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@ -10,13 +10,14 @@ This project is continously under improvement and contributors are well come.
## Fuzzy Time Series (FTS) ## Fuzzy Time Series (FTS)
Fuzzy Time Series (FTS) are non parametric methods for time series forecasting based on Fuzzy Theory. The original method was proposed by [1] and improved later by many researchers. The general approach of the FTS methods, based on [2] is listed below: Fuzzy Time Series (FTS) are non parametric methods for time series forecasting based on Fuzzy Theory. The original method was proposed by [1] and improved later by many researchers. The general approach of the FTS methods, based on [2] is listed below:
1. **Data preprocessing**: Data transformation functions contained at pyFTS.common.Transformations, like differentiation, Box-Cox, scaling and normalization. 1. **Data preprocessing**: Data transformation functions contained at [pyFTS.common.Transformations](https://github.com/petroniocandido/pyFTS/blob/master/pyFTS/common/Transformations.py), like differentiation, Box-Cox, scaling and normalization.
2. **Universe of Discourse Partitioning**: This is the most important step. Here, the range of values of the numerical time series *Y(t)* will be splited in overlapped intervals and for each interval will be created a Fuzzy Set. This step is performed by pyFTS.partition module and its classes (for instance GridPartitioner, EntropyPartitioner, etc). The main parameters are: 2. **Universe of Discourse Partitioning**: This is the most important step. Here, the range of values of the numerical time series *Y(t)* will be splited in overlapped intervals and for each interval will be created a Fuzzy Set. This step is performed by pyFTS.partition module and its classes (for instance GridPartitioner, EntropyPartitioner, etc). The main parameters are:
- the number of intervals - the number of intervals
- which fuzzy membership function (on pyFTS.common.Membership) - which fuzzy membership function (on [pyFTS.common.Membership](https://github.com/petroniocandido/pyFTS/blob/master/pyFTS/common/Membership.py))
- partition scheme (GridPartitioner, EntropyPartitioner, FCMPartitioner, CMeansPartitioner, HuarngPartitioner) - partition scheme ([GridPartitioner](https://github.com/petroniocandido/pyFTS/blob/master/pyFTS/partitioners/Grid.py), [EntropyPartitioner](https://github.com/petroniocandido/pyFTS/blob/master/pyFTS/partitioners/Entropy.py), [FCMPartitioner](https://github.com/petroniocandido/pyFTS/blob/master/pyFTS/partitioners/FCM.py), [CMeansPartitioner](https://github.com/petroniocandido/pyFTS/blob/master/pyFTS/partitioners/CMeans.py), [HuarngPartitioner](https://github.com/petroniocandido/pyFTS/blob/master/pyFTS/partitioners/Huarng.py))
Check the jupyter notebook /notebooks/Partitioners.ipynb for sample codes. Check out the jupyter notebook on [pyFTS/notebooks/Partitioners.ipynb](https://github.com/petroniocandido/pyFTS/blob/master/pyFTS/notebooks/Partitioners.ipynb) for sample codes.
3. **Data Fuzzyfication**: Each data point of the numerical time series *Y(t)* will be translated to a fuzzy representation (usually one or more fuzzy sets), and then a fuzzy time series *F(t)* is created. 3. **Data Fuzzyfication**: Each data point of the numerical time series *Y(t)* will be translated to a fuzzy representation (usually one or more fuzzy sets), and then a fuzzy time series *F(t)* is created.
@ -27,9 +28,9 @@ Fuzzy Time Series (FTS) are non parametric methods for time series forecasting b
- *steps ahead*: the number of steps ahed to predict. Almost all standard methods are based on one-step-ahead forecasting - *steps ahead*: the number of steps ahed to predict. Almost all standard methods are based on one-step-ahead forecasting
- *forecasting type*: Almost all standard methods are point-based, but pyFTS also provides intervalar and probabilistic forecasting methods. - *forecasting type*: Almost all standard methods are point-based, but pyFTS also provides intervalar and probabilistic forecasting methods.
5. **Forecasting**: 5. **Forecasting**: The forecasting step takes a sample (with minimum length equal to the model's order) and generate a fuzzy outputs (fuzzy set(s)) for the next time ahead.
6. **Defuzzyfication** 6. **Defuzzyfication**: This step transform the fuzzy forecast into a real number.
7. **Data postprocessing**: The inverse operations of step 1. 7. **Data postprocessing**: The inverse operations of step 1.