# 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.

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### Detailed reference to facilitate manual implementation of ARIMAX

ARIMAX is implemented in SAS and R (function arimax in "TSA" package). I want to implement ARIMAX in an open source library in Scala and Python. Is there any ...
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### Relation linear regression and ARMA models

I have data from a time series which I am currently fitting with a linear model. For that Im using the data as cross-sectional data, where each response corresponds to the value of each variable on ...
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### Understanding lag operators in ARMA models

I'm trying to understand the root cancellation (or sometimes pole zero cancellation of an ARMA(1,1) model as an example). I know, root cancellation occurs if the AR parameter is equal to the MA ...
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### Estimation and forecasting ARMA: differences between Matlab and Stata

I have to forecast values from an AR(1) model. My sample is composed of 192 observations. I estimate my model with the 182 first observations and forecast the 10 last observations. I have done this ...
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### Time series decomposition results interpretation

I have a long multi-seasonal time series, and the stl() decomposition got me this: The remainder is definitely not white noise. Then what should be the next step ...
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### What is the SARIMA (2,1,0)(0,0,1)_12 euqation? [duplicate]

I have problems to find the euqation for Arima (2,1,0)(0,0,1)12....would be nice to get some help!
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### AR1 term significant in ARMA(2,1) but not in ARMA(1,1) or ARMA(1,0)

I'm building an GARCH model using function garchFit from "fGarch" package in R. When specifying the mean equation I have some difficulties understanding what's ...
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### Filtering an ARMA-GARCH on residuals

I had previously fitted my time series with different ARMA-GARCH models using the "rugarch" package"in R. I found no correlation and no heteroscedasticity in the residuals. I obtained (through Pair ...
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### Are there any methods for fitting “interconnected” AR with cross-lags at times older than 0?

I'm not really sure how to explain this, so any advice about the terminology would be very welcome! So let's say that I have two independently driven AR(2) models that are connected together, for ...
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### ARMA coefficients

How to determine the ARMA coefficients for ARMA(p,q)? I explored a lot of technical literature and I understand there are standard rules like Yule-Walker for a pure AR process. Do they apply for ...
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### Time series with 24 yearly data points - advice needed

I have a dataset containing the prevalence rate of Malaria in Botswana, starting in 1990 and ending in 2014. My task is to verify whether these data can be used in order to make predictions on the ...
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### Questions about how to choose the best arima model to forecast

I'm trying to forecast the prices of gold, silver and platinum for the next 10 years using an ARIMa approach. After treating for the basics I am now stuck on the decision of which model to fit best; ...
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### AR(2) process: are leptokurtic residuals OK?

I have a time series of logarithmic returns. After inspection of the ACF and PACF plots, I tried to fit AR(2), MA(2) and ARMA(1,1) models and eventually found out that the AR(2) version can possibly ...
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### R-Monte Carlo simulations for ARMA model [closed]

I have 5 years of daily price data of an asset for which I have fitted an ARMA model. I want to generate 10000 simulations for next 6 months using the last available value for the asset as starting ...
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### GARCH Modeling Production time series

I'm working on a factory's production data (chronological) and I want to apply GARCH-ARMA Model on it, here is the plot of the data. Is applying GARCH-ARMA a good idea? If so, how do we come to the ...
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### Pacf lag axe , is not an integer

I'm trying to use ARIMA process to predict the behaviour of a time series, the probleme I face is that I can't get the order of each component of ARIMA, the lag is between 0 and 1, same goes for the ...
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### Causality and stationarity of AR models

Studying AR models, I found that there are two properties that these models can have stationarity and causality. For what concerns stationarity, I have studied that this condition is satisfied if ...
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### What would be endogenous and exogenous variables in case explained here?

Foreword: I'm working on a non-econometrics related project where we're trying to use econometrics toolboxes in order to avoid re-inventing the wheel. I'm a bit overwhelmed by it and am trying to cut ...
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### Matlab warning “linear inequality constraints active” when fitting ARMA(p,q) - GARCH(1,1)

With Matlab, I specified 9 ARMA(p,q)-GARCH(1,1) models and fitted all of them to monthly return data (I used GARCH(1,1) for every model but changed the ARMA order). Here is a very small example ...
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### Whitening Transformation with Autoregressive Model

I am new to the topic of whitening transformation. In financial time series studies on long memory in data, I have seen that researchers apply an AR(p) model to detrended return series in order to ...
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### What is the PAC function of an AR(2)?

What is the PACF(1) of the following AR(2) process? $y_t = \phi y_{t-2}+\epsilon_t$ with $\epsilon_t \sim WN(0, \sigma^2)$
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### Sequential testing and power

Consider an ARMA(p,q). Why when we run an iterated F-test in order to find p and q the statistics used are correlated and the power is likely to decrease?
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### ARMA model selection: in-sample vs. out-sample accuracy measures

I have a time series for 1000 days for many firms. I am interested to know, in general, on what basis I should select an ARMA model (the nature of my problem restricts integration order to 0). Should ...
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### Multiple regression with autocorrelated errors

I have a multiple regression model in R: ...
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### Alternative construction of ARMA(1,1) process

My question is related to the exercise 2.9, p. 79 in Brockwell & Davis, An Introduction to Time Series Analysis and Forecasting, 2nd edition, New-York, Springer, 2002 (It is also related to ...
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### Ljung-Box test for ARMA residuals: is my ARMA model fine?

I have an ARMA($p$,$q$) model. $p=q=2$ gave me the lowest BIC value, and hence I stuck to it. I know people do something with the Ljung-Box $Q$-test test for autocorrelations. I did this on Matlab ...
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### Generating the same ARMA(1,1) sequence with different parameters

If I have two ARMA(1,1) processes with different sets of parameters, then what are the conditions so that I can get indistinguishable ARMA(1,1) sequences?
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### ARMA model for Time Series about volumes? GARCH?

I am trying to do some analysis and forecasting about a Time Series which is about volumes (how many people call to a call center per hour). I have about 2000 observations, in hourly data. I am aware ...
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### Issue with forecasting a time series that is a white noise using ARMA

I am working on stock prices and stock returns and I'm supposed to do some forecast on these data. The stock prices series is not stationary and even if the stock returns series is, it is a white ...
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### ARMA errors and combining explanatory variables

Currently I'm working on forecasting the employee turnover of an organisation. To do this, I'm using a time series data of the employee turnover over the past 7 years, it is an annual data. To make a ...
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### Relationship between GARCH(1,1) and ARMA(1,1)

Consider an ARMA(1,1) for squared returns $y^{2}_t$: $$y^{2}_t=0.038+0.946y^{2}_{t-1}-0.855v_{t-1}+v_t,$$ where $v_t$ is residual. How to show that this model corresponds to a GARCH(1,1) for $y_t$:...
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### Standard errors NaN by Arima function in R

I'm working with a time series of 59 elements. I'm wondering why the R function, Arima, throws an NaN for the standard errors of ...
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### Organic vs Paid Attribution Model (Granger)

I'm wondering if there is literature or studies done on how to model organic attribution from paid user acquisition. So the context is, on our mobile app, we have paid installs that we purchase and ...
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### ARMA lag selection for ARMA-GARCH models

When I read this group questions about lag selection for ARMA part of ARMA-GARCH models I found 2 different answers from moderator: The use of GARCH and ARMA GARCH estimation process in practice I ...
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### Cancelling roots in ARMA(1,1) with external regressors

I am trying to find out what cancelling roots would imply for the estimators of my external regressors in my ARMA(1,1) model. Unfortunately however I'm stuck in my final step since I'm insecure about ...
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### How to identify best Model for univariate time series data?

I have a time series data- 53.97 63.32 57.06 60.27 69.46 75.08 78.31 73.28 85.84 69.34 62.57 60.11 55.63 47.29 61.22 58.46 66.26 59.71 51.12 39.36 51.89 53....
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### Help discussing stationarity using correlograms? ARMA/ARIMA modelling

I am currently trying to understand how to use correlograms to examine stationarity and analysis the appropriate models. Please can you advice, below I have included my ACFs and PACFs, and I am trying ...
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### How to compute estimate for the first time series value using ARIMA model?

I modeled a univariate time series in R using the Arima command. One can obtain fitted values for the original series using this command by applying the function <...
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### Algorithms For ARMA Estimation From Time Series Data

What are some algorithms that can be used to model time series data as an ARMA model? I do not have access to the input process, only the resulting output process as a time series. I don't want to ...
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### ARMA(1,1) to AR(Infinite) Help.

Hello, Could someone please help me understand how this ARMA(1,1) model can be represented as a pure or AR infinite process? I don't understand how multiplying the two lag polynomials can generate an ...
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### Proper definition of AR()-ARCH() time series model

This is how I would define it, if anyone has any objections please let me know! AR(m)-ARCH(m) time series is an ARCH(m) process in which the variance at time t is conditional on the previous m times ...
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### ARMA stationarity conditions

Are ARMA(p,q) model stationarity conditions are the same as for AR(p) or some additional requirements must be met?
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### INARMA proces in R

I have time series of with integer value numbers. I want to test if my process is Integer Valued AR(1) pocess or similar integer valued ARMA process in R. Could somebody provide me with any ideas how ...
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### how does the MA lib determine the levels for what is significant or not for ACF

I am going thru this stats course https://onlinecourses.science.psu.edu/stat510/node/48 I can follow all the steps, but have question how the lib figures out what is significant for ACF. See "ACF for ...
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### Variance of predictions on AR(8) model

Given the following AR model:$$Y_{t} = 0.16Y_{t-8}-0.36Y_{t-7}+0.2Y_{t-6}-0.8Y_{t-2}+1.8Y_{t-1} + \epsilon_{t}$$ Where $\epsilon_{t}$ is white noise with zero mean and variance = $\sigma_{\epsilon}$ ...
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### Given ARMA(p,q), can a ARIMA(p, 1, q) model be created?

I would just like to check my understanding for this question: Given that you have a generated ARMA(p,q) model, can an ARIMA(p,1,q) model be created? My thought was that it would be that this is true,...
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### Simultaneous estimation of ARMA and GARCH components

I am not allowed to comment on older questions relevant to this question, therefore I ask this myself. The question was dealt with here, here and here with a clear result: the ARMA part should be ...
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### Sum of two ARMA processes that have the same innovations

Let's say $$x_t = a + bt + \varphi e_{t-1} + e_t$$ and $$y_t = c + y_{t-1} + \varphi e_{t-1} + e_t$$ where the $e_t$ term is white noise with zero mean. Can I just sum everything as below: ...