Methods and systems for forecasting with model-based PDF estimates

1. A computer-readable storage medium storing a program that, when executed by a processor, causes the processor to:

select a reference set of profiles from previous periods;

estimate model parameters of a time series based on the reference set, wherein the model parameters comprise a first variance for a hidden noise source;

calculate a probability density function for the time series including determining a second variance for the probability density function based at least in part on the first variance for the hidden noise source; and

generate a forecast from the probability density function.

2. The computer-readable storage medium of claim 1 , wherein when the processor estimates, the program further causes the processor to differentiate the time series to obtain a stationary time series.

3. The computer-readable storage medium claim 1 , wherein when the processor estimates, the program further causes the processor to estimate using model parameters comprising coefficients of a moving average filter.

4. The computer-readable storage medium of claim 1 , wherein when the processor estimates, the program further causes the processor to estimate using model parameters comprising coefficients of an autoregressive filter.

5. The computer-readable storage medium of claim 1 , wherein when the processor estimates, the program further causes the processor to estimate using model parameters comprising an offset value.

6. The computer-readable storage medium of claim 1 , wherein when the processor estimates, the program further causes the processor to estimate using model parameters where the model accounts for recurring patterns in the time series.

7. The computer-readable storage medium of claim 1 , wherein when the processor calculates, the program further causes the processor to calculate a Gaussian probability density function.

8. The computer-readable storage medium of claim 1 , wherein when the processor calculates, the program further causes the processor to calculate the probability density function being a function of time.

9. The computer-readable storage medium of claim 1 , further comprising:

wherein when the processor estimates the time series, the program further causes the processor to estimate the time series representing a cumulative value; and

wherein when the processor generates the forecast, the processor generates the forecast being an end-of-period cumulative value.

10. A computer comprising:

a display;

a processor coupled to the display; and

a memory coupled to the processor,

wherein the memory stores software that configures the processor to:

select reference profiles from a set of profiles from previous periods;

estimate a time series based on the reference profiles and a profile of the current period; and

derive a probability density function for the time series by estimating parameters of a model that comprises a hidden noise source,

wherein the software configures the processor to determine a first variance for the hidden noise source, and wherein the software further configures the processor to determine a second variance for the probability density function from the first variance of the hidden noise source and from estimated filter coefficients.

11. The computer-readable storage medium of claim 1 wherein when the processor changes the profiles, the program further causes the processor to perform a dissimilarity calculations between the profile of the current period, and to change the profiles in the reference set based on the dissimilarity calculations.