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Questions tagged [autoregressive-model]

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1answer
18 views

Looking for suitable methods to check goodness of a model based on the residuals or prediction errors

I am looking for suitable methods to check goodness of my model based on the residuals or prediction errors. I want to make sure that the model residuals or prediction errors are normally distributed ...
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0answers
39 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 ...
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0answers
28 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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1answer
27 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-...
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27 views

Estimating Parameters (Coefficients) of Autoregressive (AR) Equation using Least Means Square (LMS) Algorithm

I want to do two things. Estimating Coefficients of AR model using LMS filter Using Coefficients found in step 1 and predict future samples of a signal using AR equation. I don't have a desired ...
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0answers
35 views

How to code this autocorrelation-related problem in MATLAB? [closed]

I am trying to implement the autocorrelation-method (also known as Yule-Walker method) to estimate the model parameters of an AR model, from the book Statistical Digital Signal Processing and ...
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1answer
42 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
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1answer
51 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 ...
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1answer
59 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 ...
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2answers
47 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 ...
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24 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
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1answer
87 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 ...
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2answers
55 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 ...
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0answers
53 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 ...
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0answers
80 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 ...
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0answers
9 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 ...
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1answer
41 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, ...
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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#...
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1answer
645 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 ...
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1answer
59 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 ...
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0answers
38 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
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1answer
252 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
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1answer
180 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
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1answer
613 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 ...
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1answer
208 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 ...
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0answers
82 views

MSE and time delay relation

I have time series for which I used autocorrelation property and made autoregression model for prediction, with different time delays $0-30$. I got diagram which is dependency MSE on time delay $0-30$...
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2answers
277 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: ...
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0answers
43 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
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1answer
230 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
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1answer
79 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
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1answer
126 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
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1answer
183 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. ...
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2answers
481 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 $v(n) \sim \mathcal{N}(0, \sigma^2)$...
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1answer
500 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
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1answer
139 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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1answer
65 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 ...
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0answers
604 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
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1answer
556 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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0answers
392 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 ...
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1answer
257 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
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1answer
210 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
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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 ...
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0answers
121 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
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1answer
281 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
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0answers
194 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 ...
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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) ...
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1answer
486 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 ...
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0answers
244 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 ...
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1answer
139 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 ...
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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 ...