Aaron Smith, "Partially Overlapping Time Series: A New Model for Volatility
Dynamics in Commodity Futures", Journal of Applied Econometrics, Vol.
20, No. 3, 2005, pp. 405-422.

There are two files in pots.zip. They are both ASCII files in DOS format.

  pots.src - GAUSS code for estimation of model
  
  corn.dat - space delimited ASCII file containing five columns of data;
  each row in the file corresponds to a particular futures contract on a
  particular day.
		
	variable 1: contract identifier (integer between 159 and 212
	            (excluding 207 and 209) that denotes the contract to
		    which a particular price observation corresponds.
	variable 2: time to delivery in weekdays
	variable 3: date in YYYYMMDD format
	variable 4: futures settlement price
	variable 5: futures price change from previous day

  The data comprise 19,745 daily observations on corn futures contracts at
  the Chicago Board of Trade between Jan 1991 and Dec 2000. The source is
  Bridge/Commodity Research Bureau.


  pots.src program file contains documentation. Changes should only need to
  be made in the initial setup part of the program. The program can
  accommodate the following variations depending on chosen parameters:
   
   1.  gdim:            1 or 2 factors 
   2.  connum:          Arbitrary number of separate splines to capture
                        seasonality (e.g., paper has 5 splines, one for each
			contract)
   3.  mix:             In a 2-factor model, some contracts can be a mix of
                        the two factors (e.g., Sept contract in paper)
   4.  knotnum & knot:  Arbitrary number and placement of nodes in spline


Except for during the final hill climbing component of the maximization
algorithm (step 6 in paper), the parameter values and splines are global.
This means that, once the user has a feel for the program, he/she can start
and stop the algorithm by selecting and executing parts of the code. 

The following variables could be of interest for troubleshooting or if the
user desires more output:

    1.  ga = vector of non-spline parameters
    2.  spline2 = vector of 2K free parameters of theta spline function
    3.  spline2u = vector of 2K free parameters of lambda spline function
    4.  est0 = parameter vector = ga|spline2|spline2u
    5.  epsilon = factor estimates from Kalman filter (one row for each unique
        date, t, in the sample)
    6.  ptt = factor precistion from Kalman filter (one row for each unique
        date, t, in the sample)
    7.  myh = GARCH conditional variance estimates (one row for each unique
        date, t, in the sample)
    8.  myspline = values of theta spline for each observation = 
        xbig*wbig*spline2   (wbig expands 2k vector of free parameters up to
	full parameter vector)
    9.  mysplineu = values of lambda spline for each observation 
        = xbigu*wbigu*spline2u   (wbigu expands 2k vector of free parameters
	up to full parameter vector)
    10. dspline_final = theta spline evaluated at designated times to delivery
        = x_out*wbig*spline2 (dspline_se is vector of associated standard
	errors)
    11. dspline_finalu = lambda spline evaluated at designated times to
        delivery = x_outu*wbigu*spline2u (dspline_seu is vector of associated
	standard errors)
    12  dspline_finalt = unconditional variance as a function of (d,t) = 
        dspline_final^2 + dspline_finalu^2 (dspline_set is vector of
	associated standard errors)

Approximate run time for 2-factor model in paper using 2.8 GHz Pentium 4
with 1 GB RAM is 180 minutes, including 121 EM iterations, and 249 optmum
iterations.

Approximate run time for 1-factor model in paper using 2.8 GHz Pentium 4
with 1 GB RAM is 70 minutes, including 141 EM iterations, and 56 optmum
iterations.

Run time shortens dramatically for smaller models, e.g., model with connum=1
(no seasonality), 1 factor, and only one knot point achieves the maximum
less than 1 minute.

In models with a large number of knots in the splines, the likelihood can be
flat with respect to the spline parameters and the maximum can be elusive.
One symptom of unsuccessful maximization is very large standard errors on
the splines. It is worth repeating the estimation from several different
starting values to ensure that a stable solution is found.