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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linear regression with autoregressive errors ~ARMA(1,0)(2,1)[12]

I am fitting monthly data that are expected to be auto-regressive (streamflow), but I want to include other independent variables (in my case it is a multivariate regression, with about 4 variables). ...
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14 views

Covariance of ARMA (2,1)

I am preparing for an exam and need help. Consider the following estimated ARMA(2,1) model, y(t) = 0,05 + 0,83y(t-1) + 0,13y(t-2)- 0,15e(t-1) + e(t): Given the unconditional variance and 1st order ...
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AR(2) model is causal

AR(2) model is : $$X_t=\phi_1X_{t-1}+\phi_2X_{t-2}+W_t$$ Where $W_t\sim N(o,\sigma^2)$ I want to prove AR(2) model is causal . So , I tried as : $$X_t-\phi_1X_{t-1}-\phi_2X_{t-2}=W_t$$ ...
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AR(1) model - which prior to use?

I want to use the following univariate model: $y_t = \mu_t + \epsilon_t, \ \epsilon_t \sim N(0,1)$ $\mu_t = \phi \mu_{t-1} + \omega_t, \ \omega_t \sim N(0,\sigma_\omega^2)$ That is, $\mu_t$ follows ...
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28 views

corARMA specification in a date*DayNight model

I'm working on a model of animal movement speed as a function of date and day/night. For each animal (50 individuals), I have 2 values for each date an animal was present - a day value and a night ...
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39 views

Using ARMA model for future forecasting

I just started learning about times-series modeling and I'm confused by the following scenario: Let's assume we train a ARMA(p, q) model on a time-series $\{x_1, x_2, ..., x_t\}$. Later in a test ...
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29 views

How to check the residuals of a ARIMA-ARCH model?

Lets say we have a AR(1)-ARCH(1) time series model and we want to check the residuals for Ljung-Box. If the residuals of the model is Fit@residuals (using ...
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68 views

Reproducing Pankratz's ARIMA models for U.S. savings rate

I'm wondering if anyone has been able to reproduce the U.S. savings rate models in Pankratz's "Forecasting with Dynamic Regression Models"? If you google: pankratz table-1.6 The first link for me ...
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34 views

How are the weights set in the AR and MA?

I am studying ARIMA models and trying to get a grip of the concept. But I cant seem to find anyone motivating the values on the weights. Consider the following AR(2) model below, $Y_{t} = \mu + ...
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23 views

Factoring Fourth degree polynomial for invertible ARMA process

I have to represent a $MA(4)$ process as an $AR(\infty)$. In this regard, I need to factorize the polynomial $(1-\theta_1L-\theta_2L^2-\theta_3L^3-\theta_4L^4)$ to have a representation $(1-z)^{-1}$. ...
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Stationarity when using ARIMA/ARMA

Why do we need the dependent variable to be stationary when using ARMA/ARIMA? Aren't we already accounting for that autocorrelation by using ARMA terms? Isn't the whole point to use its ...
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Time series model [duplicate]

I have been give a task for this: "Construct the best-fit time series model for the mean and variance process underlying the portfolio returns, use the best time series model to forecast the mean and ...
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34 views

What is the best approach to estimate the differencing order of a FARIMA model?

I am trying to fit a FARIMA model to a monthly discharge time series with long memory properties and forecast it. I have seen two type of approaches: (1) estimate Hurst parameter to find d ...
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57 views

Intuition for auto-correlation for mean reverting process

How should my auto-correlation plot look like for a mean reverting process? From what I have recently learned, auto-correlation should be low and should decay fast enough. But when I run the following ...
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27 views

Linear transformation of vector ARMA processes

Can someone help me to solve the following problem. Referring to the one above the bottom equation: I was managed to get the left hand side and first term of the right hand side. But couldn't solve ...
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115 views

ARMA Model fitting using statsmodels.tsa.ARMA()

Two questions. 1.) When I use the statsmodels.tsa.ARMA() module, I enter my parameters and fit a model as follows: ...
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Stationarity iff causal and invertible

Suppose $X_t$ is an ARMA(p,q) process. Is it true to say: "$X_t$ is weakly stationary iff $X_t$ is causal and invertible"? If so, why? If not, is there something similar?
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Time series error assumption

I have a time series of annual maxima. Theoretical arguments - where the maxima of any arbitrary distribution converge to a Generalized Extreme Value (GEV) distribution - along with empirical checks, ...
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253 views

ARMA GARCH estimation process in practice

I am trying to build an ARMA GARCH model and since I haven't found much information about the actual process I'll try it here. So, what have I allready done? I have tested my data for stationarity ...
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49 views

Is the the dependence of the residual of a ARMA time series model only based on AR term?

Lets suppose we fit two time series models AR(1) and ARMA(1,1) to a data series. Should be the results of the ljung-Box test for the residuals be the same for these models? I mean does MA term affect ...
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21 views

On a parametrization of an infinite series to recover the GARCH process

Time series analysis By James D. Hamilton (a great book) proceeds in this way to introduce the GARCH process: First it recalls that the equation that described an ARCH(m) process was the following: ...
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29 views

Power spectrum of unlogged AR(1) process

Our variable of interest $X$ is nonnegative. We model $ \log(X) $ as AR(1) process. $ \log(X) $ power spectrum: $ S_{xx}(w) = \frac{\sigma^2}{1-\varphi^2} \frac{\gamma}{\omega^2 + \gamma^2} $ What ...
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80 views

ARMA model in R

I am a bit confused using the arma() function in R regarding interpretation. So what exactly is the equation of a for example AR(1,0,2) given the output AR1, MA1, ...
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50 views

How to forecat a ARMAX model with 1 step ahead forecast in R?

I have divided my time series to 2 parts and I have used first part Y1TS[1:n2] for model fitting and Y1TS[n2:n1] for forecasting ...
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88 views

Calculation of VaR of a time series using a GARCH(1,1) ARMA(1,1) model

Please, I've been stuck all the weekend in this problem, does someone know how find the Value at Risk 10 days ahead (for example) using a GARCH(1,1) ARMA(1,1) Model. Thank you very much Rodrigo *If ...
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ARMA models and invertibility

I'm reading the book Time Series Models by Franses et al. It says that if we have an $ARMA(1,1)$ model with $\phi=1$ and $\theta=-1$ we have $y_t=\epsilon_t$. So, this means that in the equation ...
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96 views

How do you generate correlated ARMA(1,1) models?

I am interested in generating two ARMA(1,1) time series with a pre-defined cross-correlation p between x(t) and y(t). If you could please provide the mathematical framework and the code in R for ...
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124 views

Distinguish an ARMA and an ARIMA model graphically

I'm currently analyzing some time series data and I need to know how to distinguish an ARMA model from an ARIMA model just by looking at the auto-correlation function and partial auto-correlation ...
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981 views

Analyse ACF and PACF plots

I want to see if I am on the right track analysing my ACF and PACF plots: Background: (Reff: Philip Hans Franses, 1998) As both ACF and PACF show significant values, I assume that an ARMA-model ...
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What state-space representation of VARMA is commonly used for fitting

What state-space representation of VARMA is commonly used for fitting? Is Kalman filter + MLE approach used for fitting VARMA model as a common practice? Does the choice of which state-space ...
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172 views

Review of Box-Jenkins methodology

i just finished developing an ARMAX model with python (mostly statsmodels) in order to forecast some data. My next step is to test the data (24 time series) with the given ARMAX model. As i need to ...
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109 views

Automatic selection of lowest information criterion comes with warning

I am building a forecasting model (ARMA) and found the very useful code-object arma_order_select_ic(see code below). It all works, however, each calculation comes ...
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101 views

ARIMA estimate validation through arima.sim

This is out of my curiosity trying to compare time series input to an ARMA model and reconstructed series after an ARMA estimate is obtained. These are the steps I am thinking: Construct simulation ...
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185 views

raw data stationary but still can see trend and seaonality is stl

So I am looking at unit sales data. I am doing a univariate time series analysis. My data is weekly sales numbers figures, spanning 2012- 2014 (obviously no till end 2014). I first ploted my response ...
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70 views

Violation of underlying assumptions - ARMA-GARCH

I am estimating an ARMA-GARCH model using QMLE (Quasi-Maxiumum-likelihood-estimation). However, I have some trouble - when I do test to see if the residuals are uncorrelated - a Weighted Ljung-Box ...
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1answer
58 views

How to estimate an ARMA with non consecutive lag in R?

Lets say I have an ARMA with an AR(1,4) and an MA(1). Update To be more specific the model to be estimated is: $$y_t = \rho_1 y_{t-1} + \rho_4 y_{t-4} + \epsilon_t + \theta_1 \epsilon_{t-1}$$ ...
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146 views

MATLAB: modify arima model coefficients

I want to modify ARIMA model coefficients (MATLAB). I estimated my model using this code: mdl_1 = arima(2, 1, 2); estMdl_1 = estimate(mdl_1, data1'); MATLAB ...
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66 views

Zero p-value for Dickey-Fuller test

I feed sample time series data in statsmodels Dickey-Fuller test, and as a result I get exact 0 (zero) for p-value. I'm not sure how to intrepret that. I think that it doesn't imply stationarity as ...
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Adding exogenous input to data (to expand ARMAX)

I am facing the following problems: 1) I am trying to add an exogenous input to an existing ARMAX model. I already identified a good fitting model with small MSE for my system. ...
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Using A Time Series To “Scale” Another

I know the "average theoretical cost per impression" for Jan 13 - Dec 13. I have other monthly time series for "total # of impressions", "total # of clicks" and "total number of conversions" for Jan ...
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80 views

ARMA parameters estimation

I'm trying to estimate parameters of ARMA. Ljung-Box statistic reveals no serial correlation in residuals. But one coefficient is statistically insignificant. When I remove the variable corresponding ...
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137 views

Problem on time-series

I am dealing with event data (recorded over a month) which gives out a binary response from a sensor when a door opens or closes - the time is noted at every instant and can also be represented in ...
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1answer
1k views

What is the best way to do a seasonal ARMA (or ARIMA) in python?

Scikit learn and statsmodels don't seem to support this type of ARMA. I tried to use rpy2 python library, but that proved to be far too difficult to integrate, as my IDE was not able to recognize my ...
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231 views

On the Autocorrelation Matrix of an ARMA(2,2) to derive the Yule Walker Equations

For an AR(2) I can get the Yule-Walker equations: $$\begin{cases} \rho_1=\alpha_1+\alpha_2\rho_1 \\ \rho_2=\alpha_1\rho_1+\alpha_2 \\ \rho_k=\alpha_1\rho_{k-1}+\alpha_2\rho_{k-2} \end{cases}$$ ...
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71 views

Using SAR and SMA in the same regression

From this webpage: http://people.duke.edu/~rnau/arimrule.htm, of the Duke University: Rule 13: If the autocorrelation at the seasonal period is positive, consider adding an SAR term to the model. ...
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100 views

A proof for the stationarity of an AR(2)

Consider a mean-centred AR(2) process $$X_t=\phi_1X_{t-1}+\phi_2X_{t-2}+\epsilon_t$$ where $\epsilon_t$ is the standard white noise process. Just for sake of simplicity let me call $\phi_1=b$ and ...
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Wold Representation for an ARMA (1,1)

I have this ARMA(1,1) process where $\epsilon_t$ is the classical White Noise process$$X_t=\epsilon_t +\alpha_{t-1}\epsilon_{t-1}+\theta_{t-1}X_{t-1}$$ and I have to write its Wold representation. ...
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60 views

The likelihood that a time series is generated by certain ARMA(p,q) ?

I have a group ( only 20 of them, each one has 170 time pointers) of time series that I can consider as "GOOD", meaning, they have consistent statistical characteristics. I am not sure how they are ...
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3k views

How to interpret ACF and PACF plots

I just want to check that I am interpreting the ACF and PACF plots correctly: The data corresponds to the errors generated between the actual data points and the estimates generated using an ...
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113 views

My transfer function has non-stationary inputs, but a stationary output. Should I difference both the inputs and outputs during structure estimation?

I have a system of two inputs and one output that I'd like to model using the following Box-Jenkins transfer function ("dynamic regression") structure: $$y_t=\frac ...