1
vote
1answer
30 views

How to interpret the expression of MA(1) as AR($\infty$)

When AR(1) is expressed as MA($\infty$), I can interpret it as: let's say my wage this year depends only on last year's wage and a random shock (my boss' mood). But last year's wage also depends on ...
2
votes
1answer
39 views

What does “AR(p) filtered series” mean?

I guess this means that omitting some variables in a certain interval, say, $(x_1, x_2, x_3, x_4, x_5) \to (x_1, x_5)$ in AR(4) model. Is it right? Or does this means eliminating autocorrelations ...
3
votes
2answers
144 views

Differencing a time series

I am looking to find the ACF of a time series, but after it is differenced. $y_t = a_1y_{t-1} + \epsilon_t , \mid a_1 \mid < 1$ I understand that to find the ACF this process needs to be ...
1
vote
0answers
19 views

AR(2) simulation problem

Take covariances $Cov[X_{t-2},X_{t}]$, $Cov[X_{t-1},X_{t}]$ and $Cov[X_t,X_t]=Var[X_t]$ and calculate the parameters for the AR(2) process ($a_1$, $a_2$ and $\sigma^2$ (the variance of the error ...
2
votes
0answers
29 views

How to interpret the characteristic roots of moment equation of a AR(2) model?

I am learning the financial time series using the book 'Analysis of financial time series' by Ruey Tsay. In chapter 2, they introduced AR(2) models. The moment equation (which is the function between ...
4
votes
0answers
97 views

How to fit log-linear poisson autoregressive mixed model?

I have time-series count data $N_{i,j}$ (population sizes in site $i$ and year $j$) and I want to correlate year-to-year changes with the environmental conditions $x_{i,j}$. For this, I want to fit ...
0
votes
0answers
26 views

ARDL, Lag Terms and Singularity

I am interested in fitting an ARDL model that has 4 lags for each explanatory variable. However, when I fitting the model in R. R says that coefficients are not defined because of singularities. Is ...
2
votes
0answers
53 views

Estimating a VAR model with variable coefficients

I want to estimate a VAR model based on the Dufour and Engle paper "Time and the Price Impact of a Trade" (2000). There, the parameter $ b_{i} $ of the endogenous variable $ x_{i} $ is dependent on ...
1
vote
1answer
124 views

Auto-Regressional & Moving Average Model Formula Properties

I seeking help in understanding specific values underlying the formula's for the MA(p) model & the AR(q) model. I am attempting to implement the models (building up to the combined ARIMA model) in ...
2
votes
1answer
170 views

How to plot spectra of an AR(2) process

I am stuggling with this problem and was hoping to find some guidance to answer it. Let $y_t=\phi_1y_{t-1}+\phi_2y_{t-2}+\epsilon_t$, with $\epsilon_t\sim N(0,1)$. Now, I want to plot the spectra ...
1
vote
1answer
117 views

Backshift operator applied to a constant

This questions is two part: 1) What happens when you apply the backshift operator to a constant? For example, if I have the AR process $$(1-\phi B)(y_t-\mu)=\epsilon_t$$ does that equal ...
0
votes
1answer
151 views

Time series: correcting the standard errors for autocorrelation

I have performed a number of tests to detect any presence of autocorrelation in my monthly return series. The test results confirm that the standard errors are not independent. A Durbin-Watson test ...
1
vote
1answer
291 views

AR(1) coefficient is correlation?

Is the ar1 coefficient from an AR(1) model the "first order correlation of the noise" of a time series? I'm using R's aws package and one of the arguments of the ...
8
votes
2answers
265 views

AR(1) process with heteroscedastic measurement errors

1. The problem I have some measurements of a variable $y_t$, where $t=1,2,..,n$, for which I have a distribution $f_{y_t}(y_t)$ obtained via MCMC, which for simplicity I'll assume is a gaussian of ...
1
vote
1answer
211 views

How to estimate a model with fixed and random effects for a long panel dataset?

NOTE: I am using Stata for doing this. I have a long panel dataset, meaning my N is much smaller than my T. I have N = 5, T = 61. I tried to estimate my model, but I get an error related to the ...
3
votes
1answer
136 views

Residuals in double seasonal exponential smoothing

I have a time series with muliple seasonal cycles, which are 24 and 168 hours for my case. I would like to use Double Seasonal Exponential Smoothing method to forecast, which was published by James W. ...
0
votes
0answers
62 views

What is geometric autoregressive process?

Can anyone give a definition for Geometric Autoregressive Process? Any specific properties? And, in what fields is this mostly applied? To add some context to the question, here is a section of the ...
1
vote
2answers
268 views

How to understand SARIMAX intuitively?

I'm trying to understand a paper about electric load forecasting but I'm struggling with the concepts inside, specially the SARIMAX model. This model is used to the predict the load and uses many ...
2
votes
1answer
189 views

AR(1) parameter estimation

Given a time series, I'd like to estimate the parameters of an AR(1) model for it. As explained on wikipedia, there are different ways for doing that. What may be called a naive method is to compute ...
2
votes
2answers
64 views

Method to remove bad values in time series (bad values known to take on a particular value)

This sounds easy, but I don't know of a good statistical method for it. I have a time series that has (good) data points that range from ~3.5 to 30. The data are collected by an automated sensor. ...
1
vote
0answers
50 views

Regressing coffee beans in US to coffee beans in EU

We're trying to model two time series: a random walk (independent variable) vs. the sum of this random walk and a mean-reverting process. For example: coffee bean 100kg prices (EU) vs. coffee bean ...
8
votes
2answers
304 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
votes
2answers
160 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
vote
0answers
189 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
vote
1answer
256 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 ...
3
votes
1answer
163 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
votes
1answer
289 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
votes
1answer
1k views

Step-by-step example of predicting time series with ARIMAX or ARMAX model?

Could someone give me a step-by-step example of time series prediction using ARIMAX or ARMAX model? The example doesn't need to be long or complicated. It could be for example forecasting temperature ...
0
votes
2answers
544 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
votes
2answers
318 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
vote
1answer
130 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 ...
1
vote
0answers
175 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 ...
1
vote
2answers
185 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
votes
3answers
2k 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
119 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 ...
1
vote
1answer
113 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
651 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
196 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
votes
2answers
839 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
73 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
389 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
2answers
272 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
544 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
vote
0answers
49 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
443 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 ...
3
votes
1answer
1k 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
128 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
270 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
vote
1answer
342 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
299 views

Is VAR a MANOVA with auto regression?

What are the differences between VAR (vector auto regression) and MANOVA?