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Questions tagged [arima]

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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Understanding Seasonal ARIMA

I'm a bit struggling understanding the concept of Seasonal ARIMA. Because from what I've understood: when we modelize an ARIMA model, we want to transform the time series into a stationary series (...
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Long-run variance of ARMA(p,q)

Assume you have $A(L)y_t = B(L)e_t$ and $e_t$ is a zero mean white noise with variance $\sigma^2$. Why is the long-run variance of $y_t$ equal to $\sigma^2\left(\frac{B(1)}{A(1)}\right)^2$? I know ...
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Nonstationary ARIMA model fitting by stationary ARIMA

Let me have an ARIMA model like ARIMA(1,1,1): $$\left(1 - \phi L\right)\left(1 - L\right)x_{t} = \left(1 - \theta L\right)a_{t}$$. Look at reduced stationary model: $z_{t} = \Delta x_{t} = \left(1 - ...
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Recent progresses in Maximum Likelihood for ARIMA?

I am looking for recent developments in optimization for MLE and conditional least squares especially w.r.t ARIMA. I am using ARIMA to make some forecasts, in order to do that I have to find the best ...
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What is the meaning of an autoregressive parameter greater than one? [duplicate]

I have created a AR(2,1,0) model with the first two parameters equal to -1.08 and -0.33. I understand that a autoregressive parameter equal to 1 implies non-stationarity and a random walk process so I'...
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Interpreting qq plot from ARIMA residuals

Im trying to undestand this qqplot from arima residuals but im a bit lost about the underlying distribution, concretely I don't now how to interpret the tails.
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Discrepancy between line plot and ACF plot for nonstationary time series

I understand that when the ACF of a nonstationary time series is plotted it should show a very slow decay. I have data that clearly shows a trend, however the ACF shows a decay which seems to indicate ...
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What is the equaton for ARIMAX(1,1,1) and how can I undifference the 1st differenced data to fit the equation? [duplicate]

I have generated the ARIMAX(1,1,1) model to predict the future Barramundi catch. In this model, there are two exogenous variables (price and streamflow) that affect Barramundi catch. I have used 1st ...
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Can you have an ARIMA(1,1,0)x(0,1,0)12 model?

If d, or D is set to non-zero in the model ARIMA(p,d,q)x(P,D,Q), does one of {p,q} or {P,Q} have to be set to non-zero too respectively?
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Variance of the time series ARMA (1,1) model?

The ARMA (1,1) model is The variance of the white noise series is 0.09. How do you calculate Var(rt)?
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Differencing and trend in time series forecasting

I understand that a time series is differenced to remove trend. But if trend can be modeled for forecasting purposes then why difference a time series at all?
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ARIMA Valid combinations ARIMA(0,1,0)x(0,0,0)

Is ARIMA(0,1,0)x(0,0,0) a valid grid search combination using Sarimax in Python? I've built a few ARIMA models in python and have noticed that this combination is not found in the grid search so it ...
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How do you forecast ARIMA with multiple regressors? [migrated]

The complete R data and code for my question is here: https://pastebin.com/QtG6A7ZX. I am new to R and still a beginner when it comes to time series analysis, so please forgive my ignorance. I am ...
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How to interpret ARIMA(0,1,1)(1,0,0)[12] with drift from R? [duplicate]

The code that Î used to generate ARIMA summary is, arimafore = forecast(auto.arima(sales), h = 24) summary(arimafore) and i got this output Forecast method: ...
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Putting non averaged data into a R Arima Package [closed]

I have a dataset which has many values and I want to put it into a Arima R model to do predictions. At the moment, I average the data to get a single value for each time series. i.e. I have the data ...
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Recurrence of $k$-step ahead forecast with ARMA

For brevity, let's consider an AR(1) model, but this question should apply to ARMA(p, q) in general. Assume we are at time $T$ and would like to forecast $k$ steps ahead, $$ X_{T+k} = \phi_0 + \phi_1 ...
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How do I interpret ARIMA(2,1,0) with drift

The code that Î used to generate ARIMA summary is arimafore = forecast(auto.arima(sales), h = 12) summary(arimafore) For forecasting 12 months I got the summary ...
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Make daily business data stationary for ARIMA

For my master thesis I have a dataset with the daily count of orders from a company over ten years. Naturally this data follows strong seasonality with almost no orders on the weekend. To fit an ARIMA ...
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Why does my ARMA forecast get smaller over time?

I am a beginner to time series modeling but I am trying to build an ARMA model to describe a set of 24 observations. ...
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If an ARMA(p,q) model works well on differenced time series, then what model would work on raw time series?

I have an ARIMA(4,0,2) model that works well for 168-differenced data, that is, I fitted it to $Y_t-Y_{t-168}$. Based on this, would it be a good idea to try to fit a Seasonal ARIMA(4,0,2)(0,1,0)[168]...
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Removing Influence of Other Time Series in Multivariate TS Analysis

I have some non-periodic time series that are all correlated. In the absence of the others, each time series would consist of a set of responses to events. I don't know the duration or shape of each ...
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Parameters of ARMA model

In my professor's notes, it is written that if the variable $y$ is explained with an ARMA($p$,$q$) model, then $y_t$ (i.e. $y$ at time t) depends on the most recent $p$ lags of its own value and the ...
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ARIMA predictors - clarification

I'm working on multivariate time series (still), and would like some clarification. I was reading this site: Duke Forecasting and I came across this statement: "We see that the most significant ...
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acf and pacf suggests MA but auto.arima gave AR

I have this data which is residual series obtained from predicted values and observations. original series was a random walk with a very small drift(mean=0.0025). ...
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Forecast existed ARIMA model using primer time-series

I have some fitted ARIMA model: ...
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does white noise residuals suggest a stationary model?

To fit an ARMA model to a time series, the time series should be stationary to start with. If we obtain a reasonable model fit by looking at mean and variance, ACF ...
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1answer
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How to treat arima models with some non-statistical significant p-values?

This is a pretty simple question but didn't find anything relevant here, so hope it's not a duplicate. I've used statsmodels python library to find the best ...
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Why my arima model is not stationary?

I want to fit arima model to my data. To do so I run the following code: ...
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SARIMA modelling results. Choosing the right lag for seasonal data

After differentiating a monthly climatic data with a lag of 12, and being sure that, at least, one more differentiation will turn my series into white noise (ndiffs ...
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How to choose between ARIMA and ARMA model

I am doing time-series analysis in python for the dataset given below- Here's link The plot for the above time series seems to be non-stationary for me because on observing it looks like consisting ...
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Optimal Power Transformation to Reduce Heteroscedasticity in Time Series

I would like to ask: what method should we employ if the variance in time series behaves like a high order (such as $au_t^5+bu_t^4+cu_t^3$) polynomial function with respect to mean? On internet, I ...
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1answer
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Getting best fitted model using Auto ARIMA but prediction result is very bad

I saw this: time series - Poor prediction using ARIMA model But the answers aren't clear and isn't directing to me for solving the problem I have. Using only AR is giving me better prediction whereas ...
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How Differencing influences an ARIMA model

When finding a model for some data, I immediately look at the ACF and PACF to look to see if the data is stationary or if there is seasonality and so on. The moment I find out the data is not ...
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Can I use ARMA instead of GARCH?

I am a beginner to econometrics and STATA, so I would like to apologise if this is a bad question, but have accidentally dwelled down into volatility modeling. I have come to understand that the ...
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Fitting an ARIMA Model to Seasonal Data [duplicate]

I am trying to attain an ARIMA model for the following Time Series Data: There is quite obviously a seasonal component - as the plot seems to oscillate between smaller and larger peaks, its seems to ...
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Arima simulation followed by modeling in R produces bad estimates

Simulate a moving average using arima.sim in R. Then estimate the coefficients using arima. ...
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How can I identify these time series processes? (AR/MA/ARIMA/random walk with drift)

I don't understand how one would identify the stochastic process of the following models, if they are AR or MA or ARIMA etc. Consider the following models estimated over a sample $t = 1, 2, \dots,T$...
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Standard error ARIMA model

I have estimated parameters for a ARIMA model using the ML method. But now, I want to know the standard errors of these estimates. How can I calculate them? Thank in advance!
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ARIMA: Produce multi-step, out-of-sample forecasts by feeding in new history without retraining the model? [closed]

I'd like to compare the results of an LSTM model to an ARIMA model. How can I create an ARIMA model in python that trains on the first 70% of data (~2700 observations), and then produces forecasts at ...
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What if your original model suggest p or q beyond 2

I have often found comments that no MA, AR or integration in ARIMA should have a value beyond 2 in social science data. So what do you do if your ARIMA analysis suggest one of these beyond 2? I assume ...
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Can VARMA handle non-linear data?

I know that traditional ARIMA models cannot handle non-linear data but I was unable to find any place where it states whether if VARMA can handle non-linear data or only linear. Please clarify this ...
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How to interpret these acf and pacf plots?

I don't know which model to fit to these ACF and PACF. Is it an AR(3) or something else?
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Including time variable as a fixed effect to get rid of autocorrelation?

Does it make sense to include time as a fixed effect along with your predictors to get rid of autocorrelation? Why or why not?
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1answer
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Significant lags at ACF and PACF plots in GLM: what should I do?

A glm.nb model I built shows significant lags at lag 1 in both ACF and PACF plots. Please see the images below. There is no way to define random effects (or ...
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Time Series: Confused about identification of (possibly?) an ARMA(p,q) model

this is my first ever question on a website i use frequently! This time series has given me much trouble over the last couple of days even after extensive googling, I suppose with TS theres no two ...
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AR and MA signatures in these autocorrelation and partial autocorrelation plots?

These are the ACF and PACF plots of a time series (daily aggregates/counts). The first plot is un-differenced and the second plot is after a seasonal difference of 7 days. My take looking at the ...
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Forecasting using MA(2) model when past 5 observations are known

So given an MA(2) model : Xt = Wt + Theta1 * Wt-1 + Theta2 * Wt-2 Where Wt is white noise. (Normally distributed) and Theta1 and theta2 were available. Say if X96,X97,...X100 of the series were given ...
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1answer
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Error while fitting data in auto.arima - R

I am running auto.arima for forecasting time series data and getting the following error: ...
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Why is arima in R one time step off?

I've recently noticed an odd behavior in a few timeseries methods. Let's fit an arima model (ar1) to the annual subspots data ...
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Linear Forecasting with a small dataset

I am trying to get some forecast (5 years more) from a small dataset that is as follows: ...