Questions tagged [autoregressive-model]
The autoregressive-model tag has no usage guidance.
0
votes
1answer
37 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
30 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
96 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
38 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
35 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
65 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
54 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
71 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
50 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 ...
0
votes
0answers
27 views
Time Series Extrapolation from existing past values
Using the Levinson-Durbin algorithm, I am trying to predict the next value in a time series based on previous observations, but the results do not follow the trend of the time series. How can I ...
2
votes
1answer
128 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
62 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
0answers
65 views
Autocorrelation Matrix of a AR process
i'm beggining to study signal processing, and i'm having trouble on writting it ( specially defining the signal x(n) ) in matlab and finding the solution for this problem, if anyone could help I would ...
0
votes
0answers
102 views
Using Kalman filter to estimate ARR (p) model's parameters
Recently I came across the fact that Kalman filtering can be used to estimate time-varying series parameters. Since I'm totally new to the time series type of data it wasn't a surprise I couldn't ...
0
votes
0answers
11 views
Scilab: How to use of “lev” and “filter” to model AR1 processes?
(Cross-posted from Stack Overflow) I need to fit an AR1 model to a series of values. Reading Scilab documentation, I came up with the method in the example below (edited with new code and more ...
0
votes
1answer
44 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
40 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
771 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
73 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
0answers
44 views
AR filter length
I need to use the AR filter for pre-whitening a time series data to do multi taper spectral analysis on them, . How can I choose the AR filter length?
0
votes
1answer
287 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
198 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
685 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
235 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
317 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
vote
0answers
51 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
272 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
80 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
137 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
199 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
546 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
542 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
147 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
70 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
0answers
628 views
How can I estimate a signal similar to my data using ar modeling in matlab
To be more specific, I have a time series which corresponds to a section from an EEG signal. The idea is obtain AR coefficients and then use these coefficients to create a simulation where I can get a ...
0
votes
1answer
590 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 ...
0
votes
0answers
409 views
Autoregressive Model for EEG frequency analysis?
I want to do EEG frequency analysis in matlab using autoregressive models (e.g. Burg's method). How do I do this correctly?
I just treated each channel individually (loop over channels), so I go ...
1
vote
1answer
270 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 ...
3
votes
1answer
237 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
3k 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
127 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
298 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
214 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
103 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
523 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 ...
0
votes
0answers
249 views
How to determine the order from Auto-Regressive model in Matlab?
I have time series vibration signal recorded for 10 seconds. I segmented the vibration signal into a number of frames. I need to use an Auto-regressive model for this signal. AR model is used to ...
1
vote
1answer
154 views
Forecasting with ARMA models, from a filter point of view
ARMA
models are afaik just filters with transfer function
$ {MA(z) \over AR(z)} \equiv {FIR(z) \over IIR(z)} $ .
However forecasters of stock prices, market trends ...
seem to be mainly ...
1
vote
0answers
37 views
Yule walker equation limited matrix size
Definitions
For an ARMA model
$$x_n=-\sum_{p=1}^P a_px_{n-p}+\sum_{q=0}^Qb_qw_{n-q}$$
where $w_n$ is zero mean stationary white noise with unit variance.
It is straightforward to show that the ...
2
votes
1answer
175 views
Conceptual Question from Signal Processing - Impulse Response and AR Coefficients
In continuation to the previous question Conceptual questions from signal processing I have a doubt which is: Consider an Autoregressive model (AR(2)):
$$
y(t) = ay(t-1) + by(t-2)
$$
and a FIR (...
0
votes
1answer
228 views
Issues in generating AR model with a constraint
I am new to the topic of system identification and looking for a large Autoregressive (AR) model. Can anybody point out a large stable AR model which has more than 2 coefficients AND there should be a ...
