Common Forecasting System in mathematics, and how to use differential system to construct a forecasting system

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I was interested in forecasting system recently where I found a nicely written wiki that had a list of them https://en.wikipedia.org/wiki/Forecasting and, I was wondering if someone could give a summary in terms of mathematics, i.e. I was thinking we can group them like

1. Linear/Nonlinear Regression(Which should not be a method, rather a mean to obtain coefficients for methods like 2 or 3)




2. Use/construct a specific equation




3. Graph/Hyper graph




4. Black box methods: neural network (which was usually realized through convergence, with supervise or not) e.t.c.

My first question:

1. Is there any other methods that I missed?

My second question:

I tried to use differential system(basically a black box methods) to construct a forecasting system recently. Basically through $X'=AQ_past$ and obtain the $X_new$ through taylor series. However, it had many limitations. The one I meat included but not limited to: 1. calculation singularity in mechanics(Computer accuracy) 2. the choice of factors for $Q$. 3. chaotic nature of the equation.(It's easily blow up) e.t.c.

2. Could you comment on such methods, please? Further, why it's so unreliable? Was there any analytic reason?

Example A: I found out that the choice of the number of dimension(number of row of $ntimes n$ matrix $A$) could actually have a great impact in the accuracy, for different vector system a vector space of dim $10$ may be better then vector space of dim $12$, where a vector space of dim $22$ may be the same as that of dim $12$ of $30$ based on different data set.

One of the explanation I came up was the fact that the coefficient in taylor ($frac1n!$) in reality convergence to $0$ faster than the value of components of $X'$ that we choice or calculated. But there must be some other reasons, as well.

functional-analysis analysis data-analysis

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asked Jul 22 at 18:06

J C

399314

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up vote
-1
down vote

favorite

I was interested in forecasting system recently where I found a nicely written wiki that had a list of them https://en.wikipedia.org/wiki/Forecasting and, I was wondering if someone could give a summary in terms of mathematics, i.e. I was thinking we can group them like

1. Linear/Nonlinear Regression(Which should not be a method, rather a mean to obtain coefficients for methods like 2 or 3)




2. Use/construct a specific equation




3. Graph/Hyper graph




4. Black box methods: neural network (which was usually realized through convergence, with supervise or not) e.t.c.

My first question:

1. Is there any other methods that I missed?

My second question:

I tried to use differential system(basically a black box methods) to construct a forecasting system recently. Basically through $X'=AQ_past$ and obtain the $X_new$ through taylor series. However, it had many limitations. The one I meat included but not limited to: 1. calculation singularity in mechanics(Computer accuracy) 2. the choice of factors for $Q$. 3. chaotic nature of the equation.(It's easily blow up) e.t.c.

2. Could you comment on such methods, please? Further, why it's so unreliable? Was there any analytic reason?

Example A: I found out that the choice of the number of dimension(number of row of $ntimes n$ matrix $A$) could actually have a great impact in the accuracy, for different vector system a vector space of dim $10$ may be better then vector space of dim $12$, where a vector space of dim $22$ may be the same as that of dim $12$ of $30$ based on different data set.

One of the explanation I came up was the fact that the coefficient in taylor ($frac1n!$) in reality convergence to $0$ faster than the value of components of $X'$ that we choice or calculated. But there must be some other reasons, as well.

functional-analysis analysis data-analysis

share|cite|improve this question

asked Jul 22 at 18:06

J C

399314

add a comment | 

up vote
-1
down vote

favorite

up vote
-1
down vote

favorite

I was interested in forecasting system recently where I found a nicely written wiki that had a list of them https://en.wikipedia.org/wiki/Forecasting and, I was wondering if someone could give a summary in terms of mathematics, i.e. I was thinking we can group them like

1. Linear/Nonlinear Regression(Which should not be a method, rather a mean to obtain coefficients for methods like 2 or 3)




2. Use/construct a specific equation




3. Graph/Hyper graph




4. Black box methods: neural network (which was usually realized through convergence, with supervise or not) e.t.c.

My first question:

1. Is there any other methods that I missed?

My second question:

I tried to use differential system(basically a black box methods) to construct a forecasting system recently. Basically through $X'=AQ_past$ and obtain the $X_new$ through taylor series. However, it had many limitations. The one I meat included but not limited to: 1. calculation singularity in mechanics(Computer accuracy) 2. the choice of factors for $Q$. 3. chaotic nature of the equation.(It's easily blow up) e.t.c.

2. Could you comment on such methods, please? Further, why it's so unreliable? Was there any analytic reason?

Example A: I found out that the choice of the number of dimension(number of row of $ntimes n$ matrix $A$) could actually have a great impact in the accuracy, for different vector system a vector space of dim $10$ may be better then vector space of dim $12$, where a vector space of dim $22$ may be the same as that of dim $12$ of $30$ based on different data set.

One of the explanation I came up was the fact that the coefficient in taylor ($frac1n!$) in reality convergence to $0$ faster than the value of components of $X'$ that we choice or calculated. But there must be some other reasons, as well.

functional-analysis analysis data-analysis

share|cite|improve this question

asked Jul 22 at 18:06

J C

399314

I was interested in forecasting system recently where I found a nicely written wiki that had a list of them https://en.wikipedia.org/wiki/Forecasting and, I was wondering if someone could give a summary in terms of mathematics, i.e. I was thinking we can group them like

1. Linear/Nonlinear Regression(Which should not be a method, rather a mean to obtain coefficients for methods like 2 or 3)




2. Use/construct a specific equation




3. Graph/Hyper graph




4. Black box methods: neural network (which was usually realized through convergence, with supervise or not) e.t.c.

My first question:

1. Is there any other methods that I missed?

My second question:

I tried to use differential system(basically a black box methods) to construct a forecasting system recently. Basically through $X'=AQ_past$ and obtain the $X_new$ through taylor series. However, it had many limitations. The one I meat included but not limited to: 1. calculation singularity in mechanics(Computer accuracy) 2. the choice of factors for $Q$. 3. chaotic nature of the equation.(It's easily blow up) e.t.c.

2. Could you comment on such methods, please? Further, why it's so unreliable? Was there any analytic reason?

Example A: I found out that the choice of the number of dimension(number of row of $ntimes n$ matrix $A$) could actually have a great impact in the accuracy, for different vector system a vector space of dim $10$ may be better then vector space of dim $12$, where a vector space of dim $22$ may be the same as that of dim $12$ of $30$ based on different data set.

One of the explanation I came up was the fact that the coefficient in taylor ($frac1n!$) in reality convergence to $0$ faster than the value of components of $X'$ that we choice or calculated. But there must be some other reasons, as well.

functional-analysis analysis data-analysis

share|cite|improve this question

asked Jul 22 at 18:06

J C

399314

share|cite|improve this question

share|cite|improve this question

asked Jul 22 at 18:06

J C

399314

asked Jul 22 at 18:06

J C

399314

asked Jul 22 at 18:06

J C

399314

399314

add a comment | 

add a comment | 

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