What is the topic of auto regresive in math?

In summary, the conversation discusses a model known as the autoregressive model, which is described as a 1st order linear recurrence relation in math. However, in DSP, it is referred to as an autoregressive model. The topic of this model is not commonly studied in math books, but it can be explored further under the topics of autoregressive integrated moving average (ARIMA) or Box-Jenkins models. Some recommended books for understanding this concept include "Concrete Mathematics" and "Generatingfunctionology."
  • #1
stn
8
0
I have a model (autoregressive model) described as follows:
Y(n)=Y(n-1)*c
This model in math, is it considered non-linear? In DSP (digital signal processing), it is called autoregressive.
Why in math, this model is not studied? Or, what is the name of the topic discussing this model? (i want to explore more about this topic but can't find in math books).thanks
 
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  • #3
If you want models that add "noise" to the picture, see "autogressive integrated moving average" (ARIMA) models or "Box-Jenkins" models.
 
  • #4
Thank you jbunni & Stephen. I now remember studying this model in discrete math.
I appreciate your help.
 
  • #5
Any good book describing recurrence relation or difference equations?
I hardly found this topic is disccussed in math books. Often differential equations but not difference equations.

thanks
 
  • #8
thanks for the recommended books from both of you :)
 

1. What is an autoregressive model?

An autoregressive model is a mathematical tool used to analyze time series data, where the value of a variable at a given time is predicted based on its past values. It assumes that the value of a variable is dependent on its previous values and uses this relationship to make predictions.

2. How does an autoregressive model work?

An autoregressive model works by fitting a mathematical equation to a time series dataset, where the current value of a variable is expressed as a linear combination of its past values. This equation is then used to make predictions for future values of the variable.

3. What is the difference between autoregressive and moving average models?

Autoregressive and moving average models are both used to analyze time series data, but they differ in the way they use past values to make predictions. An autoregressive model uses past values of the variable itself, while a moving average model uses past values of the error terms in the model.

4. What are the assumptions of an autoregressive model?

The main assumptions of an autoregressive model are that the time series data is stationary, meaning that its mean and variance do not change over time, and that the values of the variable at different time points are not correlated with each other.

5. How is an autoregressive model evaluated?

An autoregressive model is typically evaluated by measuring its performance in predicting future values of the variable. This can be done by comparing the predicted values to the actual values using metrics such as root mean squared error or mean absolute error.

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