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)
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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 ...
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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 &:...
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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:
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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:
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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.
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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)[12] with drift, with an additionnal MA at lag 3 as when I have fitted an ARIMA(1,1,0)(0,1,1)[12] 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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Stationarity of ARMA-like time series
It is well known that for $X_t \sim ARMA(p,q)$ where $\phi(B)X_t = \theta(B)Z_t, Z_t\sim WN(0, \sigma^2)$, if $\phi(z)\neq0$ in the unit circle, $\{X_t\}$ is stationary.
Now assume $\{Y_t, t=0, \pm1, ....
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Does my ARIMA Model Fail because of the non stationary data?
I am trying to create an ARIMA model which allows to extrapolate a voltage curve of a sensor battery into the future. Is this a possible application scenario at all?
I have four different voltage ...
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Cowpertwait-Metcalfe Introductory Time Series Exercise 4.8 - Derive ARIMA Model
I am trying to solve Exercise 4.8 in Cowpertwait-Metcalfe: Introductory Time Series with R. (For self study, not for coursework.)
We are given a time series model
\begin{align*}
x_t & = x_{t - 1} +...
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Validity of Automatic Portmanteau test for serial correlation vs Ljung-Box Test
I would like to model the Value-at-Risk of U.S. sector indices and the U.S. Broad Dollar Index using the variance-covariance method. To achieve this, I model the conditional means and variances of the ...
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ACF and PACF graphs - MA, AR, ARMA, ARIMA?
The data are for areas.
How would I interpret these ACF and PACF graphs, and what model could I use?
To me, this is a non-stationary series and therefore an ARIMA would be suitable, but I don't know ...
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How to write it as the linear process for MA(2) when the characteristic root is complex? [closed]
I have MA(2) as
$$x_t=e_t-0.3e_{t-1}+0.1e_{t-2}$$
and would like to find $x_{t+1}$. But I struggle and
$$x_t(1-0.3B+0.1B^2)^{-1}=e_t.$$
I can't write it as linear process because the root of the ...
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interpret acf plot
I am trying to interpret my results from decomposing my time series and the acf/pacf plot. The adf test gave a p-value less than 0.05 so is it ok to assume that my time series is stationary with no ...
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Inaccuracies due to initial values in GARCH(1, 1) simulation
I'm experimenting with non-normal innovations standard GARCH(1, 1) model
$$\epsilon_t = \sqrt h_t z_t$$
$$h_t = \omega + \alpha \epsilon_{t-1} + \beta h_{t-1}$$
Where $E[z_t] = 0$, $E[z_t^2] = 1$, but ...
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What do you do when the lags in ACF are on the edge of significance? How would you descibe this ACF and PACF plot?
I have caluclated the first differences of a process and now created an ACF and PACF plot and I honestly don't know how to interpret it. I thought that it is an AR(1) process but I see some ...
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train, test and validation data set configuration to compare a machine learing method and ARMA method
I want to compare performance a machine learning method and Autoreressive Moving Average-ARMA(p,q) for time series data.
I do such a configuration:
First I divide data into three part:
Trainig data(...
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What is the formula AUTO ARIMA (Python's pmdarima) uses?
References
https://otexts.com/fpp3/non-seasonal-arima.html
https://otexts.com/fpp3/seasonal-arima.html
Question
According to the webpages, the formula of ...
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Does $ARMA(p,q)$ process need to be invertible and have a causal stationary solution to be written in $MA(\infty)$ representation?
Does $ARMA(p,q)$ process need to be invertible and have a causal stationary solution to be written in $MA(\infty)$ representation?
And if you write the process in terms of $Z_t$ instead of $X_t$, then ...
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Auto Arima failing with highly seasonal data
I have a highly seasonal data of a little more than 1000 observations, with a 67 seasonal cycle.
I am using auto_arima in Python and for some reason when I perform a stepwise search I get a memory ...
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Bad prediction for ARIMA timeseries
I am trying to use ARIMA for hotel reservation. I have data for a year each day and I want to make predictions.
But, my result is very poor I wonder why.
Here I attach my data
And, this is how I run ...
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Arima model generate same predictions
I know there is similar question related this topic but I still cannt solve my case.
So, I have one year data (365 days) of car request. I did 80%(+-280days) for train, and rest for test data. And, I ...
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Time Series Forecasting Improving Accuracy
Here's the sample data I got from Kaggle. This is a sample of daily temperature data for about 20 years. In my initial attempt I tried to simplify this as monthly data and attempted to use a seasonal ...
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Questions about the summary of auto ARIMA (Python pmdarima)
Questions
I trained two models by using two different data sets.
model = pmd.auto_arima(data, trend='ct')
What is intercept in ...
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Time series statistical model evaluation: weighted average across different forecast horizons
I want to use an ARIMA based or Prophet-based model to train on my data. I have split my data into train and test, and the model is trained on train only and forecasts for test.
The further the ...
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ARMA(2,1) Solution and Variance [duplicate]
I have an ARMA(2,1) model of the following form,
$$y_t=a_1y_{t-1}+a_2y_{t-2}+\epsilon_t+b_1\epsilon_{t-1}$$
Re-arranging and using lag operators:
$$(1-a_1L-a_2L^2)y_t=(1+b_1L)\epsilon_t$$
solving for $...
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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 ...
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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....
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Autocovariances of ARMA(2,2)
it's me again! Today I'm asking the question about an ARMA(2,2) and how to compute all the different autocovariances etc... I found the formula for an ARMA(1,1), however I'm having some problems.
Here ...
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SARIMA forecast is just the previous year shifted [duplicate]
I am trying to forecast using the SARIMA model. I have used
auto.arima(ts,seasonal=T,trace=T)
but the prediction I'm getting is just the previous years values ...
