Questions tagged [autoregressive-model]
The autoregressive-model tag has no usage guidance.
87
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Deterministic process, what is it ? how can i get a better intuition for it?
so I was following this code where the author cleans the data for a time series problem. He does some feature engineering , all is well and good
until he does this
...
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Particle Filter estimation: sinusoidal signal
I am designing a particle filter for the extraction of a sinusoidal wave with known frequency and sampling frequency from Gaussian noised biased measurements ($y=x+\text{bias}+\text{Noise}$)
My state ...
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How to determine the area for the coefficients of an AR model to be asymptotically stable?
I am pretty new to this topic, and I am a little confused about the definition of asymptotically stable.
If I have an AR model as follows
$$y(t)=a_1y(t-1)+a_2y(t-2)+e(t)$$
How to define the area in ...
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difference in the spectral densities of autoregressive sequence by FFT and analytical solution
I want to obtain the power spectral density (PSD) of an autoregressive sequence, AR(1). The analytical solution according to this reference (page 12) is
For $X_t = \phi_1X_{t-1}+W_t, W_t \sim N(0,\...
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Predicting at différents steps
Let an autoregressive filter, with time step $T$ seconds, model a pink noise. Raw data is available at $f >> 1/T$.
The model is trained on data undersampled and locally averaged (using a sliding ...
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146
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Frequency representation of relaxation processes
I simulated a discrete sample of a variable whose autocorrelation function (ACF) should theoretically be composed of a sum of exponential-like functions.
My goal is to represent it in the frequency ...
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Given an AR signal, find its PSD, its autocorrelation function
I am studying discrete-random signal processing, Could anyone tell me by an example or reference what it means by the following?
Given an AR signal, find its PSD (power spectral density), its ...
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2D space and 1D time evolution of a random field
I also asked this on math stack-exchange, but it is also relevant for the signal processing community.
I want to develop a 2D random field and its change with time with constant velocity. My process:
...
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204
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How to compute the theoretical power spectrum of a first order autoregression (AR1) model
I'm trying to figure out how to compute the theoretical power spectrum of a first-order autoregression model (AR1).
The AR1 model is given as
$x_i = r_1 x_{i-1} + e_i$
where:
$x_i$ is real-valued ...
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66
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System identification for a single-input-single-output-system
Let $u(n)$ be the input and $v(n)$ the output of a single-input-single-output system described by the Auto-Regressive-Moving-Average equation $$v(n)=\sum_{k=0}^{m_{0}}b_ku(n-k)+\sum_{k=1}^{n_{0}}a_{k}...
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How to select the ARMA model parameters?
I have a series of data containing 120,000 points. The mean of each N(=60) point is zero. I want to forecast the next 60 points using the ARMA model. My question is, specificaly, how to choose the ...
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How to get velocity from PSD graph
Hello everyone!
I have a graph, which is Spectra inside cavity. PSD vs. frequency.
I need to get velocity [m/s] from PSD [dB/Hz].
Does anyone know how to do that?
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Ringing/Oscillation in the reconstructed Periodogram
I have an original periodogram that I need to model with autoregressive process. However the model isn't right as it is not fitted well to the original periodogram.
I am suspecting I am doing ...
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When is Markov a Martingale
I have two questions and I am very confused about the concepts
Can a Markov process of order one also be a a Martingale?
Is any Markov process of order one also a Martingale?
For 1. I would say yes, ...
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102
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What are the most suitable methods for correcting sudden DC offsets or baseline offset? and Why? See the image for the use-case or example
The signal values should not get affected by the correction. Most methods I found were related to baseline drift or exponential baseline shift/decay. I am unable to find a method suitable for my use ...
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158
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Extrapolation of sinusoidal signal
Let there be a discrete signal that is the sum of sinusoidals and can be described by
$$s(n)=\sum_i A_i \mathrm{sin}(2\pi f_i \frac{n}{f_s}+\phi_i)$$
where $A_i, f_i, \phi_i$ are unknown but fixed ...
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Compute objective speech quality from Anritsu data
I want to compute an objective speech quality however what I have right now is the Anritsu raw data (layer between the Base Station Controller and the Mobile Switching Center), this raw data does not ...
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1
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70
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ARMA Filter Output Stationary and set up?
I have questions regarding ARMA Filters.
Is the output of a ARMA Filter stationary or just wide sense stationary?
I do know that you can obtain an ARMA filter by connecting an MA filter with an AR ...
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1
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107
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Implementing the noisy AR(1) Process
I'm trying to implement noisy AR(1) process and plot it. The observed noisy sequence x(n) = s(n) + w(n) where variance of w(n) = 0.2.
s(n) is defined as an AR(1) process with s(n) = 0.5 s(n-1) + e(n)...
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estimation of ARMA(1,1) with MA parameter greater than 1
I am working with the following simple ARMA(1,1) model:
$$
z_{t+1} = \phi z_{t} + \theta\varepsilon_{t} + \varepsilon_{t+1}
$$
In my case $\theta$ depends on some other parameters, and, therefore, I ...
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Linear prediction and filter stability
I am currently trying to implement an iterative block-wise algorithm in which AR coefficients are computed for each block.
There is a issue with my code where values get too large, and I was ...
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Learning the Coefficients of Auto Regressive (AR) Model Using Least Mean Squares (LMS) Filter for Signal Prediction
I want to do two things.
Estimating Coefficients of AR model using LMS
Using Coefficients found in step 1 and predict future samples of a signal using AR equation.
I don't have a desired signal so I ...
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What is prewhitening filter mode?
In this paper, the following prewhitening filter is described:
$$
C(z) = \sum_{k=0}^n c_{k}z^{-k}
$$
where $n$ and $c_k$ are known.
The paper also describes the values $C(\lambda_{k})$, with $\...
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Cost function for LTI system identification
I am currently reading and trying to understand a paper (Kulkarni and Colburn, 2004) that utilizes system identification methods to approximate head-related transfer functions.
The general approach ...
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1
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168
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How to characterize this whitening filter?
A little bit of background: I am interested in whitening in the least-square estimation.
In this sense, consider a univariate signal $y$. Assuming the covariance of $y$ is $\mathbf{A}\sigma^2$. ...
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426
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Zero-padding vs. nonzero-padding in computation of auto-correlation with FFT
Isn't the usual zero-padding in the computation of the auto-correlation function with FFT just one of many possible extrapolations of the original signal?
If I have a measured signal which has good ...
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Fast Recursive 1D Signal Smoothing - IIR / Auto Regressive Implementation of Gaussian Smoothing
I have just begun to dive into the field of signal processing, but there is the need to program a digital filter, that has to smooth a realtime signal from a sensor device. As far as I know, in my ...
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AR Modeling: Why residual is white noise?
I was going through AR modeling.
The AR model of a covariance stationary process can be expressed as:
$$x[n]=\sum\limits_{i=1}^{p} \alpha_i x[n-i] + \epsilon[n]$$
where $p$ is the model order and $...
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Linear Predictive Coding example in MATLAB
I have some data that is highly correlated and I wanted to see if I could try and encode it using linear predictive coding (LPC). Here is how I've been understanding the process:
Encoding
Generate ...
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158
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Understanding linear predictive coding in MATLAB
I want to test my understanding of linear prediction by running it on some test data in MATLAB. The way I understand it is if I have some data that is correlated, I can encode the signal with linear ...
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Explanation of Spectral Line Splitting when AR process is overmodeled
In the book Statistical Digital Signal Processing and Modeling by Monson Hayes, it is shown (in section 8.5.1) that when an AR(2) process described by the following difference equation
$$x(n) = 0.9x(n-...
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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 ...
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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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578
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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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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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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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136
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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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1
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332
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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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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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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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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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683
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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 ...
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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" ...
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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
...
user16743
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595
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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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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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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 ...
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765
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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 ...
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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 ...
user25356
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168
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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\...
