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# Questions tagged [autoregressive-model]

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### Why does over-modelling an adaptive AR NLMS filter fix sharp spikes?

I just simulated an auto-regressive second-order model fueled by white noise and estimated the parameters with normalized least-mean-square filters of orders 1-4. As the first-order filter under-...
5k views

### Different state-space representations for Auto-Regression and Kalman filter

I see that there are different ways to write an AR model into a state-space representation, so that we can apply Kalman filter to estimate the signal. See Example 1, 2 and 3 here. I wonder what ...
256 views

### What input to use for an AR model of a vowel sound?

I've recorded a 2-sec pronunciation of a vowel sound. The first 0.12 or so seconds of the signal are shown below. Now, I've constructed an auto-regressive (AR) 8th-order model to compress this signal....
317 views

### How to perform model fitting for system identification

I am having a really hard time in understanding how to formulate a model say linear AR model to represent a communication channel or maybe any motion. I have the experimental data representing the ...
2k views

### How to decide whether to use AR or MA for smoothing data?

Imagine I've got some offline data that I want to smooth. I could use an auto-regressive or moving-average filter of some appropriate order for conducting the smoothing. On which criteria should I ...
3k views

### ARMA vs. AR and then what?

Sorry if this sounds elementary but I am struggling to grasp the physical idea behind ARMA (auto-regressive, moving average) process. The "AR" part is intuitive and so is "MA", but put together? If I ...
7k views

### What are Autoregressive Coefficients?

Can anyone explain what are Autoregressive Coefficients? What is their meaning that is. Consider a method: ...
184 views

### ARMA (Auto Regressive Mean Average) Process Representation as AR (Auto Regressive)

Let's say we have an ARMA (Auto Regressive Moving Average Model) process where the transfer function is a minimum phase system (Namely Invertible). By Wold's Decomposition it is guaranteed to have MA ...
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 ...
267 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 ...
91 views

### Choosing inverse Z-transform equation, given that $|a|<1$

Given that $|a|<1$, then which of those inverse-Z-transform equations are we to use? I am leaning towards the first because (as I understand it), $z$ is merely a complex number that is evaluated ...
79 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 ...
295 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 ...
436 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 ...
192 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 ...
189 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 (...
225 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" ...
81 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 ...
289 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 ...
112 views

### How to estimate an auto-regressive model?

Given a periodic impulse train and it's impulse response, how is an auto-regressive model of this system computed or estimated?
447 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 ...
758 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 $v(n) \sim \mathcal{N}(0, \sigma^2)$...
191 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)&...
606 views

### Can someone show the details of how to apply AIC for sinusoidal models to specific data?

NOTE: This is a question that another user has been trying (unsuccessfully) to ask. Because the multiple questions asking, essentially, the same thing have either been deleted by me (because they were ...
86 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 ...
46 views

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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. ...
298 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 ...
60 views

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 ...
477 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 ...
78 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 ...
141 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 ...
330 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 ...
67 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 ...
155 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)?
38 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 ...
261 views

### ACF and PACF Confidence Levels for ARMA

I'm trying to figure out where exactly to draw the confidence levels for the autocorrleation function (ACF) and the partial autocorrelation function (PACF) for an ARMA model. For PACF I found that a ...
68 views

### Is a Stationary VAR Process with Zero Mean Gaussian Innovations a Gaussian Stationary Process?

Consider the stationary VAR process $${\bf X}_t = \sum_{\tau = 1}^{L} A_\tau {\bf X}_{t-\tau} +{\bf \epsilon}_t$$ If the innovations $\epsilon_t \sim MVN({\bf 0},\Sigma)$ then is ${\bf X}_t$ a ...
62 views

### Fitting VAR Process with Generalised Gaussian Noise

Consider the $m$-dimensional VAR process $${\bf x}_t = \sum_{l=1}^{P} A_l{\bf x}_{t-l} + {\bf e}_t$$ where the componenets of ${\bf e}_t$ are spatially and temporally independent and follow a ...
2k views

### Power spectral density interpretation

After reading this question: PSD (Power spectral density) explanation I am still a little confused as to what extra information the PSD gives us over simply taking the magnitude of the fourier ...
752 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 ...
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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#...