0
votes
0answers
10 views

Autoregressive model with input variables in proc arima procedure

I am currently working on the time series analysis for series Y but I have to use other two variable A and B as an input variable in SAS proc arima procedure. But I am unable to interpret the cross ...
1
vote
0answers
27 views

Is there a convenient form for this large covariance matrix?

Consider the following bivariate vector autoregression: $$X_t=\mu +X_{t-1}A+\varepsilon_t,\ \varepsilon_t \overset{iid}{\sim} MVN(0, V),\ X_t=(X_{1,t},X_{2,t})',$$ where the assumptions on the ...
4
votes
0answers
33 views

Determining parameters in AR model for non-stationary time series

I am currently trying to fit an AR model to some financial data. The time series $Y_t$ in levels is clearly non-stationary; however it appears the first differences $dY_t$ are stationary (and this is ...
4
votes
2answers
119 views

Steps to perform time series analysis

I'm trying estimate an autoregressive model with an exogenous variable. It's about the impact of changes in oil prices on the economy. I'm planning on regressing gdp growth rate on its own lagged ...
3
votes
3answers
128 views

Under what circumstances is an MA process or AR process appropriate?

I have a very basic question. Please let me know if this has been asked before, but in my defence I haven't seen it on Cross Validated. I understand that if a process depends on previous values of ...
2
votes
0answers
14 views

Methods for measuring snowball effects in a “complete” longitudinal dataset

I'm looking for ways to test for "cumulative advantage" effects in a longitudinal dataset (see image) I guess the data set is principally similar to this: http://www.caldercenter.org/whatis.cfm , ...
0
votes
1answer
47 views

Is the Moving Average of ARMA the same of Moving Average of Stock Market?

I'm studying time series prediction and I have some questions. Is the Moving Averages movel studied the methods of the ARMA family has the same concept as the methods studied in Moving Averages ...
1
vote
1answer
33 views

Predicting time series with OpenBUGS

I have a number of fairly short time series (about 4–100 observations) which I need to forecast into the future. I decided to use Bayesian inference, because there is external information about each ...
2
votes
1answer
41 views

calculating the expected value and variance of a log AR(1) process

I have an AR(1) process that looks like this: $$ \ln(g_t) = (1 - \rho_g)(\ln(\mu_g) - c) + \rho_g\ln(g_{t-1}) + \epsilon^g_t $$ where $|\rho_g| < 1$, $\epsilon^g_t \sim N(0, \sigma^2_g)$, and ...
1
vote
1answer
84 views

R fit restricted AR(p) model

I have a question about using R to fit an AR model. If we want fit a AR(p) model, the equation will be $Y_t = φ_1Y_{t-1} + φ_2Y_{t-2} + ... + φ_pY_{t-p} + Z_t$. What about I only want to fit the model ...
2
votes
1answer
67 views

Fit a moving average (MA) time series model to the data (R:stats::ar equivalent)

I am looking for some tools for automatic fitting of moving average (MA) time series model to my data in R. I know R:stats::ar ...
1
vote
1answer
58 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
53 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
157 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
23 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
44 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
130 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
80 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
72 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
172 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
208 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
176 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 ...
1
vote
1answer
206 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 ...
2
votes
1answer
464 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
320 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
245 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
183 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
68 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
376 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
276 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
65 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
55 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 ...
10
votes
2answers
410 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
191 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
226 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
357 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
189 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
368 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
2k 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
659 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
360 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
174 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
200 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
224 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
132 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
124 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
733 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
215 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
985 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?