Time Series

How to test for stationarity?

(i) |X|<1
(ii) the individual roots should be greater than 1.

When and Why?

 

1)Not |X|<1 , its a alpha should |alpha(parameter of Autoregressive(1) model)|<1
2) yes!
When you need to or you are asked to check it out.
because Stationary time series has identical statistical property for all tim, so easier to apply statistical prediction.

 

Thanks Aton!!
So when we are asked to fit the model of a time series process ARIMA(p,q,r)

I came across the Question paper solving as (2,0,3)
provided the process is stationary.
without checking for I.

 

Hi JuniorA,
I edited my post,check |alpha|<1 only in AR(1) to know Stationarity.

 

Dear hemant rupani
can u please explain question 4.13 of Q& A BANK OF CT6

 

Hi Supriyo
Autocorrelation tends to decay to zero in stationary time series.
So from the given data it's the good clue that time series is differenced 1. Lowest variance is also a strong suggestion.

Note: we difference time series until we get close enough stationarity.

 

Hi hemant
here my question is why ar process is of order 2 and ma process is of 0 order.

 

Given Order is a fact. In Q. We didn't identify that.

Even if you wanted to identify those, use asymptotic results given in The Section 2.3/2.4.
From you can get estimation of ARIMA (2, 1, 1)... that has different MA.
As you know estimation are not always right.