs. March 2009
vintage)

• Better than CFNAI
• faster
• No false alarms nor missings

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Summary

• No false alarms nor missings
• RELIABLE
• Mean lead (publication lag included)
• -3.5 months on whole sample
• -7 months on most recent sample (3 recessions)
• FAST

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Revisions

• Purely data driven (real-time filter)

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Industrial Production

• Large revisions or large errors/noise?
• Small weight attributed by the filter (consistent
  with Wildi/Sturm2008)
• September dip (see ADS index)

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Manufacturing and trade sales

• Small frequent and larger un-frequent revisions.
  Dynamics consistent.
• Medium weight attributed by filter

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Employment on non-agricultural payroll

• Small revisions (last value)
• Large weight attributed by filter

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Personal income

• Larger revisions (dynamics inconsistent)
• Small weight attributed by the filter

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Total civilian employment

• Data affected by changes in population controls
  once per year last 5 years
• Revisions (due to population controls) small and
  dynamics remain consistent
• Large weight attributed by filter

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Findings

• Series with frequent large revisions are
  down-weighted by the filter
• Expect that revisions due to the data are small
• Overall revisions should be small
• 2. priority

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Filter revisions (Feb08, Oct08, Jan09 and Mar09
vintages)

• Revisions are small because series with large
  revisions are
• down-weighted by the filter
• To be contrasted with alternative recession
  indicators

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Revisions Feb. and Oct. vintages vs. final
(Dec.) vintage
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Filter Diagnostics

• Cycles, Amplitude- and Time-Shift Functions
  (Multivariate Real-Time Filter)

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Amplitude Functions

• Largest weight attributed to lntc, followed by
  lnm and by lnpa

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Conclusion

• Fast and reliable real-time indicator
• Small(est possible) filter revisions
• MDFA Efficiency
• Insensitive to data revisions
• Series with larger weights are subject to no
  revisions or only smaller revisions
• Publication on CIRANO-website next month

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Addresses

• SEF web-page
• http//www.idp.zhaw.ch/sef
• Books, Working-book
• Articles and Working-papers
• Multivariate, Non-Linear, TP-Filters
• Software
• Projects
• NN3 http//www.neural-forecasting-competition.com
  /NN3/results.htm
• NN5 http//www.neural-forecasting-competition.com
  /results.htm