# Tagged Questions

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

40 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 ...
36 views

### ARIMA vs ARMA on the differenced series [duplicate]

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. ...
13 views

### 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..
11 views

### 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?
23 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 ...
22 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 ...
76 views

### 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: ...
29 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 ...
21 views

### Error while producing an ARMA model using the TSA package in R [migrated]

Had anyone else had this problem, or even better, does anyone know why this is giving me an error? I'm attempting to create an ARMA model of order 3, 3. I'm using the TSA package. ...
88 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 ...
160 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 ...
30 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?
28 views

### 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 ...
24 views

### 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 ...
40 views

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 ...
49 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) ...
19 views

### 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 ...
46 views

84 views

### 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 ...
99 views

### ARMA parameter estimation with constraints

Does anyone know how to estimate ARMA parameters in R with an additional constraint that the parameter estimates are positive (need not sum to one)? I used arma() ...
135 views

### 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 $\sigma_{\epsilon}^2=1$: ...
84 views

### 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 ...
51 views

### Convergence in mean square - missing step

My question regards validating the legitimacy of representing an AR(1) as a MA($\infty$) process. In my notes this is done by showing convergence in mean square, saying that: ...
198 views

### 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: $y_t=\phi_1y_{t-1}+\phi_2y_{t-2}+\theta_1\epsilon_{t-1}+\epsilon_t$ ...
78 views

### 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 ...
234 views

### 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 ...
66 views

### ACF proof for ARMA(1,1) model

I need to derive a proof for the autocorrelation function (ACF) of a stationary, invertible ARMA(1,1) model, that shows that the ACF on the first lag depends on both the $\theta_1$ and $\phi_1$ ...
301 views

### With regard to ARMA time series, what exactly is eacf (extended auto-correlation function)?

I'm going through my copy of Analysis of Financial Time Series, 2nd Edition, and I'm at the ARMA portion. One of the techniques for model selection is computation of the extended auto-correlation ...