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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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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25 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
41 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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1answer
11 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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33 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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8 views

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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25 views

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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1answer
40 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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1answer
58 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
118 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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1answer
56 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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30 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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47 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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79 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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1answer
37 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 ...
2
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1answer
334 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
43 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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16 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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1answer
51 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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36 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
60 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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61 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
181 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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144 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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42 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
82 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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1answer
97 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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342 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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163 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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1answer
152 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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27 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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47 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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1answer
56 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
92 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
60 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
116 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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26 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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1answer
50 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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1answer
39 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
301 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
134 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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26 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
134 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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1answer
106 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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1answer
272 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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128 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 ...
2
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163 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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48 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 ...
4
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1answer
48 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) ...