# Tagged Questions

15 views

### What is the “scale” parameter in “continuous autoregressive model” in cts package?

I am trying to use the "car" command in "cts package" in R program and I see the "scale" parameter there. I wonder whether this can be assumed to be equivalent to time intervals for time series ...
120 views

### Doubts in linear regression

If a linear regression model has a constant term say 1 or 0.2, for example if the original model is $y(t) = 0.2 + ay(t-1)$, then what does this constant term imply? Will it hamper the estimates if ...
20 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 ...
199 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 ...
43 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 ...
170 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 ...
135 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 ...
17 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 , ...
53 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 ...
38 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 ...
47 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 ...
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### 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 ...
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### 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 ...
63 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 ...
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### 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 ...
158 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 ...
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### 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 ...
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### 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 ...
137 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 ...
91 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 ...
75 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 ...
200 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 ...
211 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 ...
184 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 ...
224 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 ...
513 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 ...
338 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 ...
253 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 ...
193 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. ...
72 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 ...
400 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 ...
292 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 ...
66 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. ...
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 ...
441 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 $0.5x_{t-1} + 0.3x_{t-2} + 0.2x_{t-3}$. ...
200 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 ...
238 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 ...
382 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 ...
196 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 ...
383 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} \ \ \ \ \ \$ ...
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 ...
686 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 ...
369 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 ...
186 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 ...
204 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 ...
231 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 ...
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 ...
134 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 ...