The market is a controlled dynamic system. - page 56
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I'll stick to my opinion.
Well, that's up to you. I stand by my opinion: it is wrong to simulate the behaviour of an open system without taking into account the external influence, even if it is unknown, which plays a defining role in this behaviour.
I remove my scheme, those who were interested, have already copied it.
Well, that's up to you. I stand by my opinion: it is wrong to model behavior of an open system without taking into account external influence, even if it is unknown, which plays a defining role in this behavior.
I remove my scheme, those who were interested, have already copied it.
You misunderstand the mechanism of the presented scheme. The external influence is present indirectly in the form of the system's response. Anyway...
3) Having made this assumption about the presence of the shaping system, we set the task of constructing its model.
The model output y should correspond to the actual data x, taking into account the chosen proximity criterion of the processes y and x.
Let's look at this scheme from some other side as I understand it.
x(t) is a quotation that we can observe and at the same time measure
y(t) is some process which is calculated. For the following discussion it is fundamental that it is not observed - in my terminology it is the state of an observable process.
Let us write: x(t) = y(t) +d(t) + nu(t)
Where:
d(t) is the deterministic input (bias)
nu(t) - a random process independent of the rest - noise
Let us similarly describe the state of the system:
y(t) = c(t) + y(t-1) + theta(t)
where
c(t) - deterministic shift of state
y(t-1) - the previous value of the state
theta(t) - random process, independent of the rest - noise
Please note that our observed process (quote) at time t is actually determined by the previous state x(t-1), i.e. based on prediction of the system state.
The described scheme has names: structural time series, state space model, dynamic linear system.
The mathematical centre of this model is the Kalman filter, a rather computationally complex algorithm. Filling the listed variables with different contents, for example considering y(t) as a trend, any of the existing models can be obtained. Due to the amazing properties of the Kalman filter, state-space models outperform their counterparts.
There are ready-to-use software packages in R to solve the above problem. About them in following posts.
The dse package provides tools for multivariate, linear, time series independent models. It includes ARMA and state-space representations, and methods for converting between them. It also includes simulation methods and several estimation functions. The package has functions for viewing model roots, stability, and forecasting at different horizons. The implementation of the ARMA model is generic, so that VAR, VARX, ARIMA, ARMAX, ARIMAX can be treated as special cases. The Kalman filter and smoother estimates can be derived from the model in state space, and methods for fitting the model in state space are implemented. An introduction and User's Manual are available in the vignette.
The dse package provides tools for multivariate, linear, time series independent models. It includes ARMA and state-space representations, and methods for converting between them. It also includes simulation methods and several estimation functions. The package has functions for viewing model roots, stability, and forecasting at different horizons. The implementation of the ARMA model is generic, so that VAR, VARX, ARIMA, ARMAX, ARIMAX can be treated as special cases. The Kalman filter and smoother estimates can be derived from the model in state space, and methods for fitting the model in state space are implemented. An introduction and User's Manual are available in the vignette.
The KFAS package provides Kalman filter, state, disturbance and smoothing simulation functions, predicting and simulating models in state space. All functions can use exact scattered initialization when the distributions of some or all elements of the initial state vector are unknown. The filtering, state smoothing and simulation functions use a sequential processing algorithm that is faster than the standard approach, and it also allows for a feature of the prediction error variance matrix. KFAS also contains a function for computing the likelihood of exponential models in the family state space and functions for smoothing the state of exponential models in the family state space.
Guys, stop reinventing the wheel.
There are a lot of packages out there, there is a universal Simulink, on which you can build anything. But no package will replace your brain, it won't tell you which control matrix to build into Kalman filter and it won't synthesise the model's block diagram for you.
Guys, stop reinventing the wheel.
For once, a normal topic on a four-way forum that doesn't even see any flooders.
Let them invent!
Maybe I'll add something of my own when I decide to. I'll just have to figure out how to make it into these blocks, arrows and OS...