# Questions tagged [moving-average-model]

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### When forecasting by Moving Average Process, how is the error term ε calculated from data?

For simplicity, parameters have been trained. In the case of the AR process, it is able to forecast using observed data. However, the ε used for the MA process is not present in the data. I would like ...
1 vote
81 views

### Is a moving average model fitted to white noise?

I don't understand the following definition of a moving average model from Hyndman 2021, Forecasting: principles and practice A moving average model uses past forecast errors in a regression-like ...
• 321
22 views

### time series how to manually create variables for moving average model in R

I have the following dataframe. ...
• 79
1 vote
13 views

### Variance of an MA(q) model in R? [closed]

How exactly can I calculate the variance of an MA(q) model in R?
17 views

### invertible moving average (MA) and its inverted form

Since we can write any invertible MA(q) time series in the inverted form as $z_t \approx \sum_{j=1}^{p}\pi_j z_{t-j} + a_t$, does this mean that we can fit an AR(p) model (with p being high enough) ...
• 1
49 views

### How to compute the fitted values of an MA(1) model manually?

I'd like to graph in Excel the fitted values of: MA(1) model I estimated using Eviews. I can't figure how to use the MA estimated coefficient to calculate the model output. Is there any ...
127 views

### Where is $|\theta|<1$ used in recursive method derivation of invertibility of MA(1)?

Silly question: From what I understand, an MA process is invertible when it can be represented as an AR($\infty$) process. When using lag operator, it is somewhat clear that $|\theta|<1$ is ...
• 2,213
1 vote
35 views

### Writing MA and AR representations

I have to determine if $$(1 - 1.1B + 0.8B^2)Y_t = (1 - 1.7B + 0.72B^2)a_t$$ is stationary, invertible or both. I have shown that $\Phi(B) = 1 - 1.1B + 0.8B^2 = 0$ when $B_{1,2} = 0.6875 \pm 0.8817i$, ...
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1 vote
106 views

### Moving Average Model over error terms

This is a basic question on Box-Jenkins MA models. As I understand, an MA model is basically a linear regression of time-series values Y against previous error terms et,...,et−n. That is, the ...
295 views

### How to fit a MA(q) model for forecasting?

I have some trouble with understanding how to fit a pure MA(q) (Moving-Average Model of order q) to a time-series in order to forecast future values. We do not have any past forecasting errors, ...
• 51
543 views

### Intuition behind MA(q) (moving average) time series forecasting model (i.e. 'MA' part of ARIMA) and implementation

The $AR(n)$ part of ARIMA makes sense to me. If $$x_{t+1}=\sum_{i=0}^n a_ix_{t-i}$$ then we are making the intuitive assumption that the next time step will somehow depend on the previous time ...
• 207
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### Where does the white noise come from in MA(q) model?

I'm having trouble understanding the intuition of the moving average model. How is summing up a bunch of white noises related to predicting your particular time series data? Suppose I have a MA(q) ...
• 431
1k views

### What is a correct implementation of the moving average model

I would like to implement a moving average model in python as when I try to use the statsmodels library, specifically the ARMA(p,q) function and setting $p=0$ I get a lot of convergence errors in the ...
• 561
Playing around with auto.arima to see how effective it is at model selection. I first simulated an $AR(1)$ process with $X_{t+1} = 0.9 X_t + \epsilon_t$ ...