Questions tagged [autoregressive]

The autoregressive (AR) model is a stochastic process modelling time series, which specifies the value of the series linearly in terms of the previous values.

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Do low $R^2$ values mean that my vector autoregressive model is bad?

I have a VAR model, which shows very low $R^2$ values (below 0.05). Does this mean that my model is very bad in explaining?
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6k views

How to interpret coefficients in a vector autoregressive model?

Can I interpret the coefficients in a VAR model in the same way as I do in a normal OLS regression?
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818 views

Testing periodogram “peaks”: sine-like wave or AR/MA/ARMA noise?

I'm performing an harmonic fit to data I know (from physical constraints) come from a periodic source of the form $$\sum_j^M \sum_i^N a_{i,j}\sin(2\pi f_it)+b_{i,j}\cos(2\pi f_it)$$ using the Lomb-...
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Boosted AR for time series forecasting?

I have time series data recorded at multiple locations, stored in a matrix $Y$. I have fit a Vector Autoregressive Model to it which forecasts the data pretty well on a test set. However, if I plot ...
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1answer
637 views

Vector autoregression - number of lags

I am constructing a Vector autoregression model and I have used AIC to find how many lags I should use. Does 7 lags seem unreasonable? I am trying to find the impact the property market has had on the ...
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What does R do when it plots the residuals of an AR fit?

This is a question that's been bugging me for some time. The problem is this: I'm modelling the residuals of a model $f(t,\vec{\theta})$ with (what I think is) an AR process plus a white noise process ...
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1answer
2k views

Do data and residuals of a VAR model have to be of normal distribution?

Does vector autoregression (VAR) model require data to be of normal distribution? What are the pitfalls if the residuals are not of normal distribution?
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1answer
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How to fit the coefficients of a first order linear auto-regressive function without noise in the model, and the coefficient are equal?

I have a simple auto-regressive function: $x_{i+1} = c - cx_{i}$ It is linear and first order. There is no noise in the model ...
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2answers
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Invertibility of AR(p) model

Notation: $\dot{Z}_t = Z_t - E(Z_t)$, so that it is centered at 0. $a_t$ stands for the residual and we assume the $a_t$ are independent and normally distributed with mean 0 and constant standard ...
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0answers
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Use of autoregressive metric for ARIMA clustering and analysis

I wonder if anyone has put into use the autoregressive metric for ARIMA clustering proposed by Corduas and Piccolo (2008). The authors define the distance autoregressive metric between two processes $...
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1answer
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Problem simulating AR(2) process

OP EDIT: There where no problem with this. The problem was with the method I was using for obtaining the PACF. Apparently it doesn't work quite well in this case (I was using the scikits/tsa python ...
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Poisson with an autoregressive term

I want to fit a fairly "standard" Poisson model, but with an autoregressive term. $N_i \sim \mathrm{Pois}( \lambda_i E_i)$ with $\log \lambda_i = X_i \beta + \delta$ $\delta \sim AR(1)$ $X_i$ is a ...
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455 views

Test for independence of random variables

I have a time series of data (about 300-750 elements, depending on the sample) and a model that has some random residues. I used the Kolmogorov–Smirnov test to make sure that the normality hypothesis ...
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1answer
665 views

Long term and short term effect of estimators on AR model

How do we find out the long term and short term effect of estimators on AR model?
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1answer
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Calculate frequency of 1D time series using autoregressive model parameters

I'm modeling some periodic data with a second-order autoregressive model, as follows: $$ x_3 = a_{1}x_1 + a_{2}x_2 $$ $$ x_4 = a_{1}x_2 + a_{2}x_3 $$ $$ ... $$ $$ x_n = a_{1}x_{n-2} + a_{2}x_{...
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In spatial regression, what is a spherical autocorrelation structure?

I have a large gridded dataset for the globe (i.e a spherical, wraparound surface) that I'm applying spatial regression to (using a CAR model). I've been using the default autocorrelation function, ...
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664 views

Is VAR a MANOVA with auto regression?

What are the differences between VAR (vector auto regression) and MANOVA?
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1answer
603 views

How can I convert a Gauss-Markov process to i.i.d. Gaussian process?

I am wondering is there any straight forward approach to convert a Gauss-Markov process, i.e., a First order autoregressive process with i.i.d. Gaussian input, with the covariance matrix $K=Toeplitz(1,...
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688 views

What is the expected value of the sample variance under a linear regression with omitted variables of an AR(2) process?

Lately, I have been interested in phenomenons related to omission of variables. For example, it can be shown that the expected value of the sample variance under the inclusion of one variable $x_1$ ...