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Mathematical model of a large AR system for sparse system identification

I am new to the topic of system identification and looking for a large model of Autoregressive (AR). I am working on Sparse system identification http://tbayes.eecs.umich.edu/yilun/sparselms (example) ...
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ACF and PACF Confidence Levels for ARMA

I'm trying to figure out where exactly to draw the confidence levels for the autocorrleation function (ACF) and the partial autocorrelation function (PACF) for an ARMA model. For PACF I found that a ...
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1answer
57 views

Can someone show the details of how to apply AIC for sinusoidal models to specific data?

NOTE: This is a question that another user has been trying (unsuccessfully) to ask. Because the multiple questions asking, essentially, the same thing have either been deleted by me (because they ...
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1answer
57 views

ARMA models for non stationary signals

let us suppose that we have non stationary signal,whose value is given by ...
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1answer
28 views

Convert normalized frequency to real frequency in AR model

Let us suppose that we have modeled signal using AR model, and suppose we have following model: I used spectral estimation function from MATLAB pyulear Now ...
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1answer
62 views

Power spectral density interpretation

After reading this question: PSD (Power spectral density) explanation I am still a little confused as to what extra information the PSD gives us over simply taking the magnitude of the fourier ...
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45 views

Confusion regarding Dimension of AR model

I have a confusion regarding what is meant by dimension of AR,ARMA,MA model? Considering an AR model $x(t) = a1*x(t-1) + a2*x(t-2)$ is a 2 order AR model with $a1,a2$ as the parameters. This equation ...
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14 views

Relationship between phase space volume and entropy minimization

I would like to know if there is any analytical proof or relationship which can show that for a dynamical system in presence of chaos signal, if the phase space volume (PSV) minimization leads to the ...
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26 views

Using output error model to model colored noise (using a prefilter)

I have a "black box" SISO system. I use zero input to measure pure noise on the output. After preprocessing (peakshave and removing DC) I try to model the noise using AR (and also ARMA). When ...
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36 views

Is a Stationary VAR Process with Zero Mean Gaussian Innovations a Gaussian Stationary Process?

Consider the stationary VAR process $${\bf X}_t = \sum_{\tau = 1}^{L} A_\tau {\bf X}_{t-\tau} +{\bf \epsilon}_t$$ If the innovations $\epsilon_t \sim MVN({\bf 0},\Sigma)$ then is ${\bf X}_t$ a ...
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60 views

Autoregressive spectral estimation or windowed FFT?

I always use windowed FFT in my work, but I have seen lot of people using AR to do spectral estimation. What is the difference between these two methods? My understanding is that AR can capture some ...
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45 views

Fitting VAR Process with Generalised Gaussian Noise

Consider the $m$-dimensional VAR process $${\bf x}_t = \sum_{l=1}^{P} A_l{\bf x}_{t-l} + {\bf e}_t$$ where the componenets of ${\bf e}_t$ are spatially and temporally independent and follow a ...
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1answer
126 views

ARMA vs. AR and then what?

Sorry if this sounds elementary but I am struggling to grasp the physical idea behind ARMA (auto-regressive, moving average) process. The "AR" part is intuitive and so is "MA", but put together? If I ...
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1answer
65 views

Choosing inverse Z-transform equation, given that $|a|<1$

Given that $|a|<1$, then which of those inverse-Z-transform equations are we to use? I am leaning towards the first because (as I understand it), $z$ is merely a complex number that is ...
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1answer
274 views

What are Autoregressive Coefficients?

Can anyone explain what are Autoregressive Coefficients? What is their meaning that is. Consider a method: public double[] calculateARCoefficients(double[] inputseries, int order) When this method ...
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1answer
122 views

How to perform model fitting for system identification

I am having a really hard time in understanding how to formulate a model say linear AR model to represent a communication channel or maybe any motion. I have the experimental data representing the ...
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65 views

How to estimate an auto-regressive model?

Given a periodic impulse train and it's impulse response, how is an auto-regressive model of this system computed or estimated?
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2answers
732 views

Different state-space representations for Auto-Regression and Kalman filter

I see that there are different ways to write an AR model into a state-space representation, so that we can apply Kalman filter to estimate the signal. See Example 1, 2 and 3 here. I wonder what ...
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1answer
946 views

How to decide whether to use AR or MA for smoothing data?

Imagine I've got some offline data that I want to smooth. I could use an auto-regressive or moving-average filter of some appropriate order for conducting the smoothing. On which criteria should I ...
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1answer
220 views

Why does over-modelling an adaptive AR NLMS filter fix sharp spikes?

I just simulated an auto-regressive second-order model fueled by white noise and estimated the parameters with normalized least-mean-square filters of orders 1-4. As the first-order filter ...
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2answers
134 views

What input to use for an AR model of a vowel sound?

I've recorded a 2-sec pronunciation of a vowel sound. The first 0.12 or so seconds of the signal are shown below. Now, I've constructed an auto-regressive (AR) 8th-order model to compress this ...