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Arima Output - Relationship between my raw data and the residuals generated

L

Larakine

#1
Hello

I'm an undergraduate at the university of Leeds, I'm currently working on my dissertation and at the moment this involves analysing time series data (Tree ring width series for a number of trees at a number of sites over about a century). This data is fairly noisey and it was suggested to me that I use ARIMA to smooth my data and then utilise the residuals.

I'm half aware of what I'm doing and what it means but I'm not confident enough in my knowledge to fully describe it and justify doing it in my dissertation write up so feel free to asume I know nothing when replying because I don't know much beyond that.

My main questions:

+ What is the nature of the relationship between my raw data and the residuals generated after perfomong an ARIMA (I'm altering the autoregressive and the moving average and ignoring the d function).

+ What do the output values in the session window mean? (I'm used to simple hypothesis testing but as I'm supposedly smoothing the data and not testing a hypothesis when perfoming and ARIMA the value of P in relation to any pre-determined significance level means nothing to me)

Any response will be greatly appreciated!


Thank you!

Caroline


p.s. I'm also not using ARIMA to plot future values so don't worry about explaining that either.
 
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#2
My main questions:

+ What is the nature of the relationship between my raw data and the residuals generated after perfomong an ARIMA (I'm altering the autoregressive and the moving average and ignoring the d function).
The residuals are the differences between the values predicted by your ARIMA model and the actual values. Residuals should be normally distributed, and should display random patterns when plotted versus fits and versus order.

+ What do the output values in the session window mean? (I'm used to simple hypothesis testing but as I'm supposedly smoothing the data and not testing a hypothesis when perfoming and ARIMA the value of P in relation to any pre-determined significance level means nothing to me)
The p-value in ARIMA is testing the hypothesis that the coefficient/constant is = 0. A p-value < 0.05 means the coefficient/constant is not = 0.
 
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