# 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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### ARIMA - GARCH or AR-GARCH

I am looking at equity returns and they are not stationary at level. So i take the 1st difference to make them stationary. My GARCH(1,1) model is modeled using an AR(1) parsimonious model. But, since ...
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### How does the dynamic regression component from TBATS differ from the one in SARIMAX?

Both TBATS and SARIMAX support the modeling of long-term seasonality by using dynamic regression. Dynamic regression in this case involves the use of sin and cos terms to model seasonal components. In ...
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### Difference between cross validation vs model accuracy measures

I have a time series ARIMA model and I want to validate the accuracy my prediction. But I dont understand the difference of using cross validation vs model accuracy measures such as MAPE, MAE, MSE and ...
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### Fitted ARIMA on new time series

Based on the accepted answer from this post: How to use a fitted model parameters for forecasting other time series, it is possible to use a fitted ARIMA model for forecasting another time series. ...
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### Time series - ARIMA Model gives bad result of prediction

I don't understand why I get poor prediction results with ARIMA Model Here is my program and my results: for the dataset I am using a file (which represents CPU traces of one VM)that contains 288 ...
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### Is SARIMA(0,0,1)$_\text{s}$ actually MA(s)?

Since for SARIMA(0,0,1)$_\text{s}$ the model equation is $x_t =e_t+a e_{t-s}$, can we say this is a kind of a MA(s) model?
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### R package for order selection of a vector ARIMA(p,d,q) for multivariate time series

I'm currently working on a project that requires dealing with multivariate time series. What I would like to fit to my dataset is a VARIMA(p,d,q) . I'd like to proceed using the Box-Jenkins procedure, ...
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### Can you generate correlated ARMA time series with different lag orders?

Is it possible to generate correlated ARMA time series when the ARMA models are different? For example, can you generate two time series which are correlated when one is an AR(5) model and one is an ...
1 vote
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### When does the Instrumental Variable (IV) method fail?

Consider the following ARMAX model: $$y[k]=\alpha y[k-1]+\beta u[k-1]+e[k]-0.7e[k-1]$$ where $e[k]$ is a white noise. One can see that $e[k]-0.7e[k-1]$ is a filtered noise and thus using ordinary ...
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I would like to know if there is a function that can filter work days in my temporary serie. I need to include 2 intervention variables, easter days and work days, in order to estimate with Arima I ...
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### ACF and PACF Plot

I am a first year stat student. We are tasked to create a SARIMA model from trial and error using ACF and PACF plot. Now here is my generated plot: Now I am trying to understand the plot but I don't ...
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### Arima model always predicts the same value in python implementation, R's Auto Arima however gives me a well function model. How to replicate?

I have a series that looks like . (https://gyazo.com/8a460fed032c8989b93cf26d8820e431) It shows very strong auto correlation ![AC] (https://gyazo.com/4acd9b9bd32c70509bde1b8b874d6e33). I have ...
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### Mean-level forecast from rugarch does not match manual calculation

I am looking into the rugarch package and am trying to understand how the one-step-ahead forecast is calculated. Specifically, I am fitting an AR(2)-GARCH(1,1) ...
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### Conflicting ACF/PACF after first-difference

I have yearly data. When I do a Dickey-Fuller test it gives me insignificant results, indicating that the series are non-stationary. After differencing them the DFT tells me they are now significant ...
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### Why is non-normality of time series not a problem for ARIMA and GARCH?

My time series is very leptokurtic and non-normal, which is of course highly common for time series data. However, I don't exactly understand why that is not a problem for ARIMA modeling and GARCH ...
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### VAR model with AR(p) and ARMA(p,q) data?

I want to estimate a VAR-model with 6 variables, all of them are stationary. But when I analyse the time series by examining ACF, PACF and auto.arima in R. ...
1 vote
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### Do we need to check normality of the residuals when using 'CSS' method to fit ARIMA model?

I'm using auto.arima to fit my model. When I used the default CSS-ML method, I noticed that the residuals are not normal. So I ...
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### When do ARMA models fail?

I have just started learning about Autoregressive–moving-average model (ARMA). On the Wiki page, it has been mentioned that: ARMA is appropriate when a system is a function of a series of unobserved ...
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### Is ARIMA-GARCH nested within ARIMA?

I wanted to compare ARIMA(1,1,1)-GARCH(1,1) and ARIMA(1,1,1) model forecasts with a Diebold-Mariano test, but I know that it cannot be used for nested models. Is ARIMA-GARCH technically nested within ...
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### Why does my ARIMA predictions on monthly data form a straight line?

For short detail, the goal was to forecast using 51 monthly observations of KPI of project implementations which I aggregated by sum from 463 observations from about 4 years of data (May 2017 to July ...
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### Autocorrelation function of Arima(1,1,0)

I have ARIMA(1,1,0) model: (1-ΦB)(1-B)X_t = ε_t Where ε_t ~ WN(0,σ^2), |Φ|<1, DX_0 < ∞. How do I calculate the autocorrelation function?
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### Fitting of moving average process

I have been trying to wrap my head about the parameters estimation and forecasting of moving average model. It appears that the fitting use the innovations algorithm. If I understood correctly you ...
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### Tuning ARIMA/ETS for univariate time series

I am running auto.arima/ETS models from the forecast package in R on monthly seasonal time series. I see the following fitted ...
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### Non anticipative sampling an ARIMA(1,1,0) process with known terminal value

I have an $\mathrm{ARIMA}(1,1,0)$ process $X_t$, for which I know the values $X_0=a$ and $X_T=b$. I want to sample paths $(X_t)_{t=1..(T-1)}$ consistent with the boundary conditions. One way to do it ...
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### Can an ARIMAX estimate this model?

So I have this AR data series, AR1, mostly (for the argument). I also have an exogeneous regressor, only the DGP I suspect is something in the line of: $y_t=y_{t-1}+\alpha x_ty_{t-1}+\varepsilon_t$ ...
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### What would be best the best way for multiple companies to consolidate their demand forecasting together?

I am currently reading up on my demand forecasting knowledge and had this question where I can't seem to find a quick answer for. Let's say you have a couple of stores/restaurants/etc that sell more ...
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### In SARIMA model do we start by first differences or seasonal differences?

I don't know the general formula for SARIMA model for additive and multiplicative model. I don't know whether we start by first differences or seasonal differences. I only know the formula of ...
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### model summary output from auto_arima

what does [1, 2] mean in SARIMAX(2, 0, 0)x(0, 1, [1, 2], 12) in the model summary output especially the seasonal order printed out to be (0,1,2,12)? This is the model summary output based on the best ...
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### Getting different AIC / BIC values for AR(2) estimation via AutoReg(2) vs ARIMA(2,0,0) through python statsmodels

I am trying to fit an AR(2) model to a data series claims_df['initial claims'] via statsmodels.tsa.ar_model.AutoReg and ...
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### With Stationarity How can ARMA Modelling have any Validity?

I have recently been thrown into the deep end with time-series econometrics. The first thing I have learned is that in order to avoid the spurious correlation trap, I need to ensure that all the ...
1 vote
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### AIC/BIC of ARIMA and ARIMA-GARCH

I was modelling a time series with an ARIMA(1,1,1) model which had an AIC of -4782.96. However, after checking squared residuals and performing ARCH tests (Engle's and McLeod-Li) I detected the ...
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### My fit looks shifted in respect to the observed time series [duplicate]

I am using an ARIMA to find the fit and forecast a time series. The fit looks good despite the shift when i overlay the observed series and my fit model. Please see pic below: What is possibly ...
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### Why ADF test indicates non stationarity but auto_arima selects I argument as 0?

I have a timeseries dataset with 1 min frequency and have modeled it with ARIMA for forecasting purpose. Before modeling, I ran Augmented Dickey Fuller test and the result is: ...
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### Predictive Distribution of Time series with Uncertain Future Values

In machine Learning, and especially in Turning Point Detection Problem, it is important to have the best estimate for the probability distribution function (PDF) of the future samples. Lets say that ...
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### Unsure If I should do a seasonal difference in my dataset

I'm doing my final project for my bachelor's on Time Series, I'm using a dataset for precipitation for São Paulo City here in Brazil. My goal is to divide the dataset into training and testing and ...
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### How do I write a mathematical equation for ARIMA(0,1,2)(2,1,0)[12] [duplicate]

I would appreciate if someone could help me write the mathematical equation for the seasonal ARIMA (0,1,2) x (2,1,0) period 12, given the coefficient for MA1: -0.1, MA2: -0.3, SAR1: -0.7, SAR2: -0.4 I ...
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### Arima model not showing seasonality in its forecast

The following is a seasonal(not perfectly) time series sequence that I am trying to fit an ARIMA model to: I performed box-cox transformation, 1 seasonal differencing and 1 regular differencing to ...
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### SARIMA Model and Arima model

I am trying to model data that looks like this. (daily log return of crude oil) I have decided to use SARIMA model with order $(0, 0, 0) (1, 0, 1)_{[14]}$. Is this same thing as ARIMA model with ...
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### Why does the performance of prediction_in_sample() very different from predict() in ARIMA models

I try to use prediction_in_sample() in an ARIMA model (python package pmdarima) to estimate the whole time series and ...
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### Adding "weekly" seasonality in arima R

I've found the internet fairly unhelpful with this issue and thought I'd turn. I have the following arima model: ...
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### Is ARIMA the right model to use for the questions I am trying to answer?

I am looking for guidance or suggestions on the best model or method to solve the questions below. My dataset is a time series that contains date, number of orders, and number of Customer Service (CS) ...
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### Stationary time series and ARMA process

Based on the shown tests ADF, ACF and PACF is the differenced time series stationary and could it be characterized by an ARMA process? Thanks!
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### Recalculate fitted values/Simulate of an Arima model with different xreg values

I have about 100 ARIMA models, where each models the demand of a separate household using the temperature as an exogenous value. I've used the auto.arima from the ...
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### Best model(s) & suggestion for correlation between two variables , "lag" effect, & forecasting time series

I am looking for guidance or suggestions on the best model or method to solve the questions below. My dataset is a time series that contains date, number of orders, and number of Customer Service (CS) ...
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### Anomaly detection and root cause analysis

ARIMA is widely used for anomaly detection on time-series data e.g. stock price prediction. ARIMA assumes that future value of a variable (stock price in our case) is dependent on its previous values. ...
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### One anomaly detection model for all industries

Background - I'm creating a time-series anomaly detection (TSAD) model for the wifi throughput. My customers are 2 banks, 5 retail stores, 4 universities, 6 hospitals. Currently, I have 2 options to ...
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### What is the meaning of mean reverting level and what this metric tells us?

I was modelling an ARMA process of the Unemployment rate of the USA and I was required to calculate the mean reverting level of the model. I chose the following model: ARIMA(1,0,2) (The data was ...
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### How to define degree of freedom for Ljung Box text?

I am using Ljung-box test after fitting an ARIMA model to a time series to investigate whether residuals do look like white ...
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### AIC, BIC and log likelihood which more important?

I am currently searching for the best ARMA(p,q) model for my conditional mean. When comparing the AIC, BIC and LL, I see that some model perform better in AIC, some in BIC and some in LL. The AC and ...
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