[Savannah-register-public] [task #5868] Submission of Special Interest Group Time Series

[Johann Rost]

URL:
  <http://savannah.gnu.org/task/?5868>

                 Summary: Submission of Special Interest Group Time Series
                 Project: Savannah Administration
            Submitted by: johann0
            Submitted on: Tuesday 09/05/2006 at 11:10
         Should Start On: Tuesday 09/05/2006 at 00:00
   Should be Finished on: Friday 09/15/2006 at 00:00
                Category: Project Approval
                Priority: 5 - Normal
                  Status: None
                 Privacy: Public
             Assigned to: None
        Percent Complete: 0%
             Open/Closed: Open
                  Effort: 0.00

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== REGISTRATION DETAILS ==

Full Name:
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  *Special Interest Group Time Series*

System Group Name:
-----------------
  *sigtis*

Type:
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  non-GNU software &amp; documentation

License:
-------- 
  GNU General Public License V2 or later

Other License: 
--------------
  I imagine to use a dual licensing model: one license is GPL the other
license could be a propriatary license (somthing similar like MySQL). What do
you think about it?


Description:
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  Extensive library of algorithms for Time Series Analysis. (Time Series
Analysis is a part of Econometrics which belongs to Mathematical Statistics.
The library is written in C++. The Code is finished and tested. However it is
not online. For this reason I prefer to sent it by email. Please let me know
where I should send the code.

The following algoritms are implemented



Preprocessing: Eliminating Trend and Seasonality
Differencing
Logarithm

Additive Seasonality
-       Parameter Estimation according Brockwell/Davis S1 – adapted to MSE, MAD,
MAPE, MdAPE
-       Parameter Estimation according Brockwell/Davis S2 – adapted to MSE, MAD,
MAPE, MdAPE
-       Optimum parameter estimations for MSE, MAD, MAPE, MdAPE

Multiplicative seasonality
-       Parameter Estimation according Brockwell/Davis S1 – adapted to MSE, MAD,
MAPE, MdAPE
-       Parameter Estimation according Brockwell/Davis S2 – adapted to MSE, MAD,
MAPE, MdAPE
-       Optimum parameter estimations for MSE, MAD, MAPE, MdAPE

Extraction of a non-zero mean
-       Optimum parameter estimations for MSE, MAD, MAPE, MdAPE

Linear Trend
-       MSE parameter estimation according Abraham & Ledolter
-       Optimum parameter estimations for MSE, MAD, MAPE, MdAPE
-       Preliminary trend estimation heuristic for seasonal TS for MSE, MAD, 
MAPE,
MdAPE

Logistic Trend
-       Optimum Parameter estimation MSE – using LinMin optimization
-       Optimum Parameter estimation MSE – using Simplex-Downhill optimization
-       Optimum parameter estimations for MAD, MAPE, MdAPE
-       Heuristic parameter estimation according Schlittgen
-       Improved heuristic parameter estimations for MSE, MAD, MAPE, MdAPE

Exponential Trend
-       Heuristic for Non-Seasonal TS for MSE, MAD, MAPE, MdAPE
-       Heuristic for Seasonal TS for MSE, MAD, MAPE, MdAPE
-       Optimum parameter estimation for MSE, MAD, MAPE, MdAPE

Damped Trend
-       Heuristic parameter estimations for seasonal and for non-seasonal TS 
using
MSE, MAD, MAPE, MdAPE
-       Optimum parameter estimation for MSE, MAD, MAPE, MdAPE

Combined estimation of trend and seasonality
-       Heuristic algorithms for MSE, MAD, MAPE, MdAPE
-       Optimum algorithms for MSE, MAD, MAPE, MdAPE

Algorithms for extracting an identified mean, trend and/or seasonality from a
TS

3. ARMA Models


Model Identification
-       Model identification according to Hannan/Rissanen
-       Identification using Hold-Out Sample
-       Model identification according to “Rectangle”-Heuristic

Preliminary Parameter Estimation
-       Brockwell/Davis
-       Hannan/Rissanen
-       Burg’s Algorithm
-       Durbin/Levinson
-       Trench/Zohar
-       “Hybrid” Heuristic

Final Parameter Estimation
-       Conditioned Least Squares
-       Unconditioned Least Squares
-       Exact Likelihood (Luceno’s Algorithm)
-       Exact Likelihood (Melard’s algorithm)
-       Non-linear optimization algorithms for final parameter estimation: 
DFP-MIN,
Powell’s Algorithm, FRPR-MIN, Simplex-Downhill

H-step ahead forecast and predicted values for observations

4. AR Models
“Model Identification”
-       “Proximity” Algorithm 
-       “Rectangle” Heuristic

Exact Parameter Estimation
-       ULS Algorithm
-       CLS Algorithm
-       Melard’s Algorithm for exact likelihood
-       Luceno’s Algorithm for exact likelihood

Preliminary Parameter Estimation
-       Burg’s Algorithm
-       Durbin/Levinson

H-step ahead forecast and predicted values for observations


5. Exponential smoothing

Forecasting algorithms according Recurrence Form and Error-Correction Form
(where applicable)

Implemented algorithms for estimating the smoothing parameters
-       Simplex-Downhill
-       Numerical Method
-       Grid-Min
-       Grid-Min Heuristic
-       Powell’s Algorithm
-       FRPR-MIN

ES - Constant Level
Constant level, no seasonality - estimation of start-value
-       First Value
-       Local average
-       Global average
-       Backcast
-       DLS (Discounted Least Squares)
-       Combined estimation of start value and smoothing parameter.

Constant level, additive seasonality - estimation of start-value
-       First Value
-       Local average
-       Global average
-       Backcast
-       Combined estimation of start value and smoothing parameter.

Constant level, multiplicative seasonality - estimation of start-value 
-       First Value
-       Local average
-       Global average
-       Backcast
-       Combined estimation of start value and smoothing parameter.

Constant level, multiplicative seasonality - estimation of start-value 
-       First Value
-       Local average
-       Global average
-       Backcast
-       Combined estimation of start value and smoothing parameter.

ES - Damped Trend
Damped Trend, no seasonality (Gardner’s “model 1”) - estimation of
start-values 
-       First Value
-       Local average
-       Global average
-       Non-Seasonal “Fiber”- Heuristic
-       Combined estimation of start values and smoothing parameters.

Damped Trend, no seasonality (Gardner’s “model 2”) - estimation of
start-values 
-       First Value
-       Local average
-       Global average
-       Non-Seasonal “Bloc”- Heuristic
-       Combined estimation of start values and smoothing parameters.

Damped Trend, additive seasonality - estimation of start-values 
-       Local average
-       Global average
-       Seasonal “Fiber”- Heuristic
-       Combined estimation of start values and smoothing parameters.

Damped Trend, multiplicative seasonality - estimation of start-values 
-       Local average
-       Global average
-       Seasonal “Bloc”- Heuristic
-       Combined estimation of start values and smoothing parameters.

ES - Exponential Trend
Exponential Trend, no seasonality - estimation of start-values 
-       First Value
-       Local average
-       Global average
-       Combined estimation of start values and smoothing parameters.

Exponential Trend, additive seasonality - estimation of start-values 
-       Local average
-       Global average
-       Combined estimation of start values and smoothing parameters.

Exponential Trend, multiplicative seasonality - estimation of start-values 
-       Local average
-       Global average
-       Combined estimation of start values and smoothing parameters.

ES - Linear Trend

Double Exponential Smoothing
-       First Value
-       Local average
-       Global average
-       Heuristic
-       Combined estimation of start value and smoothing parameter.


Holt-Winter’s non-seasonal Model - estimation of start-values
-       First Value
-       Local average
-       Global average
-       Combined estimation of start value and smoothing parameter.
Fast estimation of confidence limits according Yar & Chatfield


Holt-Winter’s Model with additive seasonality - estimation of start-values
-       Local average
-       Global average
-       Combined estimation of start value and smoothing parameter.
Fast estimation of confidence limits according Yar & Chatfield

Holt-Winter’s Model with multiplicative seasonality - estimation of
start-values
-       Local average
-       Global average
-       “Fiber”-Heuristic for linear trends
-       Combined estimation of start value and smoothing parameter.
Fast estimation of confidence limits according Yar & Chatfield

Brown’s non-seasonal Model - estimation of start-values
-       First Value
-       Local average
-       Global average
-       Combined estimation of start value and smoothing parameter.

Brown’s Model with additive seasonality - estimation of start-values
-       Local average
-       Global average
-       Combined estimation of start value and smoothing parameter.

Brown’s Model with additive seasonality - estimation of start-values
-       Local average
-       Global average
-       Combined estimation of start value and smoothing parameter.
-       “Bloc”-Heuristic for linear trends

6. Multivariate Linear Regression
   Selection strategy for Variables
-       Forward Selection
-       Backward Elimination
-       Stepwise Selection
-       Complete Search

8. User defined Multivariate econometric models
Implementation of user defined models
7. Random Walk
Implementation of the Random-Walk model


8. Confidence Limits
Calculation of confidence limits for forecasts

9. Tests
-       Has the TS a non-zero mean
-       Has the TS a seasonality of given lengths
-       Has the TS a trend
-       Has the TS outliers
-       TS has all-positive values

10. Model Evaluation
-       Penalty function: BIC, AICC
-       Evaluation via Hold-Out-Sample
-       Error measure: MSE, MAD, MAPE, MdAPE

11. Transformations
Auto-Correlation
Auto-Covariance
-       Algorithm for computing the Auto-Covariance directly
-       Algorithm using Fast-Fourier-Transformation (FFT)

ACF
ACF according Tunicliffe & Wilson
Direct Computation of the ACF

Fast Fourier Transformation (FFT)

Periodogram
-       Compute periodogram without filter
-       Use Parzen-Window

Structural Math
- Selection of the optimum forecasting model - out of a given model set
- Selection of the necessary preprocessing (trend & season) – out of a
given “Preprocessing Set”
- Computation of optimum parameters for Models and Preprocessing
- Consistency Test for Multivariate Regression
- Generation of a report, why the suggested model has been preferred over
alternatives









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