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Is SARIMA(0,0,1)$_\text{s}$ actually MA(s)?

I have some doubts about the notation, i.e. whether SARIMA(0,0,1)$_\text{S}$ should be interpreted as SARIMA with all the nonseasonal lag and differentiation orders set to zero. It would be less less ...
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Fit an ARMAX model in R

As of 2022, Hyndman is using fable::ARIMA, but in his otherwise excellent time series regression guide (https://otexts.com/fpp3/) is still only showing how to do a linear regression with arima errors. ...
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PACF for MA(1) process

From Time Series Analysis, 1990 by William W. S. Wei book \begin{eqnarray*} \phi_{kk} = \frac{ \det \begin{pmatrix} 1 & \rho_1 & \rho_2 & \cdots & \rho_{{k}-2} & \...
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Conflicting ACF/PACF after first-difference

There is nothing conflicting here. Differencing a unit root process removes the unit root. If the original process is AR(1) with a unit root, $y_t=y_{t-1}+\varepsilon_t$, the differenced process is ...
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Why is non-normality of time series not a problem for ARIMA and GARCH?

Why should it be a problem? Note that modelling assumptions are typically made about the distribution of residuals or the conditional distribution of the dependent variable. I have just seen some ...
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VAR model with AR(p) and ARMA(p,q) data?

Any method being the correct method is a strong claim that is hard if not impossible to prove in practice. Yet you can seek methods and models that are useful for your goals and justifiable from a ...
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Is ARIMA-GARCH nested within ARIMA?

ARIMA-GARCH is not nested within ARIMA, but ARIMA is nested within ARIMA-GARCH. This is because you can obtain ARIMA from ARIMA-GARCH by simplifying the latter model's conditional variance equation to ...
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Can an ARIMAX estimate this model?

A simple ARIMAX(1,0,0) should be of the form $y_t = α_1y_{t-1} + α_2x_t + e_t$. From your question it seems that is what you wanted to write, isn't it? As @Richard pointed out, the equation you wrote ...
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Tuning ARIMA/ETS for univariate time series

A model with a better fit =/= a model with better forecasts in the time series world. Most 'auto' tuning frameworks optimize based on an approximation of the forecast accuracy rather than in-sample ...
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Getting different AIC / BIC values for AR(2) estimation via AutoReg(2) vs ARIMA(2,0,0) through python statsmodels

When AutoReg was first included in Statsmodels in e.g. v0.12, it used the AIC definition from Lutkepohl's book New Introduction to Time Series Analysis, which ...
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Looking for advice: Short-term forecasting using actual forecasts and real time data

The first step is to organise all of your historical data and clean it - you say you have inconsistent reporting due to network problems, this will lead to gaps in your historical dataset which will ...
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AIC/BIC of ARIMA and ARIMA-GARCH

It is highly implausible that the AICs of such relatively similar models differ as much. Most likely they are not directly comparable due to quirks of definitions of AIC (and the likelihood on which ...
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Recalculate fitted values/Simulate of an Arima model with different xreg values

You can use simulate(arima_model, xreg = new_x) with a the parameter xreg to simulate a time series with a different regressor ...
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How to put an ARMA(2,2) model in state-space form

One way to do it is to define the state vector as $$ \xi_t = \begin{pmatrix} y_t \\ y_{t-1} \\ w_{t} \\ w_{t-1} \\ 1 \\ \end{pmatrix} $$ The measurement equation is just $$ y_t = \begin{pmatrix} 1 &...
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Why does the performance of `prediction_in_sample()` very different from `predict()` in ARIMA models

The "in-sample predictions" are rolled 1-ahead forecasts: $$p_t := \mathbb{E}(X_t | \mathcal{F}_{t-1})$$ But the out-of-sample predictions are $h$-ahead forecasts: $$f_h := \mathbb{E}(X_{T+h}...
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