ARMA is an acronym for auto regressive moving average; a stochastic process modelling time series. It adds moving average terms to the AR model.

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ARMA Model Output & Excel

I am using my Eviews Output of an ARMA Model, taking the coefficients in other to perform my Forecasts in Excel. However, I am not being able to match the residuals of the in-sample estimations ...
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Correlated state-space models

I'm struggling with Reinsel's book "Elements of Multivariate Time Series Analysis," because I thought that it would be a good idea to switch from Vector ARMA to state-space representations; ...
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Representation of ARMA processes

Question Consider the following process: $$2y_t-3y_{t-1}+y_{t-2}=\epsilon_t-\theta\epsilon_{t-1}$$ What is the model for the process $w_t=\Delta y_t = y_t-y_{t-1}$? Attempt I have solved the ...
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ARMA - GARCH fitting

I have an ARMA model which has these terms Constant + AR23 + MA1 + MA3 + MA24. The residual of this model has heteroskedasticity (from ...
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39 views

Which arma model is best one?

I am studying ARMA models. ARMA(25,25) or ARMA(1,1) which one better model? Why? I think that the reason is the ommission of irrelevant variable
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How to forecast a Markov Switching Model

I have the following Markov Switching Model. Transition Matrix: $$ \left[\begin{matrix} 0.85387 & 0.91973\\0.14613 & 0.080265 \end{matrix}\right] $$ With Regime 1: Intercept: 0.00839 ...
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Fitting ARMA model with MATLAB R2012b

I want to fit an ARMA model on a time series (quarterly log returns of a 10 year bond) using MATLAB R2012b. This is part of an exercise. I have problems with the code and the interpretation of a ...
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Shrinkage estimation for regression with ARMA errors

I was wondering if someone knows a R-package or function library for the topic of shrinkage for regression with ARMA errors. Please let me know if you came across something related. Thank you! ...
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Calculating phi11 (or phi22) from an MA(1) process

I've come across a question where I have an MA(1) process like so: $X_t = b_t - 0.4 b_{t-1}$ (where $b_t$ is a white noise process and $t$ is the time index) The question asks me to find $\phi_{11}$ ...
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Single ARMA model for multiple time series

I have 365 days of hourly data (24points each) of a prediction error (realised -pred_day_before). I want to model the evolution of the prediction error as an ARMA process. Matlab System ...
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ARMA/GARCH estimation in sequence

I have a time series that shows a non stationary seasonal autoregressive component as well ask known heteroshedasticity. In order to model the series, I have fit a seasonal arima model for the mean ...
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33 views

Autoregressive moving average or feed-forward neural network

When we have to make a forecast, the books tell us that the main method is the autoregressive moving average model. In my opinion there is another big tool, the feed forward neural network (FFNN). So ...
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Combining forecast from ARMA models

I have three ARMA(p,q) models for the variable X and using each model I produce forecasts for 12 months ahead. Note that in all three models the residual is normally distributed. Now if I want to ...
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Is there an “initial condition” for ARMA model?

ARMA model is a stochastic version of recursive relation. For deterministic recursive relations, we solve them and need initial conditions to fully get the solution. So I wonder what is an "initial ...
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58 views

ARMA conditional density

Consider the ARMA(1,1) process \begin{align} y_t=a_1y_{t-1}+b_1\epsilon_{t-1}+\epsilon_t, \end{align} and assume $\epsilon_t$~$N(\mu_t,\sigma_t)$. And $\mu_t$ and $\sigma_t$ are all known. ...
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66 views

ARIMA modelling

How can an ARIMA (2,1,0) model be estimated without attempting to calculate the coefficients of the model? What info would I need for this estimation? Issy
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ARIMA Model building

Can someone help me with this please: it's revision and I am extremely stuck with what to do and it's holding me back! A previous exam question asks: explain the following ARIMA printouts and ...
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ARIMA model identification

Having a bit of difficulty identifying the appropriate ARIMA model by looking at ACF/PACFs. I know that AR(1) models, the ACF has a geometric progression from its highest value at lag 1 and the PACF ...
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Are Arma models on levels and first differences related?

Imagine I find a good fit of an Arma 4,4 model on the levels, and on the first difference I find Arma 3,4. Are both models ...
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Theorem about ARMA process existing

I have met the theorem: "For each stationary time series there is ARMA model with finite number of parameters." Could you indicate official source with proof (bibligraphy) of this theorem?
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Number of observations used for ARIMA modeling

Our professor keeps on writing in his slides that when you test different ARIMA models on your time series, one always has to keep T fixed. I assume he is talking about fitting your model using the ...
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How do I calculate the fitted values of an Arma model

I am studying the ARMA models, and I am breaking my head on something probably straightforward but that I can't see. I generated in R a simple AR(1) model, and used the function ARIMA to estimate its ...
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130 views

How to calculate the conditional variance for AR(2) model?

I need to find the conditional variance of $Y_t$ given information up to time t. $Y_t$ = $\mu $ + $\phi_1$$Y_{t-1}$ + $\phi_2$$Y_{t-2}$ +$\epsilon_{t+1}$ Need to find the conditional variance of ...
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121 views

Is the selection of ARMA(0,0) wrong?

From my model selection based on information criteria such as SBIC returns me a ARMA(0,0) model. Should I choose it or reject it? and Why? Need some guidance on this.
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What are some examples of real-world processes that are well-described by AR, MA, ARMA, or ARIMA?

Subject says it all - AR/MA/ARMA/ARIMA are often described as workhorses of time series analysis. But what are some real-world examples where these methods gave great results, and another more modern ...
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ARIMA vs ARMA on the differenced series

In R (2.15.2) I fitted once an ARIMA(3,1,3) on a time series and once an ARMA(3,3) on the once differenced timeseries. The fitted parameters differ, which I attributed to the fitting method in ARIMA. ...
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Why is that the mean forecasting error is minimized when Conditional Expectation is used

As the title suggests, why is that the mean forecasting error is minimised when conditional expectation is used for forecasting in ARMA model? Need some guidance on this..
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Estimate ARMA((1,9),1) in rugarch?

I would like to estimate an arma model with a ma1 & ma9 component, and not the components in between. Is it possible to do so in rugarch?
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36 views

Forecasting differentiated timeseries with ARMA?

If I apply ARMA on a stationary differentiated time series and want to make forecasts with this model, the forecast will be on the differentiated values. I need the values to be non-differentiated, is ...
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44 views

Differentiate a ARMA(p,q)-GARCH(p,q) or not?

I'm confused about the stationarity condition. I'm fitting a ARMA to a time series that might not have a constant mean. When I fit a ARMA model to it the residuals looks stationary. Do I have to ...
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74 views

ARMA(1,1) Unique Solution

Assume that we have a white noise process. When you try to fit an ARMA(1,1) model on it (clearly wrong model but bear with me): $y_t=ay_{t-1}+b\epsilon_{t-1}+\epsilon_t$ you will end up with a ...
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38 views

What part of an ARMA model requires a stationary time series - the AR or the MA?

Could I use a non-stationary time series with simply an Autoregressive model?
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Correlation of one binary input series and continous response series

I have one input series of type 0/1 (it is an intervention time series) and some metric response series. I need to have a look at cross correlations. Normally I would use Box-Jenkins-technique. But ...
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Proving that the best minimum squared predictor for a stationary ARMA model is the conditional mean

I am trying to prove that the best minimum mean squared predictor of $r_{t+l}$ for a stationary ARMA model is the conditional mean $E[r_{t+l}|r_t,r_{t-1},...]$ Attempt: $$r_t = \psi(B)a_t = a_t ...
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339 views

Does applying ARMA-GARCH require stationarity?

I am going to use the ARMA-GARCH model for financial time series and was wondering whether the series should be stationary before applying the said model. I know to apply ARMA model the series should ...
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Raw return vs. percentage return to calculate volatility

I am using squared return as a proxy to calculate volatility, however i'm not sure whether to use raw return or percentage return. Under raw return all return estimates are below 1, however under ...
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606 views

ARIMA with seasonality in Statsmodels

I'd like to have a seasonal ARIMA model implemented with Statsmodels ARIMA. Specifically, I'd like to log before the weekly seasonality and then be able to make forecasts. Perhaps an example with ...
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109 views

Confusion about Moving Average(MA) Process

Let's assume there is a time series Y of length n with Y(1) being the most recent observation. In MA process we plot auto-correlation function (ACF) to see how many lags to use. If we look at MA(3) ...
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Fitting ARMA(p,q) by conditional maximum likelihood

I have found a lot of information on fitting ARMA(p,q) using exact maximum likelihood, but very little for conditional maximum likelihood. Can anyone direct me to an R function that fits ARMA(p,q) by ...
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115 views

Difference between using ARMA and GARCH to model volatility?

I just went through the following work http://epublications.bond.edu.au/cgi/viewcontent.cgi?article=1199&context=ijbf and was wondering what is the difference between model (9) on page 12 which ...
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174 views

Is ARMA model possible for series with non significant ACF/PACF?

I am playing around with SP500 data from MASS package and from observation of the ACF and PACF there seem to be no significant autocorrelation. Now I want to model the volatility of the returns but I ...
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56 views

Can I get an univariate ARMA(2,1) representation from a bivariate VAR process?

Suppose the VAR is on (x,y) and I want to get an ARMA(2,1) expresion for x, how can i do that? For example, $\left[ \begin{array}{l} x_t\\ y_t \end{array} \right] = \left[ \begin{array}{l} ...
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How to use error term in AR (2) model for predicting future values?

We use turbidity to estimate suspended-sediment concentration (SSC)- our data was serially correlated. We ran an ARMA process and ended up with a AR (2) model. Our equation in log form is: ...
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How to fit different ARMA models by group in R?

I have $Y$ measurements per several Subjects and I'm studying impact of factor on $Y$ measurements. I've fit a lognormal mixed model with a random interaction, but I'm finding autoregressive ...
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How do I reconcile how EViews estimates an AR(1) model with OLS?

I discuss estimation of the following $ARX(1)$ model: $Y_t=α+βX_t+u_t$ where $u_t=ρu_{t-1}+ϵ_t$ Substituting the the value of $u_t$ in the first equation into the second, we have that: $Y_t-α- ...
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Is the AR(1) process always Gaussian given Gaussian innovations?

I found that $AR(1)$ process $x_t=\phi x_{t-1}+\epsilon_t$ is not always Gaussian given Gaussian innovations $\epsilon_t$. This only happens when the $AR(1)$ model coefficient is very large. This goes ...
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Is this process an AR(1)?

The following process $X$ is generated as the sum of a structure $y$ and an $AR(1)$ process with $\phi=0.4$ and $\sigma_{\epsilon}^2=1$: ...
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Autocovariance of an ARMA(2,1) process - derivation of analytical model for $\gamma( k)$

I need to derive analytic expressions for the autocovariance function $\gamma\left(k\right)$ of an ARMA(2,1) process denoted by: $y_t=\phi_1y_{t-1}+\phi_2y_{t-2}+\theta_1\epsilon_{t-1}+\epsilon_t$ ...
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Wide-sense stationary linear process = ARMA process?

In Brockwell and Davis' Introduction to Time Series and Forecasting, a linear process is defined to be An ARMA process/model is defined to be Note that by "stationary", the book means ...
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auto.arima does not recognize seasonal pattern

I have a daily weather data set, which has, unsurprisingly, very strong seasonal effect. I adapted an ARIMA model to this data set using the function auto.arima from forecast package. To my ...