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| 7-means clustering of points drawn from 3-dimensional White-Noise |
Wednesday, May 30, 2012
K-means packet clustering for IDSs
Monday, May 28, 2012
The Grey Model: Predicting 'grey' time-series
In many scientific disciplines like meteorology, finance, cognitive-radio (CR), etc., it is vital to predict future values of a time-series based on online observed values or historical data. Statistical methods like those proposed by Box-Jenkins (Auto Regressive
Integrated Moving Average aka ARIMA, etc.) and artificial neural-networks have received significant attention in the literature.
While the statistical methods are not as precise as artificial neural-networks, the later demands a great deal of data for training (i.e. training, testing, validating) not to mention the length of the training period itself. In many real-life cases (like predicting the daily market price of the Shanghai Stock Exchange), these limitations are simply unacceptable.
Question
Given 21 consecutive daily market prices of the Shanghai Stock Exchange 1241 1233 1246 1260 1276 1247 1286 1281 1278 1316 1324 1327 1323 1338 1362 1365 1378 1380 1364 1351 1376, predict the price on the next day.
Grey Theory
Grey prediction theory is a method that was first introduced in the early eighties by Professor Deng (1982). Since then, the theory has become quite popular with its ability to deal with the systems that have partially unknown parameters (so-called 'grey' systems). As a superiority to conventional models, grey models require only a limited amount of data to estimate the behavior of unknown systems (Deng, 1989). For a comprehensive introduction to Grey Prediction, see this.
Answer to question above
About 1399.553
Continuation
If you're interested, let me know so I explain the details of Grey Theory, outline the different error-correcting schemes (corrections in time and space domains using FFT, corrections modelling relative errors as 'fuzzy' Markov chains, etc.), post some lovely R and MatLab code, and more.
While the statistical methods are not as precise as artificial neural-networks, the later demands a great deal of data for training (i.e. training, testing, validating) not to mention the length of the training period itself. In many real-life cases (like predicting the daily market price of the Shanghai Stock Exchange), these limitations are simply unacceptable.
Question
Given 21 consecutive daily market prices of the Shanghai Stock Exchange 1241 1233 1246 1260 1276 1247 1286 1281 1278 1316 1324 1327 1323 1338 1362 1365 1378 1380 1364 1351 1376, predict the price on the next day.
Grey Theory
Grey prediction theory is a method that was first introduced in the early eighties by Professor Deng (1982). Since then, the theory has become quite popular with its ability to deal with the systems that have partially unknown parameters (so-called 'grey' systems). As a superiority to conventional models, grey models require only a limited amount of data to estimate the behavior of unknown systems (Deng, 1989). For a comprehensive introduction to Grey Prediction, see this.
Answer to question above
About 1399.553
Continuation
If you're interested, let me know so I explain the details of Grey Theory, outline the different error-correcting schemes (corrections in time and space domains using FFT, corrections modelling relative errors as 'fuzzy' Markov chains, etc.), post some lovely R and MatLab code, and more.
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