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Thread: I want to learn to create ARX, ARMAX, Box-Jenkins and Output-Error

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    I want to learn to create ARX, ARMAX, Box-Jenkins and Output-Error




    Hello.

    I'm am a control engineer and I want to upgrade my skills in simulation of dynamic physical systems. Normaly I describe my physical system as transferfunction or a statespace model depending what I want to know.

    But those models are not exactly equal to the system. Very old technique. So I want to learn ARX, ARMAX, Box-Jenkins and Output-Error modeling to create a better dynamic model for simulation. Modern technique.

    The problem is that I don't know anything about statiatics, probability, Inference and regission.

    But I have downloaded 13 playlist from JBstatistics at youtube. I'm planning to watch them depending what I need to know.

    The names of those playlists are:

    - Discrete probability distribution
    - Continuous probability distribution
    - Hypothesis testing
    - Inference for variances
    - One-way ANOVA
    - Inference for proportions
    - Inference for population means
    - Confidence intervals for population means
    - Simple linear Regission
    - Chi-Square test for Count data
    - Using a standard Normal table
    - Sampling distribution

    Questions:
    1. Do I really need to know all those to learn more about statistical regissions analysis? Or could I only jump directly to regissions analysis? I don't want to waste any time on statistical methods that I not going to use in control engineering.

    2. Am I right that to create ARX, ARMAX, BJ and OE models, I need to know regissions analysis, not statistical inference/distribution?

    3. If i need to know all those, can you say in what order I should watch them?

    Ofc I know the programming language R.

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    Re: I want to learn to create ARX, ARMAX, Box-Jenkins and Output-Error

    The methods you are describing appear to be time series. If so they have little to do with the terms you referenced from the play list. Normally you are not conducting statistical test with a time series you are forecasting future values. While assumptions supposedly exist they get little attention in the time series literature (for univariate models such as Box Jenkins or its multivariate equivalent ARIMAX) or for ARMA. ARIMA is Box-Jenkins (the statisticians you popularized this approach). For regression based time series this is not true, but aside from economists I don't think many use regression based time series (examples of this are VAR, error correction models, and ARDL). They are much more likely to use univariate models notably ARIMA.


    Time series is one of, if not the, most difficult type of statistics and the approaches you mention are among the more difficult in time series, because they are as much an art form as science. Worse real world data rarely matches the training that university courses provide for this. ARIMAX is incredibly time consuming, because you have to difference and determine the MA and AR order of each variable in the model.

    Personally I think you would be better off to start with exponential smoothing, such as Holt Winston, rather than learn ARIMA. The forecast results are similar in terms of accuracy I believe and its infinitely easier to use.

    This is as good a start as any for ARIMA. Note that I have a huge collection of such links and books - and still have not been brave enough to run it outside class.

    https://people.duke.edu/~rnau/411arim.htm
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: I want to learn to create ARX, ARMAX, Box-Jenkins and Output-Error

    Thank you for your reply!

    So I don't need to look at any regression analysis or statistical at all? Just focus on so called "Time series analysis"?

    Can I just go and read a book about introduction about Time Series, without no knowledge about statistics?

    I don't want to describe a physical system with differential equations, to much work. I going to measure input and output, much easier.
    Is there any model that you recommend for me who can be used in simulation? Notice this will be used in control engineering, not stock market analysis.
    Last edited by Volvo742; 01-06-2017 at 03:19 PM.

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    Re: I want to learn to create ARX, ARMAX, Box-Jenkins and Output-Error

    I am not sure what you want to do. I was only responding to the methods you noted. Time series is statistical, but it does not normally use statistical test (you are forecasting not doing hypothesis testing - there is a partial exception in ARIMA as you try to determine what order of the AR and MA to add to your model).

    You can read a time series book without knowledge of statistics, but time series is actually one of the more complex forms of statistics I feel. Many of the time series books, including those that are 'introductory', are very complex and stress the math rather than the information you are likely looking for. One of the better authors is Chatfield from the U of Bath. I recommend him.

    I am not an engineer or a true statistician (I use it to do analysis, but I am not at the level of many others here). I am not really sure what you are trying to do. I don't see that time series is useful for input and output although physicist use a special form of time series to describe signals. This is fundamentally different than the normal time series literature and I know nothing of that.

    I think you should detail more specifically what you are trying to do and wait until Miner gets here. He knows a lot more about what you appear to be interested in than I do.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: I want to learn to create ARX, ARMAX, Box-Jenkins and Output-Error

    Quote Originally Posted by noetsi View Post
    I am not sure what you want to do. I was only responding to the methods you noted. Time series is statistical, but it does not normally use statistical test (you are forecasting not doing hypothesis testing - there is a partial exception in ARIMA as you try to determine what order of the AR and MA to add to your model).

    You can read a time series book without knowledge of statistics, but time series is actually one of the more complex forms of statistics I feel. Many of the time series books, including those that are 'introductory', are very complex and stress the math rather than the information you are likely looking for. One of the better authors is Chatfield from the U of Bath. I recommend him.

    I am not an engineer or a true statistician (I use it to do analysis, but I am not at the level of many others here). I am not really sure what you are trying to do. I don't see that time series is useful for input and output although physicist use a special form of time series to describe signals. This is fundamentally different than the normal time series literature and I know nothing of that.

    I think you should detail more specifically what you are trying to do and wait until Miner gets here. He knows a lot more about what you appear to be interested in than I do.
    Hi!

    What I'm want to do is called System identification to estimate/create models by input and output data. Those models will be used in simulation for example Simulink/Matlab/R. Example: Measure input (Voltage Pulse width modulation) and output (electric engine shaft) of a process and create a model of it.

    I'm not good at mathematics, only known the basics. That's why I'm using R when it comes to mathematical and statistical calculations.

    I have noticed that R have a built-in function called ARIMA. I's that a good function?

    The only I need from a statistical model is to know what I get when I give, and when do it happens.
    Example: If I give an electric motor 12 Voltage, I get 2000 RPM, If I give the electric motor 6 Voltage, I get 1000 RPM. But what happens if I give 3 Voltage? Do I get 500 RPM then?

    That's the purpose with the model.

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    Re: I want to learn to create ARX, ARMAX, Box-Jenkins and Output-Error

    Is it a good function for what? That is what I mean by details, you have to state specifically what you are using this function for to get a good answer.

    I suspect that if you really are interested in time series what you want is the specialized form of time series that physicist use to look at how signals change over time. Pretty much the only one who use it are physicists and engineers, it is fundamentally different than the time series used in social sciences such as economics I know.

    I am not sure however, that you really are looking for time series at all. It seems like you are interested in multivariate regression with voltage being the dependent variable.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: I want to learn to create ARX, ARMAX, Box-Jenkins and Output-Error

    Quote Originally Posted by noetsi View Post
    Is it a good function for what? That is what I mean by details, you have to state specifically what you are using this function for to get a good answer.

    I suspect that if you really are interested in time series what you want is the specialized form of time series that physicist use to look at how signals change over time. Pretty much the only one who use it are physicists and engineers, it is fundamentally different than the time series used in social sciences such as economics I know.

    I am not sure however, that you really are looking for time series at all. It seems like you are interested in multivariate regression with voltage being the dependent variable.
    Multiple regression might be a good idea. But have a look at this picture. This is system identification. In this case, this user are going to estimate a transfer function by input and output data.


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    Re: I want to learn to create ARX, ARMAX, Box-Jenkins and Output-Error

    Why don't you read a book in automatic control (like this one).

    - Discrete probability distribution
    - Continuous probability distribution
    - Hypothesis testing
    - Inference for variances
    - One-way ANOVA
    - Inference for proportions
    - Inference for population means
    - Confidence intervals for population means
    - Simple linear Regission
    - Chi-Square test for Count data
    - Using a standard Normal table
    - Sampling distribution
    No, you don't have to read this, but many of them are special cases of a linear model. As you maybe can find by reading this site.

    But if you work with empirical data, isn't it reasonable that you at least have an elementary knowledge of statistics? If you work with chemisetry, isn't it natural to learn elementary chemistry? Get an elementary statistics book of 100 pages and read it.

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    Re: I want to learn to create ARX, ARMAX, Box-Jenkins and Output-Error


    Hello!

    I'm not a chemist. I'm a control engineer/mechanical engineer. We use estimation when we are going to create transfer functions/state space models for simulation, or other types of models like Fuzzy control models.

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