DIFFUSION INDICES: A Potentially Fruitful Application of the Direct Filter Approach ISF 2005, June 1

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DIFFUSION INDICESA Potentially Fruitful
Application of the Direct Filter ApproachISF
2005, June 13, San Antonio, TX

• Thomas B. Fomby
• Department of Economics
• Southern Methodist University
• Dallas, TX 75275
• tfomby_at_smu.edu
• website faculty.smu.edu/tfomby
• and
• Federal Reserve Bank of Dallas

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OUTLINE

•        I. REASONS FOR MY INTEREST IN DFA
•  
•            II.      THE NEED FOR BUSINESS
  OUTLOOK SURVEYS
•  
•          III.     OECD DIFFUSION INDEX
  METHODOLOGY
•  
•         IV.     SOME ISSUES CONCERNING
  DIFFUSION INDICES
•  
•            V.      DFA RESULTS FOR PHILADELPHIA
  DIFFUSION INDICES
•  
•         VI.     CONCLUSIONS

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Reasons for My Interestin DFA
                 
                                 I.      Reasons
for My Interest in DFA A.
Bernd Schips and Marc Wildis ISF 2004
Presentation Signal
Extraction A Direct Filter Approach and
Clustering in the Frequency
Domain B. The Application
of DFA to Bounded Time Series
C. Boundary Problems and Incorrect Imposition
of Unit Roots in the
Identification of Such Series
D. My Consultancy with the Federal Reserve Bank
of Dallas on Building
a Business Outlook Survey Index
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The Need for Business Outlook Surveys
                           II. The Need for
Business Outlook Surveys A. The
Summarization of Qualitative Responses of Survey
Respondents B. Some Producers of
Diffusion Indices i.
Institute of Supply Managers (ISM) (formerly
National Association of
Purchasing Managers (NAPM))
ii. Federal Reserve Banks of Philadelphia and
New York iii. OECD
C. Some Example Questions
D. The Data is Immediate and Easily Summarized
E. In Contrast Government
Statistics Issues of Timeliness and Revisions
i. Delay in Reporting of
Government Statistics (e.g. GDP)
ii. Inevitable Revisions That Occur in the
Data iii. Conflicting
Statistics e.g. Household Survey versus
Business Survey of
Employment Statistics  
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OECD Diffusion Index Methodology
            III. OECD Diffusion Index
Methodology A. Concurrent versus
Forward Looking Questions B.
Respondents Are Asked to Seasonally Adjust
Their Answers
C. Stratification of the Sample By Industry and
Small versus Large Firms
D. Some Mathematical Formulas
E. Boundedness of Balance (-100, 100) and
Diffusion (0, 100) Indices
F. Some Plots of Philadelphia
Diffusion Indices
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AN EXAMPLE SURVEY

• Business Outlook Survey
• Federal Reserve Bank of Dallas

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Conflict Between Job Surveys

• Dallas Morning News
• Job Growth Comes Up Short
• Saturday, June 4, 2005

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Job Growth Comes Up Short Dallas Morning
NewsSaturday, June 4, 2005
 

• The Labor Department reported disappointing jobs
  numbers Friday, with U.S. businesses adding
  78,000 positions in May about 100,000 short of
  economists expectations.
• The herky-jerky pattern in non-farm payrolls
  has resulted in some very red-faced economists
  and sizable moves in financial markets on
  employment Fridays, summed up Joseph Abate, a
  senior economist with Lehman Bros. in New York.
• That thinking (the economy is not swinging as
  wildly as the data) is bolstered by the household
  survey used to calculate the unemployment
  rate.
• Two competing surveys produced by the U.S. Labor
  Department The business payroll survey and the
  household survey.
• In any case, the erratic pace of job growth
  shouldnt be given too much attention, Brian S.
  Wesbury, chief investment strategist at Claymore
  Advisors, wrote in a recent research note. The
  payroll data is volatile, and is often revised
  significantly, he wrote. Reading too much into
  the May report would be a mistake.

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Some Mathematical Formulas
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Overall Balance Index Across Industries
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Some Issues Concerning Diffusion Indices
                  IV. Some Issues Concerning
Diffusion Indices A. Seasonal
Adjustment of Time Series i.
Conventional Method of Using X12-ARIMA or
TRAMO/SEATS
ii. Use of Transformed Series
iii. DFA Approach B. Validation of
Diffusion Indices i.
Predictive Content of Diffusion Indices
ii. Turning Point Analysis The 2x2
Business Cycle
Contingency Table
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Seasonal Adjustmentof Diffusion Indices

• Various Approaches
• X12-TRAMO/SEATS (MBA)
• Log Transformation
• Direct Filter Approach (DFA)

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New York FedSeasonal Adjustment Process
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Consider the log-ratio of the unadjusted
diffusion index   We work with the
log-ratio of the Diffusion index because the
Diffusion index has a natural range of 0 to 100
and the log-ratio is an ideal transformation to
take the Diffusion into the real line, a natural
metric for seasonal analysis. (No similar
transformation exists for Balance indices that
range in value from 100 to 100). After
transformation, one can use X12-ARIMA or some
other seasonal adjustment program to produce
seasonally adjusted log-ratios  
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It follows that    
  Therefore,   is the
formula that allows a translation of the
seasonally adjusted log-ratio to the seasonally
adjusted Diffusion index.
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Ideally, if one wants to produce a seasonally
adjusted overall Diffusion index one would
first seasonally adjust each industry Diffusion
index producing and then use the following
formula to produce a seasonally adjusted overall
Diffusion index  
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Graphs of Some PhiladelphiaDiffusion Indices
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Validation of Diffusion Indices

• 1) Predictive Content vis-à-vis
• Transfer Function Modeling
• 2) Turning Point Analysis

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2x2 Business CycleContingency TableIFO Germany
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DFA Results for Philadelphia Diffusion Indices
        V. DFA Results for Philadelphia
Diffusion Indices (Marc Wildi and
Associates) A. Marc Wildis Experiment
Involving 85 series from the
Philadelphia FED Diffusion Index Database
B. DFA versus MBA Difference in Mean-square
Filter Errors
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Philadelphia Diffusion Index Database

• 168 Diffusion and Balance Indices
• Over Multiple Questions
• Both NSA and SA

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Comparison of DFA with MBA

• 85 Philadelphia Series
• Criterion One-Step Ahead
• Mean Square Revision (Filter) Error

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DFA Asymmetric FilterTransfer Function(Implement
ed by Symmetric MA(120) Filter)
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DFA Versus MBA Results

• The Mean Square Revision Error increased by 33
  in the mean (over all 85 series) when using the
  MBA instead of the efficient DFA
• Equally Weighted Combination of MBA and DFA
  produced 8 higher MSE (over all 85 series) than
  DFA.
• DFA outperformed the MBA for 79 out of 85 series
  (93 of series)
• DFA outperformed the Equally Weighted Combination
  for 67 out of 85 series (79 of series)
• The above results suggest that DFA encompasses
  MBA

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Conclusions
             VI. Conclusions A. Trend
Extraction Results Look Promising B.
Prediction Comparisons should consider
Different Forecast Horizons, Different Loss
Functions, and Concentrate on the
Non- seasonally adjusted series
C. Consider More Sophisticated
Combination Methods
D. What about Logarithmic Transformation (NY
Fed) technique? E.
Compare Turning Point Prediction Errors of
Competing Methods (e.g. IFO Cycle
Diagram)
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Thank YouCongratulationsISFon your 25th
Anniversary!