Questions tagged [autoregressive-model]
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94 questions
1 vote
1 answer
82 views
Jittering in time-interleaved ADCs
I am doing some research on Time-interleaved Analog-to-Digital Converters impairments modeling and I am trying to figuring out which physical phenomenon I am witnessing (I am not an engineer, so my ...
- 113
0 votes
1 answer
38 views
How to Solve a Least Absolute Deviation Problem in R
We have the following time series model: $$y_t=a+b\cdot t+e_t\quad\text{for}\quad t=1,\ldots,T$$ where $y_t$ is the observation at instant $t$, $e_t$ is an AR(1), i.e. $$e_t=\psi\cdot e_{t-1}+\...
- 111
1 vote
0 answers
61 views
Parameter value in bias instability modeling
In IMU error modeling, bias instability/flicker noise is often modeled by a first order Gauss-Markov process whose standard deviation is equal to the given BI coefficient [1, p.185][2, p.31]. Because ...
- 11
1 vote
1 answer
85 views
Understanding Autoregressive Models
I am studying autoregressive models such as ${\it AR}(1)$, ${\it AR}(2)$, ${\it AR}(p)$, and ${\it ARMA}$, as well as the Yule-Walker equations, specifically in the field of electrical engineering. ...
- 109
1 vote
0 answers
137 views
Proof that the order of a linear prediction model cannot be reduced by analysing non-adjacent points
I have a signal, for which a linear prediction model of order $M$ can be constructed. This means, that a system of the shape $$ \begin{bmatrix} s_0 & s_1 & \cdots & s_M \\ s_1 & s_2 &...
- 11
2 votes
2 answers
328 views
insights into making AR Burg extrapolate finite periodic signals
Following a past question, I'd like to extrapolate a periodic signal using AR Burg, but when doing so, it seems that I need to sample "enough" for that to work. For example, if I use the ...
- 588
1 vote
1 answer
240 views
Interpretation of a non-canonical Allan Variance plot
I am currently working on characterizing the noise sources of a Global Navigation Satellite System (GNSS) sensor using an Allan Variance plot, which is commonly employed to analyze frequency stability ...
- 13
7 votes
3 answers
574 views
Why use an ARMA process theory instead of just performing linear regression?
I am studying ARMA processes. At the end of the course the professor told us that estimating the next sample in an arma process using past of length $p$ (so performing a projection of $X_t$ on $\text{...
2 votes
0 answers
36 views
Haykin - permissible region for asymptotic stationarity of 2 parameter AR process
My question is about an example in Adaptive Filter Theory, Haykin 4th ed (refer figures 1.8 and 1.10 of Haykin). We want to determine the region for asymptotic stationarity of an AR process in the 2D ...
- 23
0 votes
0 answers
81 views
Reconstruction of original signal after minimum phase filter
The question is pretty self explanatory. I want to know if it is possible to recover a signal originally injected into noisy data (coloured gaussian noise) after whitening the data with an AR minimum ...
- 31
2 votes
2 answers
1k views
Why is ARMA preferred instead of AR?
ARMA basically is an AR model which considers past inputs to the filter as well. But what is the benefit of taking past inputs to the filter if we are considering real-time processes which are all ...
1 vote
0 answers
40 views
How to show that the autocorrelation function of the given discrete function is this for autoregressive model(AR(2))?
This question is related to white noise representation of WSS sequences using AR(2) (autoregressive) model The function is given as: $$x(k)=\frac{1}{p_1-p_2}(p_1^{k+1}-p_2^{k+1})w[k]u[k]$$ where $w[k]$...
- 195
-1 votes
1 answer
181 views
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 ...
2 votes
1 answer
147 views
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,\...
- 131
4 votes
1 answer
196 views
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 ...
- 55