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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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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39 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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57 views

linear regression on future values of ARMA process

We consider a stationary process $X_{t}$ $X_t - \frac{1}{2}X_{t-1}=\varepsilon_t - \frac{1}{4}\varepsilon_{t-1}$ $\varepsilon_t$ is a white noise with variance $\sigma^2$ How to compute ...
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13 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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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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56 views

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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33 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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36 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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1answer
26 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 ...
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11 views

unconditional volatility from an Arma-Garch process

I know that one can easily get variance (unconditional) of a Garch (r,s) process : $\sigma^2= \frac { \alpha_0 } { (1- \Sigma_{i=1}^r \alpha_i - \Sigma_{j=1}^s \beta_j ) }$ However I am struggling ...
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32 views

Can AIC be used to compare an ARMA model to an ARMA-GARCH model?

Suppose I have one time series and two competing models that describe it. Model 1 is ARMA$(p_1,q_1)$, model 2 is ARMA$(p_2,q_2)$-GARCH$(r,s)$. I obtain AIC values of model 1 and model 2. I would ...
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22 views

Continuous AR model from a Discrete AR model

I have a model of an $\mathrm{AR}\left(2\right)$ process, thus: $X_n + a_1X_{n-1}+a_2X_{n-2}=Y_n \qquad \mbox{for} \qquad n=0,\pm1,\pm2,\ldots $ and I have the equivalent stochastic differential ...
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26 views

ARMA(p,q) model interpreting PACF and ACF

Here I have two time series (ACF, PACF), one on the left and one on the right. I have difficulties interpreting the results. Both PACF/ACF couples look the same and I can't distinguish any geometric ...
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2answers
40 views

AR terms and independent variable as regressors

After trying several models with my data, R^2 and p values are showing my model looks like below. ACF plot tells me AR term is significant. Insights into data tells me change in 'x' would have ...
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46 views

is it possible a nonstationary time series, to produce a stationary ARMA model?

I Have a variable (time series) which is nonstationary. I found that from the graph which seems to have a stochastic trend and the correlogram has a typical nonstationary pattern. After that, I've ...
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1answer
141 views

Filtering using a SARIMA model in R

I am not an expert in statistics, but I would like to work on a SARIMAX model representing power consumption. The exogeneous variable would be the temperature, but for now I found here I might need to ...
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81 views

ACF and PACF plot analysis

I am new to ARIMA, and I am trying to understand these lag plots. Are the following ACF and PACF suggesting that the lag of my time series is 4? If I am wrong, please help me understand these plots. ...
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40 views

Inverse Differencing and ARIMA Model Equivalence

I've developed a ARIMA model with exogenous variable. Before fitting the model, I made every time series stationary by differencing (each variable had a different order of integration). For ...
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1answer
67 views

Time series estimation on specific lags in ARMA model

How can I fit this ARMA model having specific lags using R?
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21 views

Structural break test on an arma model any statistical software packages [duplicate]

Is there a way to do a structural break test on an arma model using any of the statistical packages except eviews? My dataset is too large for eviews. I have a policy change about the middle of a ...
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79 views

Estimating ARMA equation using lm() in R

Is there a way to estimate an ARMA equation using the lm() function in R without using arima()?
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209 views

Consequences of modeling a non-stationary process using ARMA?

I understand we should use ARIMA for modelling a non-stationary time series. Also, everything I read says ARMA should only be used for stationary time series. What I'm trying to understand is, what ...
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147 views

How to compare time series with cyclical data, and describe any changes or trends

I have a bunch of time series where the data has a natural (known) cycle, for example daily or annual (or both). Here is an example (this is 6 years worth of temperature data sampled hourly): ...
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104 views

strucchange package on ARIMA model

Is there a way to use strucchange package in R on ARIMA models? I haven't been able to find any. Thanks a lot.
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21 views

Properties of MLE and least squares methods for estimating parameters of ar(ma) models

I have annual data that seem to have a bimodal density function. My explaination is that there is a distinction between wet and dry years. For my work I would like to use an ar(1)-model for this. ...
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31 views

Box-Ljung degrees of freedom for residuals of advanced GARCH-like model

Diagnostic checks of ARMA-GARCH residuals via Box-Ljung tests. I am not sure if I use the correct degrees of freedom. An arbitrary example: ARMA(0,1)-eGARCH(2,1)-SkewedStudent's-t. Output: ...
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54 views

First order autocorrelation of a certain AR process

How could I compute the first order autocorrelation of the process $x_t = \delta + \phi x_{t-1} + \eta_t$? Could anyone give me some pointers? I tried this: $E(\delta + \phi x_{t-1} + \eta_t - ...
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2answers
67 views

Prove expression for variance AR(1)

For the AR(1) process $x_t = \delta + \phi x_{t-1} + \eta_t$, I am trying to prove that the variance is: $\sigma_x^2 = \sigma_\eta^2/(1-\phi^2)$ And that the first-order covariance is: ...
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1answer
50 views

Why is an ARMA model a parsimonous approximation of an AR model?

I am reading a book on time series and I came across the following: "In addition to being a parsimonous approximation to a high-order AR(p) model, ARMA models...". Why is an ARMA model a (parsimonous) ...
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1answer
106 views

relationship between ARMA and AR

I once heard some statements regarding the relationship between ARMA and AR process, such as An average of severl lags of an autoregression forms an ARMA process ...
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25 views

comparing ARMA coefficients

I am comparing two sections of a single time series on the date that a policy change has occurred. How do I compare two ARMA coefficients? Do I use t test? Thanks a lot.
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46 views

Different estimated parameters in similar models in R

A particular series (std), seems to exhibit a trend-like behavior. According to the ADF test for this series: ...
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31 views

VAR model with zero coefficients

ll, I'm working with a bivariate time series $(X_{t},Y_{t})$. Looking at the two time series separately, $X_{t}$ appears to be white noise. This is supported by looking at the empirical ACF and PACF ...
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1answer
206 views

Fitted values of ARMA model

I'm trying to understand how fitted values are calculated for ARMA(p,q) models. I've already found a question on here concerning fitted values of ARMA processes but haven't been able to make sense of ...
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2answers
82 views

Variance of ARMA(2,1)

How do I find the variance of this ARMA(2,1) model? $$ X_t=0.5X_{t-2} + e_t + e_{t-1} $$ I know the formula for ARMA(1,1) but when trying to solve I just keep getting an endless path of higher ...
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25 views

Covariance of ARMA(2,1) series

Consider the ARMA(2,1) time series $$ x_t−0.1x_{t−1}−0.06x_{t−2}=w_t−0.5w_{t−1} , $$ where $w_t$ is white noise with mean zero and variance $\sigma^2_w$. Find the expectation of $$ ...
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1answer
95 views

GARCH-M(1,1) where ARMA(0,0) is “removed” in R

Which of the following is the correct code for fitting a GARCH-M(1,1) model where the ARMA(0,0) is "removed"? Or what is the correct code? ...
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85 views

Is ARMA(0,0) equivalent to white noise?

If the EACF of my TS suggests ARMA(0,0) and the Box-Ljung test does not suggest my TS has correlation, can I conclude that my TS is white noise or merely that there is no reason to suspect that it is ...
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128 views

How do you choose the order p and q for ARMA(p,q) process for modeling a time series?

How do you choose the order p and q for a ARMA(p,q) process for modeling a time series? Can that be told from ACF or PACF alone, just like for a AR(p) or MA(q) process?
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97 views

Building an ARMA or GARCH estimation battery for models of increasing order (rugarch in r)

A loop should be build to fit ARMA and/or GARCH models of increasing order, say GARCH(0,1), GARCH(1,0), GARCH(1,1), GARCH(0,2) etc. The language is r, and I'm using the ...
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132 views

Prewhitening time series: ARIMA-modelling versus polynomial trendelimination

I'm concerned with Box-Jenkins-models and especially the first step, the prewhitening to obtain meaningful crosscorrelations for identifying transfer functions and building regression models. I'm ...
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42 views

condition for a ARMA process to be wide-sense stationary

For a ARMA process, some (e.g. in Tsay's Financial Time Series) said: it is wide-sense stationary, iff all the roots of its AR characteristic polynomial are greater than 1 in magnitude. This is ...
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42 views

can an ARMA process with complex unit roots be made stationary by differencing?

If an ARMA process (or just a AR(p) process) has real unit roots (i.e. 1 or -1), then differencing it repeatedly will make the differenced process weakly stationary. An ARMA process (or just a AR(p) ...
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51 views

When is a ARMA(p,q) process ergodic?

We know that a ARMA(p,q) process is weakly stationary, iff there is no root of the characteristic polynomial of its AR part lying on the unit circle. But what is the necessary and sufficient ...
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75 views

What are the difference between an ARMA(2,1) model and an ARMA(13,9) model?

I was wondering if there are any other things that I can say about the differences between these 2 models, besides the comments about the ACF and PACF. Specifically, I was wondering which model would ...
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84 views

what is the return value of predict in the fGarch package

I have a question about a quit sophisticated model for a time series. Suppose $ \{X_t:0\le t\le T\}$ is a time series. The plot of autocorrelation function and partialcorrelation function suggest and ...
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133 views

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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57 views

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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1answer
47 views

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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52 views

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 ...