# Questions tagged [autoregressive-model]

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### prediction error in AR model

Stoica, Petre, and Randolph L. Moses. "Spectral analysis of signals." (2005) page 91 eq. 3.4.7 describes $y(t)$ as autoregressive process of order $n$ by Here, $e(t)$ is the system input ...
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### Compute objective speech quality from Anritsu data

I want to compute an objective speech quality however what I have right now is the Anritsu raw data (layer between the Base Station Controller and the Mobile Switching Center), this raw data does not ...
39 views

### ARMA Filter Output Stationary and set up?

I have questions regarding ARMA Filters. Is the output of a ARMA Filter stationary or just wide sense stationary? I do know that you can obtain an ARMA filter by connecting an MA filter with an AR ...
62 views

### How to calculate the coefficients of Auto regression model of multiple data?

I have ACF of a time series data, I want to interpolate the ACF using AR model for which I need to calculate the coefficient of the AR model The problem is I have (6000x6000) matrix of ACF and I cant ...
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### Implementing the noisy AR(1) Process

I'm trying to implement noisy AR(1) process and plot it. The observed noisy sequence x(n) = s(n) + w(n) where variance of w(n) = 0.2. s(n) is defined as an AR(1) process with s(n) = 0.5 s(n-1) + e(n)...
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### estimation of ARMA(1,1) with MA parameter greater than 1

I am working with the following simple ARMA(1,1) model: $$z_{t+1} = \phi z_{t} + \theta\varepsilon_{t} + \varepsilon_{t+1}$$ In my case $\theta$ depends on some other parameters, and, therefore, I ...
56 views

### Linear prediction and filter stability

I am currently trying to implement an iterative block-wise algorithm in which AR coefficients are computed for each block. There is a issue with my code where values get too large, and I was ...
176 views

### How to find Coefficients of Autoregressive (AR) model using least means square (LMS) Algorithm without having future signal?

I want to do two things. Estimating Coefficients of AR model using LMS Using Coefficients found in step 1 and predict future samples of a signal using AR equation. I don't have a desired signal so I ...
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983 views

### Linear Predictive Coding example in MATLAB

I have some data that is highly correlated and I wanted to see if I could try and encode it using linear predictive coding (LPC). Here is how I've been understanding the process: Encoding Generate ...
108 views

### Understanding linear predictive coding in MATLAB

I want to test my understanding of linear prediction by running it on some test data in MATLAB. The way I understand it is if I have some data that is correlated, I can encode the signal with linear ...
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### Physically understanding autoregressive model (really basic question)

I would like to basically understand what an autoregressive model is used for (so I don't really attempt maths in the answers). I just started a signal processing course and the model was introduced. ...
861 views

### Practical examples of ARMA model

I am studying the Kalman filter and its basic implementation, and it was asked to use the filter to estimate a signal observed in noise $$y(n) = x(n) + v(n)$$ where $v(n) \sim \mathcal{N}(0, \sigma^2)$...
907 views

### How to estimate the autocorrelation from nonuniformly spaced data

Assume a continues-time random process $X(t)$ sampled nonuniformely in time to acquire discrete signal $x[n]$. The sampling times are known but the autocorrelation is not. Is there an accurate ...
351 views

### How do I test stability of a MIMO system?

Let's say I have a system similar to two interconnected IIR filters described like this: \begin{align} x_1(t)&=a_{11} x_1(t-1)+a_{12} x_1(t-2) +a_{13} x_2(t-1) + a_{14} x_2(t-2)+y_1(t)\\ x_2(t)&...
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### Different results for different orders of estimating AR model using Yule-Walker equations

I'm trying to use MATLAB to estimate the AR parameters to the following filter: $$H(z) = \frac{1}{1-0.5z^{-1}+0.25z^{-2} -0.25z^{-4}}$$ As I can see, the process at the output of this filter depends ...
781 views

### Determining the autocorrelation sequence from an AR model

I have the following equation: $$x(n)=\frac{14}{24}x(n-1)+\frac{9}{24}x(n-2)-\frac{1}{24}x(n-3)+w(n)$$ where, $w(n)$ is a stationary white noise process with variance $\sigma^2_w$ Now, I want to ...
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### How can I reconstruct a Time series using it AR coefficients in MATLAB?

I have estimated AR coefficients of a time series using "aryule" function in MATLAB. Now I want to obtain the error of the estimated model. I think at first I must reconstruct it. so How can I ...
331 views

### Linear Prediction of AR Process

A discrete signal x is generated by the recursive process $$x_n = x_{n-1} - 0.2 x_{n-2} + w_n$$ where $w_n$ is white noise with zero mean and unit variance. What is the optimum order of a linear ...
5k views

### Filtering a signal using Autoregressive (AR) filter and finding the coeff of AR filter using Yule Walker equation in MATLAB

I have a random signal x of 1000 samples and I've to generate y1 by filtering x using an ...
184 views

### What is a “Unit Shock” in an Impulse Response Function?

Is a "one unit shock" in an impulse function of variable "temperature" a 1% increase or 1 more "unit" (1 degree)?
324 views

### AR model order selection for half second EEG fragments

I am using MATLAB to evaluate power spectral density estimates of half second EEG signals, using modified covariance method. Can anyone suggest me how to select the AR model order for this process? Is ...
434 views

### How to evaluate performance of an ARMA, MA or AR model?

How to evaluate performance of a model after estimating ARMA/MA/AR parameters for any process x(n)? How to regenerate back a process after estimating average parameters? what kind of performance ...
I obtained this polynomial equations: $$A(z) = 1 - 0.7987 z^{-1} - 0.125 z^{-2} - 0.511 z^{-3} + 0.06889 z^{-4} + 0.3465 z^{-5} + 0.4809 z^{-6} + 0.04951 z^{-7} - 0.5298 z^{-8} + 0.1828 z^{-9}$$ How ...