SHAZAM reply

SHAZAM reply to McCullough's paper

B. D. McCullough, "Econometric Software Reliability: EViews, LIMDEP, SHAZAM and TSP", Journal of Applied Econometrics, Vol. 14, 1999, pp. 191-202.

A number of algorithm improvements have been implemented in response to the tests proposed in the software review. These include:

  • Section 2 and Section 3.1, pp. 192-4 -- the algorithm for calculating a sample variance has been improved.
    The results for the Michelso dataset are available.
    The results for the NumAcc4 dataset are available.
  • Section 4, p. 199 -- the random number generator has been modified so that a "pass" is obtained for all DIEHARD tests. The DIEHARD results that were produced with a sample of random numbers generated by SHAZAM can be studied.
  • Section 5, p. 200 -- numerical accuracy of critical values for statistical distributions has been improved. An example of the 1% critical value of the F(3,3) distribution can be viewed.

Some documentation of algorithms is provided.

Example

A description of the Michelso dataset is available. SHAZAM commands for calculating summary statistics follow. 

SAMPLE 1 100
READ (MICHELSO.txt) Y
STAT Y / MEAN=YBAR STDEV=S
FORMAT(F30.16)
PRINT YBAR S / FORMAT
* Get the sample autocorrelation at lag 1
ARIMA Y / NLAG=1 ACF=ACF1
PRINT ACF1 / FORMAT
STOP

The SHAZAM output is below. 

|_SAMPLE 1 100
|_READ (MICHELSO.txt) Y
UNIT 88 IS NOW ASSIGNED TO: MICHELSO.txt
   1 VARIABLES AND      100 OBSERVATIONS STARTING AT OBS       1

|_STAT Y / MEAN=YBAR STDEV=S
NAME        N    MEAN        ST. DEV      VARIANCE     MINIMUM      MAXIMUM
Y           100   299.85     0.79011E-01 0.62427E-02   299.62       300.07
|_FORMAT(F30.16)
|_PRINT YBAR S / FORMAT
    YBAR
         299.8523999999999000
    S
           0.0790105478190507

|_* Get the sample autocorrelation at lag 1
|_ARIMA Y / NLAG=1 ACF=ACF1
    ARIMA MODEL
NUMBER OF OBSERVATIONS = 100
...NOTE..SAMPLE RANGE SET TO:     1,   100

     IDENTIFICATION SECTION - VARIABLE=Y
NUMBER OF AUTOCORRELATIONS =   1
NUMBER OF PARTIAL AUTOCORRELATIONS =   1

             0     0 0
SERIES  (1-B) (1-B  )  Y

  NET NUMBER OF OBSERVATIONS =  100
MEAN=    299.85       VARIANCE=   0.62427E-02   STANDARD DEV.=   0.79011E-01

  LAGS                      AUTOCORRELATIONS                          STD ERR
  1  -1    0.54                                                          0.10

  LAGS                  PARTIAL AUTOCORRELATIONS                      STD ERR
  1  -1    0.54                                                          0.10
|_PRINT ACF1 / FORMAT
    ACF1
           0.5351996686212657
|_STOP

A comparison of the SHAZAM results with the certified values follows. Inaccurate digits for the SHAZAM results are underlined. 

                  Std.Dev.              Autocorrelation at lag 1
SHAZAM         0.0790105478190507          0.5351996686212657
                               --                         ---
certified      0.0790105478190518          0.535199668621283

Univariate Summary Statistics

A description of the NumAcc4 dataset is available. SHAZAM commands for calculating summary statistics follow. 

SAMPLE 1 1001
READ (NUMACC4.txt) Y
STAT Y / MEAN=YMEAN VAR=YVAR
FORMAT(F20.8)   
PRINT YMEAN YVAR / FORMAT
STOP

The SHAZAM output is below. 

|_SAMPLE 1 1001
|_READ (NUMACC4.txt) Y
UNIT 88 IS NOW ASSIGNED TO: NUMACC4.txt
   1 VARIABLES AND     1001 OBSERVATIONS STARTING AT OBS       1

|_STAT Y / MEAN=YMEAN VAR=YVAR
NAME        N    MEAN        ST. DEV      VARIANCE     MINIMUM      MAXIMUM
Y          1001  0.10000E+08 0.10000     0.10000E-01  0.10000E+08  0.10000E+08
|_FORMAT(F20.8)
|_PRINT YMEAN YVAR / FORMAT
    YMEAN
  10000000.20000010
    YVAR
         0.01000000
|_STOP

Statistical Distributions

SHAZAM commands for calculating the 1% critical value of the F(3,3) distribution follow. 

SAMPLE 1 1 
GEN1 ALPHA=0.01
DISTRIB ALPHA / TYPE=F DF1=3 DF2=3 INVERSE     
STOP

The SHAZAM output is below. 

|_SAMPLE 1 1
|_GEN1 ALPHA=0.01
|_DISTRIB ALPHA / TYPE=F DF1=3 DF2=3 INVERSE
F DISTRIBUTION- DF1=   3.0000     DF2=   3.0000
MEAN=   3.0000     VARIANCE=   0.0000     MODE=  0.20000

              PROBABILITY CRITICAL VALUE   PDF
  ALPHA
 ROW     1    0.10000E-01  29.457     0.48920E-03
|_STOP

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