The autoregressive tag has no wiki summary.
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24 views
Prediction of $X_{t+2}$ of an AR(2) process.
I want to find the best linear predictor, in MSE sense, of $\hat{X}_{t+2}$ in terms of $X_s'$s where $s \le t$ and $$X_t = \phi_1X_{t-1}+\phi_2X_{t-2} + Z_t\,,\, Z_t \sim WN(0,\sigma^2)$$
$X_t$ is ...
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1answer
42 views
what is the intuition behind stationarity condition for AR(p) process?
i get that you have to find the roots of the characteristic polynomial but can someone explain the intuition behind the roots must be outside the unit circle? what is a unit circle?
before anyone ...
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1answer
35 views
Exogeneous regressors in auto.arima and using them in forecast function in R
I'm trying to forecast a seasonal time series based on its historical values, and also two more time series (that are seasonal themselves.)
I'm trying to use an auto.arima, and I'm going to input ...
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1answer
77 views
Why are MA(q) time series models called “moving averages”?
When I read "moving average" in relation to a time series, I think something like $\frac{(x_{t-1} + x_{t-2} + x_{t-3})}3$, or perhaps a weighted average like $0.5x_{t-1} + 0.3x_{t-2} + 0.2x_{t-3}$. ...
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1answer
32 views
Question on Autoregressive equation.
Hi I was given a reduced form VAR model, where dependent variable is inflation, and independent variables include Inflation lagged by four periods (L.Inflation) and other exogenous variables.
The ...
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43 views
Testing for autocorrelation of the residuals
I'm trying to test for autocorrelation in the residuals of an AR(p) model in stata using the command varlmar.
The stata output is: "the exogenous variables may not be collinear with the dependent ...
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44 views
STATA - Procedure for properly estimating an AR(p)
I'm trying to estimate an autoregressive process AR(p).
Following the literature:
1) I checked if the series is stationary or not running the augmented Dickey-Fuller test (as I expected, the ...
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25 views
STATA - Correction for finite sample
I need for running an autoregressive model with correction for finite sample coefficients, following the model proposed by Shaman & Stine in 1989.
I usually use stata and matlab for my analysis, ...
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2answers
75 views
Need a clear and simple auto-regressive model example
This may be hard to find, but I'd like to read a well-explained auto-regressive model example that:
uses minimal math
extends the discussion beyond building a model into using that model to forecast ...
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0answers
32 views
Converting ARMA models to infinite AR process in R
I'm trying to recreate some test statistics that use the infinite AR representation of normal ARMA models. I found out about the function ARMAtoMA but have not been able to find the same functionality ...
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0answers
17 views
Estimating the variance of linear prediction coefficients and parameters
I'm using linear prediction with singular value decomposition (LPSVD) to analyze signals that are damped sinusoids. If my understanding of the theory of linear prediction is correct (and it may not ...
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1answer
37 views
How to estimate certain parameters of an AR model in R?
I need to estimate parameters of an AR model which is in the form of AR(1,11) it means that coefficients of AR orders from order 2 until order 10 are zero. How can I estimate these two parameters in ...
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56 views
TIme series analysis: ARCH-LM statstics and length of a time series
I have four 30-year long time series of daily correlated weather variables. I estimated a VAR model to the series using vars R package. Then, I executed seriality and normality test on VAR residuals, ...
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1answer
96 views
Why don't we look at $R^2$ when fitting an autoregressive model?
$R^2$ measures explained variance. In an autoregressive model like AR(k), we are carrying out a linear regression, and as such we would have an $R^2$ and an ...
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1answer
58 views
Autoregression model with a time trend term. Statistically valid?
Assume we have a time-series with a deterministic trend.
I'm wondering if the following model is well specified as an AR model:
$y_{t} = b_{0} + b_{1}t + b_{2}y_{t-1} + \epsilon_{t} \ \ \ \ \ \ $
...
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1answer
122 views
Step-by-step example of predicting time series with ARIMAX or ARMAX model?
I'm a newbie studying time series and I have a basic understanding of time series and the procedures, but from all the books and resources I have studied from I have not found a clear step-by-step ...
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0answers
32 views
State space representation using KFAS package
I am using KFAS package for R.
You can run
install.packages("KFAS")
library(KFAS)
?regSSM
...
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0answers
55 views
lag in prediction outputs in one-step ahead neural network autoregressive model
I am working on an ARX forecasting problem mostly using feed-forward neural networks in MATLAB. The functional model is of the form
$y(t) = f(y(t-1),...,y(t-n),u(t))$. My data is at half hourly ...
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53 views
How do I find the equation of an autoregressive process given its mean and non-constant growth rate?
A paper I'm reading states that:
$X$ is non-stationary with a growth rate of $g_t = \log \left(\dfrac{X_t}{X_{t-1}}\right)$ and follows an AR(1) process with mean $\mu$.
I know that AR(1) ...
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2answers
186 views
Time series prediction - what is Autoregressive Tree model ? (Python)
Our problem: model evolution of values of a continuous variable over time.
I came through a paper presenting an approach for predicting the next values for a time series. Whereas ARIMA model is more ...
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62 views
Help with determining the optimal AR-model order when using BIC?
I'm trying to build an AR-model for my temperature data and I'm using the Bayesian information criterion to determine the model order, but it seems my BIC-values keep decreasing the more I add ...
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2answers
124 views
Help with my time series ARX model prediction?
I have created an ARX-model where I predict the nitrogen oxide levels based on past values of nitrogen oxide with past exogenous input values nitrogen dioxide, temperature, atmospheric particulate ...
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54 views
Forecasting volatility using HAR-RV, residuals are greater than predicted value
I have tried using the following model (HAR-RV) to forecast volatility:
...
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1answer
126 views
How to decide the optimal AR-model order?
I'm trying to create AR-model on wheather data and I wondered is there a method or algorithm which can find the optimal order for an AR-model?
I'm using Matlab for my data-analysis, is there a ...
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0answers
64 views
What's a stationary VAR?
What is a stationary VAR (vector autoregression)?
Can a VAR with non-stationary variables be stationary?
How do you test whether a VAR is stationary or non-stationary? (Example in ...
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1answer
112 views
VAR vs STAR for space-time autoregression in Python
I want to use autoregressive model to build a predictor for some sets of spatio-temporal data. For example, I have historical traffic data (speeds at various segments of freeways). similarly, I have ...
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2answers
80 views
Confusion related to the calculation of autocovariance
I have a confusion related to the calculation of autocovariance
Suppose
$X_t = \phi X_{t-1} + \epsilon_t$
Then how the autocovariance
$E(X_{t+n}X_t) - \mu^2 = ...
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0answers
115 views
Difference between unrestricted VECM and restricted VECM?
What's the difference between an unrestricted and a restricted VECM?
I believe a hint lies within the cajorls()[1] function of R language's ...
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1answer
100 views
Putting stationary variables through Johansen procedure
Is it okay to feed $I(0)$ variables into the Johansen procedure? I've read three sources that seem to state that this is not what you're supposed to do. However, whenever I've done this, I notice that ...
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1answer
218 views
Biased estimates when intercept is included in a linear regression
I am simulating 10000 data-sets, each of length 20, that follow an autoregressive model with lag 1, using the following code:
...
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2answers
94 views
Evaluation of Autocorr/Part Autocorr values
I am practicing MA and AR modelling by using autocorrelation and partial autocorrelation values. My data is in the image below; I can see that only at lag 12 there is a value that might be considered ...
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3answers
809 views
AR(1) selection using sample ACF-PACF
The following graph shows the ACF (sample autocorrelation function) and PACF (partial autocorrelation function) of the residuals in a linear regression. There is a sinusoidal decay in the ACF and two ...
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1answer
74 views
Autoregressive model with exponential lags
I have a very highly sampled time series that I would like to fit an autoregressive model (AM) to (~3 million samples). From knowing what they represent, I have believe there should be unique ...
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431 views
R and EViews differences in AR(1) estimates
The main problem is: I cannot obtain similar parameter estimates with EViews and R.
For reasons I do not know myself, I need to estimate parameters for certain data using EViews. This is done by ...
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0answers
280 views
Autocorrelation of daily time-series using acf and pacf plots
I have a time series dataset with daily entries over the past 20 years.
I would like to see whether the series is autocorrelated.
To do so I have done the following>
...
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4answers
121 views
How to compute the standard error of the mean of an AR(1) process?
I try to compute the standard error of the mean for a demeaned AR(1) process $x_{t+1} = \rho x_t + \varepsilon_{t+1} =\sum\limits_{i=0}^{\infty} \rho^i \varepsilon_{t+1-i}$
Here is what I did:
$$
...
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1answer
317 views
Newey West standard errors give me more significance
I had a time series model with 5 time series variables and it's a model that's reputed in the literature for having autocorrelation problems. Why when I use standard OLS var-covar matrix only 2 ...
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0answers
77 views
(Quantile regression) AR(1) variable in the design matrix
I'm not doing a pure QAR (quantile auto regression) but I do have a lagged dependent variable (AR(1)) as a predictor. I'm using the quantreg package in ...
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229 views
Computing correlation coefficient for an AR(2) process in R using Yule-Walker equation for rho (for several lags) [closed]
I have a time series problem where I could easily work out the solution manually. The only problem is that it would take a long time since I have 4 different AR(2) processes and want to calculate at ...
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1answer
85 views
Deriving PDF in AutoRegressive Model
I hope that this is a right place and way to ask this question. I am trying to understand how to derive the probability density function of x(t) in an AR model of order K given (t-k) past ...
2
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1answer
392 views
Different results of Engle's Lagrange multiplier test for conditional heteroscedasticity from SAS and FinTS
To fit a simple AR(5) model, I use SAS PROC AUTOREG. I called the option ARCHTEST=(QLM) which provides Engle’s Lagrange ...
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2answers
172 views
What is better for time series prediction: AR or ARIMA?
I am trying to make a prediction in a time series with window 512 and horizon 2. I want to know if it's worth using ARIMA, that seems to be hard to understand, instead of the simple Autoregressive ...
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2answers
522 views
Stationary ARMA model as infinite AR or MA process
How can a stationary, invertible ARMA(1,1) process be represented as
either an infinite order AR or infinite order MA process?
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2answers
626 views
How to perform Prais-Winsten autoregression in SPSS 16? [closed]
When performing a linear regression on my dataset, Durbin-Watson was very low (0.276). I found a tutorial online that suggested performing an Prais-Winston autocorrelation. The tutoral came with ...
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1answer
61 views
Quantify volatility on a time series data
I am now working on a set of time series data and I would like to quantify the series' volatility.
I have think of an approach which is first model it as some auto-regressive model like ARCH and ...
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2answers
277 views
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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1answer
348 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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1answer
248 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 ...
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1answer
152 views
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
198 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 ...
