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7 votes

What does the I operator stand for in the context of time series modeling?

The main answer by Stephan is correct, but it is odd to use the identity operator (with the symbol $I$) in a scalar context instead of just using the number one. It would be simpler here if they just ...
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7 votes
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What does the I operator stand for in the context of time series modeling?

It is the identity operator, $IX_t=X_t$, and is typically used in ARIMA type formulas where you also have the backshift operator $B$ (sometimes people use $\nabla$ for the backshift), or polynomials ...
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7 votes

ARIMA(0,1,0) predictions are previous values from one year before

As frank writes, predicting last year's data point is exactly what an I(1) model is all about, so there is no reason for concern here. ARIMA modeling is quite non-trivial, and the old Box-Jenkins ...
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4 votes

ARIMA(0,1,0) predictions are previous values from one year before

The dickey-fuller test shows that the data is stationary and looking at the acf and pacf I decided to use an ARIMA (0,1,0) to model the data.* This is a strange decision, as your ADF test result ...
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4 votes

ARIMA(0,1,0) predictions are previous values from one year before

The ARIMA(0, 1, 0) model is just the I(1) model, which is: $$ y_{t+1} = y_t + \epsilon_{t+1}, $$ also called the random walk. As you can see, the expectation of $y_{t+1}$ is then just the previous ...
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2 votes
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How to investigate annual time series data?

I would be very careful about fitting an ARIMA model to a time series that has only 21 observations, especially if there is a predictor involved. Let's plot your series: We see an upward trend, then ...
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2 votes

Simulation of ARIMA (1,1,0) series

While it's true that you can inspect arima.sim to see what it's doing, I found this blog post more helpful for pedagogical purposes. It starts from a single white ...
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1 vote
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Time Series is not white noise but Random Walk

To proceed with this series for building forecasting , I read many places if your data is not white noise and does not have random walk then you can model forecasting , Otherwise if your time series ...
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  • 503
1 vote

Lag operator; particular solution to ARMA as a MA$(\infty)$ process

A brief overview of the lag operator in time-series analysis In the answer below I will give a brief overview of the lag operator, showing its definition and properties, and how it applies in the ...
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1 vote

ARMA-GARCH python implementation

You are right, but the proposed method is correct. Residuals is what your first model was not able to capture from the original signal. In this case you re trying to get this residual part by a model ...
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