ADFuller Test Intuitive explanation for checking Time Series Stationarity

The toughest part is here!! the ADFuller Test.

As we know(I hope) the ADFuller test has been the go-to method for detecting whether a time series is stationary or not.

But how?

Let us unfold its layers one by one. To be very clear, it would only be an intuitive explanation with bits of mathematics!!

But first of all!!

what is Dickey Fuller Test?

It is a Hypothesis Test with Null Hypothesis stating that a unit root exists for AutoRegressive Time Series(AR models).

but what the hell is unit root?

TAKE A BREATHE & SEE THE PICTURES BELOW

Consider this environment. The picture can be interpreted as flowing water in a sink. The unique feature of such a system is that wherever you put any object, whether the top left corner or the top right corner, the motion will be forward and would appear to converge at the bottom left corner.

JUST IMAGINE

Moving on!!

But as in nature, the path followed by any object won’t be straight but a little wagered(due to turbulence and other disturbances), though the direction remains the same(like towards the convergence point). The white noise term we often see in the AR equation represents these irregularities.

Now consider this situation!!

The irregularities can sometimes be so heavy that the object might lose out its path and miss the convergence point(the bottom point). It may get entangled in some sort of eddies and hence never even converge.

Any Time Series is a sequence of numbers thought to behave like certain flows(like the above illustration). Hence they might be random at times, but would appear convergent towards a central location.

The flow directions of any Time Series depends on some ‘characteristic’ directions which are associated with some numerical values called as root value.If the value of these root values is less than equal to 1, convergence will happen else not.

Hence an AR process can be stationary if and only if all characteristic values are less than unity in size.

If these values are greater than 1, series might not converge (as in 3rd figure ) and hence would be nonstationary!!!

ADFuller test is an upgraded version of DickeyFuller Test where more complex time series models can be incorporated and not only AR models.

I hope now you have an intuitive understanding of the ADFuller Test!!

Explore More Learn More!!!!!