statsmodels.tsa.interp.denton.dentonm¶

statsmodels.tsa.interp.denton.
dentonm
(indicator, benchmark, freq='aq', **kwargs)[source]¶ Modified Denton’s method to convert lowfrequency to highfrequency data.
Uses proportionate firstdifferences as the penalty function. See notes.
Parameters: indicator
A lowfrequency indicator series. It is assumed that there are no presample indicators. Ie., the first indicators line up with the first benchmark.
benchmark : arraylike
The higher frequency benchmark. A 1d or 2d data series in columns. If 2d, then M series are assumed.
freq : str {“aq”,”qm”, “other”}
“aq”  Benchmarking an annual series to quarterly. “mq”  Benchmarking a quarterly series to monthly. “other”  Custom stride. A kwarg, k, must be supplied.
kwargs :
 k : int
The number of highfrequency observations that sum to make an aggregate lowfrequency observation. k is used with freq == “other”.
Returns
——
benchmarked series : array
Notes
Denton’s method minimizes the distance given by the penalty function, in a least squares sense, between the unknown benchmarked series and the indicator series subject to the condition that the sum of the benchmarked series is equal to the benchmark. The modification allows that the first value not be predetermined as is the case with Denton’s original method. If the there is no benchmark provided for the last few indicator observations, then extrapolation is performed using the last benchmarkindicator ratio of the previous period.
Minimizes sum((X[t]/I[t]  X[t1]/I[t1])**2)
s.t.
sum(X) = A, for each period. Where X is the benchmarked series, I is the indicator, and A is the benchmark.
References
 Bloem, A.M, Dippelsman, R.J. and Maehle, N.O. 2001 Quarterly National
 Accounts Manual–Concepts, Data Sources, and Compilation. IMF. http://www.imf.org/external/pubs/ft/qna/2000/Textbook/index.htm
 Cholette, P. 1988. “Benchmarking systems of socioeconomic time series.”
 Statistics Canada, Time Series Research and Analysis Division, Working Paper No TSRA88017E.
 Denton, F.T. 1971. “Adjustment of monthly or quarterly series to annual
 totals: an approach based on quadratic minimization.” Journal of the American Statistical Association. 99102.
Examples
>>> indicator = [50,100,150,100] * 5 >>> benchmark = [500,400,300,400,500] >>> benchmarked = dentonm(indicator, benchmark, freq="aq")