Refers to the AutoRegressive Integrated Moving Average model used in time series modeling both for data description and for forecasting. This model generalizes the ARMA model by including a term for differencing, which is useful for removing trends and handling some types of non-stationarity.

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How to get observations from residuals in an ARIMA model?

If we have residuals of an ARIMA(p,d,q) with known parameters, how can we retrieve the original observations of the time series?
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21 views

Reproducing ARIMA error terms

When forecasting a moving average (MA) model using R's forecast, why does using residuals(fit) produce different results than ...
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0answers
19 views

How do I determine the innovation term in an ARIMA equation?

I am not a statistics specialist : I had to take over the internship subject of another student to include it in mine. He was working with $SARIMAX$ models and I would like to import them in an ...
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0answers
20 views

Interpretation of the partial autocorrelation function for a pure MA process

I have been working with some time-series theory and I noticed something that I can understand "mathematically", but not based on the intuitive explanations of what the partial auto-correlation ...
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14 views

Seasonal vs non-seasonal coefficients in R ARIMA

Let's say I have the two following ARIMA models: ARIMA(7,1,1) (no seasonality) ARIMA(6,1,1)(1,0,0)7 (seasonality of period 7). Are they conceptually the same? If so, why is that when I model ...
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20 views

Why is $R^2$ poor for AR model selection used for forecasting?

There is a related question here, about how to calculate the R-squared on a regression with ARIMA errors. I found the answer quite useful, and hoped for some elaboration, particularly on Rob's closing ...
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1answer
39 views

Why we check the residuals of ARIMA model for white Gaussian?

I have problem about the assumptions and model verification of ARIMA models. I know that Gaussian distributed assumption is not necessary for fitting ARIMA models but I wonder why a lot of people ...
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11 views

Autoregressive model with input variables in proc arima procedure

I am currently working on the time series analysis for series Y but I have to use other two variable A and B as an input variable in SAS proc arima procedure. But I am unable to interpret the cross ...
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18 views

time-series analysis Vs statistical signal processing

Is there a way to identify when to use time series analysis or signal processing. Time series data analysis can be divided to signal processing and normal time series analysis. In signal processing ...
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32 views

Estimating error in ARIMA(p,d,q)

I am trying to model my data with ARIMA(1,2,12) and since the variance is not stationary I have also included GARCH (2,3). I have saved all the parameter of my model in a variable called mdl. I have ...
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0answers
20 views

How do I calculate the standard error of the ACF if the errors are t-distributed?

I am modeling my data with ARIMA and to check if my model is good I have to compute the residuals and plot the correlation function and partial correlation function of the residuals. If the results of ...
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1answer
52 views

R: forecast function accuracy for ARIMA models

I have a problem with the forecast function for ARIMA models in R. It calls predict that calls ...
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1answer
59 views

Sample Mean of AR(1) model

Consider the AR(1) model with iid innovations with finite mean and variance. Also, let $X_0 = 0$. \begin{align} X_t = \phi X_{t-1} + \epsilon_t \end{align} The goal is to derive the asymptotic ...
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20 views

Retreiving Integrated Fitted Data from Stationary Fitted Data

Note that this is a simplified example: I have some time series that I made stationary by differencing twice. Then I ran arima on it, and set d = 0 to prevent ...
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2answers
39 views

Arima with xreg, rebuilding the fitted values by hand

I'm using R to do some time series estimation. I'm trying to rebuild the fitted values from an Arima model by hand to use in an Excel spreadsheet using the estimated coefficients and the input data. ...
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12 views

What are the benefits of normality assumption for AR(I)MA models?

I know normality assumption is not necessary for all of the ARIMA models. My question is that if we have a non-normal time series, is it better to transform it to normal state by transformations like ...
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35 views

Determining parameters in AR model for non-stationary time series

I am currently trying to fit an AR model to some financial data. The time series $Y_t$ in levels is clearly non-stationary; however it appears the first differences $dY_t$ are stationary (and this is ...
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1answer
62 views

ARIMA, adjustments and intervention analysis

I have very little knowledge of time-series analysis (despite my stat master - didn't do anything else than an introductory course) but now I'm facing a statistical problem whose answer is this very ...
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56 views

Arima function doesn't consider seasonal components

Currently trying to fit several models to some data sets in order to find an accurate enough one, I ran into some difficulties with the Arima function of the ...
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18 views

VARMAX model in R

Is there a function in R that estimates the VARMAX model? There is one for a VARX (MTS package), but I didn't find one that works with the MA part also...
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48 views

Multiple and long seasonality for a SARIMA model in R

While working on a big data set made of 10-minutes-points of information - i.e. 144 points per day, 1008 per week and ...
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0answers
19 views

Obtaining the Psi Weights of a seasonal ARIMA in R

I am trying to quantify the effect of a future random shocks on my seasonal ARIMA model. If I have understood the theory correctly, the easiest way is to express my seasonal ARIMA model in its "random ...
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1answer
14 views

Can I have multiple individuals for each time point in ARIMA?

I am a novice learner of ARIMA modeling. I have a dataset which includes many cities that are followed up regularly for several years. Each city has its own record (household income, and well-being ...
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16 views

Missing Value in Commodities Prices

I am trying to model the prices of four energetic commodities with ARIMA models in R. Unfortunately the price series is not regular, as for some days, like Christmas, no price is given. My series is ...
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1answer
29 views

How are error terms calculated for moving average model in R [duplicate]

For an ARIMA (0,0,1) model, I understand that R follows the equation: xt = mu + e(t) + theta*e(t-1) (Please correct me if I am wrong) I assume e(t-1) is same as the residual of the last observation. ...
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1answer
47 views

Errors when fitting a SARIMAX model in R

Currently working on big data sets, I would like to fit a SARIMAX model to it in order to forecast future values. Here are my questions : Q1. As a matter of information, does anybody know how does R ...
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28 views

R function which uses innovations algorithm?

I can't seem to find much info on the following: I have a dataset D at time t which I use to fit an ARIMA model. I forecast the value of the time series at time t + 1. Now, when I'm in t + 1, I would ...
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2answers
46 views

Using AIC to determine best ARIMA Model

I'm trying to fit an ARIMA model to housing data set. Playing around with the p's and q I was able to get an ARIMA Model (2,1,2,)(2,0,0) with an AIC value of AIC=4946.76 I used auto.arima to see if I ...
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1answer
91 views

Intervention Analysis - Pulse over several periods

I have a couple weekly time series and an intervention occurred over several weeks and then for some, after a period of no intervention, began again. So, the pattern is off for a period of weeks, then ...
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1answer
66 views

Getting Residuals to be White Noise

I'm on a time series project for an undergraduate course. For the project I'm trying to come up with an ARIMA model for the housing starts data set. ...
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32 views

Problem when doing pre-whitening before ccf analysis [migrated]

I have following R code which does not work when trying to pre-whiten other series by the model generated for the other series. ...
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0answers
19 views

Can we easily avoid the “maximum supported lag is 350 error” when using the ARIMA function in R? [migrated]

I am currently fitting a SARIMAX model to big data sets. Information is retrieved every 10 minutes, so I have a vector of size 52560 for a year of data. Considering it is representing electricity load ...
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39 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
63 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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33 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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45 views

Arima model - multi step forecast

The following code shows a forecast of the next 24 hours of my electricity prices with two exogenous variables. My problem is, that I don't know how to build a forecast for the next 3 days or more ...
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12 views

ARIMA model forecast

why is it that after I forecast an ARIMA model, the forecast has wide prediction intervals as opposed to some of the other time series models such as a VAR?
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0answers
14 views

How to check if data needs to be seasonally differenced in MATLAB

I am forecasting data using ARIMA. I would like to know if there is any test to check if seasonal differencing is needed in the ARIMA model. I know R uses Canova Hansen test, but does MATLAB provide ...
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3answers
242 views

ARIMA Intervention Transfer Function - How to Visualize the Effect

I have a monthly time series with an intervention and I would like to quantify the effect of this intervention on the outcome. I realize the series is rather short and the effect is not yet concluded. ...
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1answer
39 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
21 views

Stationarity consideration in ARIMA using KPSS test

I have data, which I am sure has a downward trend. I am trying to forecast this data using ARIMA and I want ARIMA to consider the trend when it is forecasting. The first step in ARIMA is to ...
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26 views

Kalman Filter Correction efficiency

I was wondering if Kalman Filter used in a way to correct and reduce forecast errors is useful in real life forecast.Since we are using output forecast data and measurement data from t-1 to correct ...
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0answers
8 views

ARIMA - is it normal to be unable to recover DGP of simulated data with 200,000 datapoints?

When learning how to use a statistical model, I often create a simulation of the DGP, and run simulated data through the software to make sure I know what I'm looking at. I've done this for Proc ...
2
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4answers
176 views

Can a trend stationary series be modeled with ARIMA?

I have a question / confusion about stationary series required for modeling with ARIMA(X). I am thinking of this more in terms of inference (effect of an intervention), but would like to know if ...
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14 views

Forecasting the impressions a specific ad campaign will recieve

I am currently working on forecasting the impressions an ad campaign will get given certain constraints specified by the ad provider (eg. only target men in California on websites with certain ...
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1answer
60 views

R: How to to simulate ARIMA using starting values?

I have built an ARIMA(p,d,q) model, m using say, m <- Arima(ts.data, c(p,d,q)) Given some starting values, I want to simulate future values based on the ...
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1answer
86 views

How to dampen forecast to improve accuracy?

According to Armstrong there is ample empirical evidence that dampening trends in uncertain and complex long term forecasting helps improve accuracy/reduce forecasting errors. What I'm not able to ...
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0answers
22 views

Predicting the missing data out of three values in each of the two vectors [duplicate]

I have 2 vectors of rural and urban populations of the same country. (years from 1975 to 2020) with only three values (1980, 1990 and 2001 years) in each. And I need to predict the missing data. My ...
2
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1answer
73 views

Get fitted values estimated in ARIMA in Matlab

I am using Matlab to forecast time series data using ARIMA algorithm. I am able to get forecasted values, but unable to get the fitted values. This is what I mean. In R: ...
2
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1answer
54 views

Show Regression with Arima Errors Equivalent Form of Differenced Variables

How can you show that the regression $y_{t}=\beta_0 + \beta_1x_{t}+\eta_t$ where $\eta_t$ is arima(1,1,1) is equivalent to $y'_t = \beta_1x'_{t}+\eta'_t$ where $\eta'_t=\phi_1\eta'_{t-1}+e_t$ and $'$ ...