Sheet 1: Trading Day Methodology

	
	

		
NOTES ON TRADING DAY ADJUSTMENT
	
	

		
METHODOLOGY
	
	

		


	
	

		
The shipments data in the M3 survey are adjusted for calendar month variations, both length of
	
	

		
month and number of trading days per month. The selection of these adjustment factors is based
	
	

		
primarily on recognition of patterns contained in the data using the regression and spectral analysis
	
	

		
capabilities of the X-13ARIMA-SEATS seasonal adjustment software.
	
	

		


	
	

		
Factors are considered optimal when the daily weights assigned to the industry eliminate or
	
	

		
diminish the peaks in the spectral plots, which are based on calendar frequencies, and lower the
	
	

		
absolute value of the month-to-month change in the residual irregular component of the data
	
	

		
series.
	
	

		


	
	

		
New orders data in this publication are implicitly trading day adjusted by using the trading day
	
	

		
adjusted shipments as input to their derivation. The difference in unfilled orders is typically not
	
	

		
trading day adjusted.
	
	

		
 
	
	

		
Because monthly stock series, such as inventories and unfilled orders data, may be considered
	
	

		
to be accumulations of monthly flows, it is possible to adjust these series for trading day effects. 
	
	

		
Using diagnostics similar to those described above, particular inventory, stage-of-fabrication
	
	

		
inventory, and unfilled orders series have been adjusted for stock trading day effects. 
	
	

		


	
	

		
For shipments series, the chi-square statistics for the 6-coefficient trading-day regressors are 
	
	

		
shown and should be compared to the appropriate upper percentile of the chi-square distribution 
	
	

		
with 6 degrees of freedom when testing for statistical significance at a specified level.  For example, 
	
	

		
at the 10% level of significance, the critical value would be 10.64.  For the particular stock series 
	
	

		
that have been adjusted for stock trading day effects, because the number of coefficients
	
	

		
in the model could be either 1 or 6, similar diagnostics are not shown for these series, but are
	
	

		
available upon request.