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

learn more… | top users | synonyms

6
votes
2answers
115 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 ...
1
vote
0answers
20 views

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 ...
4
votes
1answer
85 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 ...
1
vote
1answer
30 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 ...
1
vote
0answers
23 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 ...
4
votes
2answers
102 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 ...
0
votes
0answers
27 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 ...
0
votes
1answer
42 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: $$y_t = \rho_1 y_{t-1} + \rho_4 y_{t-4} + \epsilon_t + \theta_1 \epsilon_{t-1}$$ ...
1
vote
1answer
31 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 ...
2
votes
0answers
34 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 ...
1
vote
0answers
9 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. ...
1
vote
0answers
29 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 ...
1
vote
1answer
44 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 ...
1
vote
2answers
100 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 ...
1
vote
1answer
289 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 ...
2
votes
1answer
68 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: $$\begin{cases} \rho_1=\alpha_1+\alpha_2\rho_1 \\ \rho_2=\alpha_1\rho_1+\alpha_2 \\ \rho_k=\alpha_1\rho_{k-1}+\alpha_2\rho_{k-2} \end{cases}$$ ...
0
votes
0answers
36 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. ...
4
votes
0answers
49 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 ...
1
vote
0answers
84 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. ...
1
vote
1answer
38 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
votes
1answer
545 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 ...
2
votes
1answer
51 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 ...
0
votes
0answers
18 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 ...
1
vote
1answer
55 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 ...
0
votes
0answers
50 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 ...
2
votes
2answers
68 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 ...
1
vote
0answers
70 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 ...
1
vote
1answer
200 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 ...
3
votes
0answers
204 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. ...
1
vote
1answer
47 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 ...
1
vote
1answer
86 views

Time series estimation on specific lags in ARMA model

How can I fit this ARMA model having specific lags using R?
1
vote
0answers
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 ...
2
votes
2answers
118 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()?
10
votes
2answers
379 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 ...
1
vote
0answers
181 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): ...
1
vote
1answer
174 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.
0
votes
0answers
35 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. ...
0
votes
0answers
57 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: ...
4
votes
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 - ...
2
votes
2answers
118 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: ...
1
vote
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) ...
2
votes
1answer
120 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 ...
1
vote
0answers
28 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.
1
vote
1answer
56 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: ...
0
votes
1answer
41 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 ...
5
votes
1answer
329 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 ...
0
votes
2answers
165 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 ...
1
vote
0answers
29 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 $$ ...
1
vote
1answer
150 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? ...
1
vote
1answer
121 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 ...