Questions tagged [autoregressive-model]
The autoregressive-model tag has no usage guidance.
73
questions
0
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0answers
58 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 ...
0
votes
1answer
36 views
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)...
0
votes
1answer
43 views
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 ...
0
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0answers
30 views
Autocorrelation of an AR model
When I plot the autocorrelation function of an autoregressive signal, I get this instead of a damping sinusoid.
I am having trouble understanding why this is happening. My signal is an generated ...
0
votes
1answer
35 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 ...
0
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0answers
137 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 ...
0
votes
0answers
37 views
What is prewhitening filter mode?
In this paper, the following prewhitening filter is described:
$$
C(z) = \sum_{k=0}^n c_{k}z^{-k}
$$
where $n$ and $c_k$ are known.
The paper also describes the values $C(\lambda_{k})$, with $\...
0
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0answers
7 views
After fitting auto ARIMA's order, in prediction I'm getting bad result
For sunspot dataset.
Below is the ARIMA code. Auto ARIMA finds the best ARMA(2,1,2)(2,0,1) model. But when I plot the prediction seems wrong:
...
1
vote
1answer
115 views
Cost function for LTI system identification
I am currently reading and trying to understand a paper (Kulkarni and Colburn, 2004) that utilizes system identification methods to approximate head-related transfer functions.
The general approach ...
0
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0answers
112 views
Finding time-varying coefficients for a VAR model by using the Kalman Filter
I'm posting this again, since after my last post i've been able to advance the code quite alot. I'm still trying to write some code in R to reproduce the model i found in this article.
The idea is to ...
0
votes
1answer
105 views
How to characterize this whitening filter?
A little bit of background: I am interested in whitening in the least-square estimation.
In this sense, consider a univariate signal $y$. Assuming the covariance of $y$ is $\mathbf{A}\sigma^2$. ...
1
vote
0answers
104 views
Zero-padding vs. nonzero-padding in computation of auto-correlation with FFT
Isn't the usual zero-padding in the computation of the auto-correlation function with FFT just one of many possible extrapolations of the original signal?
If I have a measured signal which has good ...
0
votes
1answer
145 views
Fast Recursive 1D Signal Smoothing - IIR / Auto Regressive Implementation of Gaussian Smoothing
I have just begun to dive into the field of signal processing, but there is the need to program a digital filter, that has to smooth a realtime signal from a sensor device. As far as I know, in my ...
0
votes
1answer
65 views
AR Modeling: Why residual is white noise?
I was going through AR modeling.
The AR model of a covariance stationary process can be expressed as:
$$x[n]=\sum\limits_{i=1}^{p} \alpha_i x[n-i] + \epsilon[n]$$
where $p$ is the model order and $...
1
vote
0answers
751 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 ...
1
vote
0answers
97 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 ...
1
vote
1answer
63 views
Explanation of Spectral Line Splitting when AR process is overmodeled
In the book Statistical Digital Signal Processing and Modeling by Monson Hayes, it is shown (in section 8.5.1) that when an AR(2) process described by the following difference equation
$$x(n) = 0.9x(n-...
1
vote
1answer
710 views
Simplest way to generate AR(2) process on MATLAB
As part of a project I need to use autocorrelation method of estimating model paramters of an autoregressive process on MATLAB.
Can anyone tell me the simplest way to generate an AR(2) process on ...
0
votes
1answer
92 views
ARMA & MA methods: how do you know the error terms?
Reading the ARMA model for the first time, and I'm confused.
Let's say I have a time series
x = [1, 2.1, 2.9, 3, 4.1]
According to the ARMA model, $X_t$ is a ...
1
vote
1answer
203 views
Find filter coefficients to model a device using its measurement
I am trying to realize a digital filter that has the same freq. response of an existing speaker. I have fed an audio sine sweep to the speaker and measured the speaker output, both at 48kHz. Then I ...
2
votes
2answers
81 views
Finding the auto-correlation sequence $r_{xx}[k]$ for an AR(2) process
Consider the following recursive difference equation of a LTI system, where $v[n]$ is a white noise, zero-mean process with $\sigma_v^2 = 1$.
$
x[n] = v[n] + 0.75x[n-1]-0.25x[n-2]
$
I want to ...
2
votes
1answer
404 views
Linear Predictive coding vs AR modeling
I'm looking for a suitable explanation of the circumstances in which the LPC error polynomial for a discrete time process x[n] is replaceable with an error polynomial categorized under the AR model? I ...
1
vote
2answers
85 views
Difference Between Two Forms of Equations of Auto Regressive (AR) Model
I found equation 1 for Autoregressive model in various books and articles but i also found equation 2 for AR model, I understand the physical meaning of the equation but two different equations ...
0
votes
1answer
116 views
Find the coefficient of an AR-model
How can I infer the coefficients for an AR(2) model given an autocorrelation plot?
What I have tried so far: I can see this a cos-wave of 0.4 Hz, and then i find the values for each step $(1, 0.9211, ...
0
votes
2answers
44 views
Confusion regarding model order and lags
I have similar questions as the one asked in these posts: https://stackoverflow.com/questions/47083890/fir-filter-length-is-the-intercept-included-as-a-coefficient-matlab/47085339?noredirect=1#...
0
votes
1answer
1k views
How to generate colored Gaussian noise and adding it to a ODE system - Do I need Euler-Maruyama method?
In the tutorial, when white noise process is added to ordinary differential equations (ODE), the ODE becomes a stochastic process. Then the stochastic process needs to be solved using Euler Maruyama ...
0
votes
1answer
150 views
Autoregressive Exogenous model on multiple datasets in MATLAB
I had trouble translating this exact question into search queries, which is why I am turning to you. Any sources you can provide on the topic would be greatly appreciated.
Say your data contains ...
0
votes
1answer
480 views
Finding autocorrelation matrix of an autoregressive process AR(1)
Having that $\ v(n) = [x(n),x(n-1),x(n-2))]^T $, and being $\ x(n) $ an autoregressive process AR(1) with known variance $\ \sigma_v^2 $ and transfer function $\ H(z) ={ 1 \over {1-0.7z^-1}}$, how ...
2
votes
1answer
232 views
Autoregressive modeling (linear prediction) of electrical transmission lines?
I've read that the reflection coefficients in speech processing (as computed by the Levinson-Durbin algorithm for solving the Yule-Walker equations) "represent the fraction of energy reflected back" ...
0
votes
1answer
1k views
How to create an AR filter in Matlab
My goal is to replicate the procedure described on pages 15-16 (1461-1462) in this paper, prior to adaptive mixture ICA (AMICA): Overlearning in Marginal Distribution-Based ICA: Analysis and Solutions
...
1
vote
1answer
384 views
autoregressive moving average code implementation
I am new to DSP and i am trying to take a wav (human speech) file and apply ARMA filter and plot its PSD graph in python.
I see that there are a lot of AR implementations but almost none ARMA. I ...
-1
votes
2answers
528 views
Levinson Method
i have just one question about Levinson, my question is: can we apply this method to determine the coefficients for FIR filter? if yes, please help me !
this is an example:
...
1
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0answers
80 views
derive AR model based on the autocorrelation of jakes model
I am trying to derive the channel model based on the autocorrelation of Jakes model.
In step 2, i am trying to get rid of $s(n+1)$ by inserting it to $s(n-k)$ in which the limit will change. However i ...
2
votes
1answer
544 views
Predicting account balance based on historical data
Given the values of a bank account balance over time (see figure below as an example), how can one predict the account balance at a given date in the future ?
Should I just fit one linear regression ...
2
votes
1answer
83 views
Two-Box-Model of a nonlinear amplifier
A nonlinearity with memory can be modelled by a two-box-model, which consists of a filter and a memoryless nonlinearity. I am referring to chapter 5.3.2 of the book "Simulation of Communication ...
1
vote
1answer
157 views
Fourier transform relationship
I am having trouble understanding the relationship between a frequency function and it's Inverse Fourier transform.
The Frequency function is
$$\frac{1+0.8(e^{-j 2\pi f}+e^{j 2\pi f})+0.64}{1+1.4\...
1
vote
1answer
253 views
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.
...
1
vote
2answers
813 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 $v(n) \sim \mathcal{N}(0, \sigma^2)$...
0
votes
1answer
835 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 ...
1
vote
1answer
261 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)&...
0
votes
1answer
130 views
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 ...
0
votes
1answer
753 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 ...
1
vote
1answer
322 views
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 ...
2
votes
1answer
320 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 ...
2
votes
1answer
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 ...
1
vote
0answers
168 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)?
0
votes
1answer
320 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 ...
2
votes
0answers
373 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 ...
0
votes
0answers
119 views
how to find the distance of the root from the origin?
Good Day, I have 9 polynomial roots. i have plotted the roots. my problems are:
1)how to find the distance of the roots from origin? I want to find the distance of all the roots from the origin.
2) ...
0
votes
1answer
750 views
How to plot the root of polynomial in Matlab?
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 ...
