# 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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### Detrending these time series

I have the following time series. Its clearly not a simple linear trend. I want to explore the relationship among these variables using a VAR, or even a time-varying VAR. The biggest issue in my data ...
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### Exact steps for rolling window CV evaluation or sliding window CV evaluation for SARIMA

So far I have using this process: 1)split data into training and test 2)do model selection(p,d,q, P,D,Q,etc) using training data(in this case, I used autoarima) ...
1 vote
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### SARIMA model selection for my data

I am new to time series analysis. I need to determine whether my series is seasonal or not, and if it requires differencing for building an ARIMA model if it is possible? The time series data is ...
1 vote
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### If $X_t$ is an AR(2) process, what is $Y_t := X_t - X_{t-1}$?

Q: If $X_t$ is an AR(2) process, what is $Y_t := X_t - X_{t-1}$? Attempted solution: $X_t = \phi_1 X_{t-1} + \phi_2 X_{t-2} + W_t$, where $W_t$ is white noise. \begin{equation} \begin{split} Y_t &:...
1 vote
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### Seasonal differencing applied to exogenous variable (xreg)? Forecast package R by Hyndman

Im currently working on specifying a seasonal ARIMA model with an exogenous variable. I'm using the forecast package developed by Hyndman for this. I have specified the following: ...
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### How to use MAPE with auto.arima model?

The code below gets a: error in mean(abs((y_true - y_pred)/y_true)) : argument "y_true" is missing, with no default I've seen MAPE used on forecasts. Can one use this and similar methods on ...
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### GARCH fit to the residuals of AR/ARMA mean equation previously fitted

Suppose I have an ARMA (p,q) (let it be ARMA (2,2)) fitted to my original returns series and have the residuals of said ARMA model extracted. Next, it is my understanding that I need to fit a GARCH ...
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### Prove that white noise + normality = independence

If the time series process is linear, then the ARIMA model is specified. The residuals from this model are $(1.)$ no autocorrelation $(2.)$ mean equals zero $(3.)$ constant variance. We say that this ...
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### Can I compare forecasting performance of rolling window VAR and usual forecast of model with ARIMA errors?

Can I compare forecasting performance of rolling window VAR and usual forecast of model with ARIMA errors? Or maybe there is exist better way to compare forecasting performance?
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### Estimating and fitting a GARCH model

By far I've become really familiar with the concept of GARCH but I'm still confused on how to go on with the implementation especially that I've seen multiple sources using different approaches: ...
1 vote
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### How to convert R output from auto.arima function into mathematical model?

I'm building a model using the auto.arima function in R, and it gives the following output: ...
1 vote
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### Interpreting lagged exogenous variables in ARMAX and regression with ARMA errors

There is an interesting post about the connection of lagged exogenous variables and the autoregressive time series model: Forecasting - Lags vs. AR terms for Exogenous Variables Consequently, by using ...
1 vote
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### How to apply heteroscedasticity tests in model with ARIMA errors? [closed]

How to use heteroscedasticity tests in model with ARIMA errors?
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### Rejection of ADF-test for log returns and AIC selected ARIMA(0,0,0) and ARIMA (0,0,0) with a drift?

I use monthly log returns for some stock portfolios and rejects the null of the ADF-test for both. Hereafter I use AIC to select best fitting models using auto.arima in R. The selected models are ...
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### What happens if you difference a IMA?

When we over-difference a time serie, we are introducing units roots in its moving average component, hence obtaining an IMA. My question is: IMA is an integrated time serie, hence it has unit root ...
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### What should I do with structural breaks at return time series?- R

Let say I have the below time series data(It is a return data of a financial derivative): ...
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### How to model structural break in ARIMAX/VAR/ARDL

I tried to use a QLR test for structural breaks for a variable that I am forecasting, and I found a break, which is very accurate to geopolitical events in 2022. Because of this, my significance of ...
1 vote
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### How to calculate Prediction Intervals for time series forecasting with CI

I'm working on a project on time series multi-step ahead forecasting in Python. I have a time series, and I apply an ARMA model on it (statsmodels SARIMAX library). I know that ARMA models, as many ...
1 vote
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### Auto_arima and ARCH

I Have an auto_arima model that works in python but I want to optimize it using ARCH. I have run an ARCH model on my Arima residuals but I do not know what to do with my results. How do I incorporate ...
1 vote
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### auto_arima straight line prediction python

I know this has been asked a lot but I have checked everything and still don't understand. To start, I have a dataset of global temperatures averaged over years. There is a trend in the series and I ...
1 vote
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### ARIMAX model for Google trends: trouble with lots of zeros

I want to apply ARIMAX model on Google trends. I used python package to get daily data. However, this data contains a lot of zeros, so if I do first difference of logs, I see a lot of (inf) in python. ...
1 vote
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### ARIMA, VAR and State Space Model (SSM) forecasting comparison

I am trying to compare the asset price forecasting abilities of SSMs with ARIMA and VAR models. To keep it brief, this is the plan that I am following: Collect multivariate data Perform ADF ...
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### what R function can be used to fit an additional MA term at lag 3 to my ARIMA model?

I want to fit an ARIMA(1,1,0)(0,1,1) with drift, with an additionnal MA at lag 3 as when I have fitted an ARIMA(1,1,0)(0,1,1) with drift model, I have seen there was still autocorrelation in ...
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### Does Arima (1,0,1) exist? Are there any articles station Arima (1,0,1)? How to intrpret Arima (1,0,1) summary results? [duplicate]

I have dataset that corresponds to year (from 1930-2020) and volume of sediment. I have to predict the volume for next 50 years. While trying ARIMA in R I tried different models like (1,0,0), (1,1,0) (...
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### How to stationarise a univariate time series in R when auto.arima gives a model to fit that doesn't stationarise it? [closed]

I am currently working on a univariate time series that I try to modelize (following the Box-Jenkins methodology, I try to identify the model before I estimate it, using correlograms, in order to ...
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### Variance of ARMA (1,1) Model

I'm trying to find the variance of an ARMA(1,1) model of the following form: $$y_t=a_0+a_1y_{t-1}+\epsilon_t+b_1\epsilon_{t-1}$$ where $\epsilon_t$ is a white noise process. I have found it more ...
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### Exogenous variables having negative impact on ARIMA

I have already a SARIMA model working at my company (an ecommerce) to predict sales. Right now I am only trying to improve it. The current model is only using endogenous variables (i.e the sales ...
1 vote
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### Which specification does the statsmodels ARIMA use?

I am estimating a model with exogenous variables using ARIMA, from the statsmodels package. But I can't interpret the results, ...
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### Convert ARMA(p,q) to MA$(\infty)$ and find ACF

$Xt-0.4X_t+0.03X_{t-2}=Zt-0.4Z_{t-1}$ This process is causal and invertible. For the $MA(\infty)$ representation, I wrote it as $X_t=\frac{1-0.4B}{1-0.4B+0.03B^2}Z_t$, where \$\psi(B)=\frac{1-0.4B}{1-0....