Tagged Questions

1
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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 $0.5x_{t-1} + 0.3x_{t-2} + 0.2x_{t-3}$. ...
0
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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 ...
1
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0answers
31 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 ...
1
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1answer
35 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 ...
0
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0answers
55 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, ...
3
votes
1answer
95 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 ...
0
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1answer
57 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} \ \ \ \ \ \ $ ...
0
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1answer
116 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 ...
0
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0answers
52 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) ...
0
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2answers
180 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 ...
0
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0answers
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 ...
0
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2answers
123 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 ...
1
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0answers
62 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 ...
0
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0answers
114 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 ...
0
votes
1answer
99 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 ...
0
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3answers
805 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 ...
2
votes
1answer
73 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 ...
0
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0answers
227 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 ...
1
vote
1answer
84 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
votes
1answer
391 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 ...
2
votes
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 ...
2
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2answers
520 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?
1
vote
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 ...
3
votes
1answer
247 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 ...
2
votes
1answer
151 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 ...
3
votes
2answers
372 views

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 ...
1
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0answers
40 views

Modeling a TAR model that can handle the problem of outliers in nonlinear data

Can somebody please share idea on how I can model a TAR model that can handle outliers in nonlinear data? I need to compare such model with the general form of TAR model. Which computer software can ...
1
vote
1answer
289 views

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 ...
2
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0answers
437 views

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 ...
2
votes
0answers
102 views

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 ...
2
votes
2answers
208 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 ...
1
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1answer
256 views

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} + ...
7
votes
2answers
255 views

Is VAR a MANOVA with auto regression?

What are the differences between VAR (vector auto regression) and MANOVA?
3
votes
1answer
239 views

What is a vector autoregressive model?

I'm looking to understand this from a managerial perspective. For example if I was explaining linear regression I would say it is a line of best fit through some data points and it can be used to ...