this is what the time series looks like , if one can provide r code to help me our that would be really helpful as well
Fractional differentiation (or differencing) is a technique that transforms an input series to a stationary series while retaining "long-term" memory.
Consider the following example based on S&P 500 closing prices.
The daily returns pass the ADF test however the memory is now lost:
t-stat: -13.77 p-value: 0.00 CV 1%: -3.43 CV 5%: -2.86 CV 10%: -2.57
The question is, are there transformations that produce stationary series but retain most of the features of the underlying series? One of the solutions is applying differentiation with a factor that is not an integer, but a fraction. This parameter is often called
d and is typically constrained to
[0, 1] range, and often produces reasonable results in the
[0.25, 0.50] range.
t-stat: -1.84 p-value: 0.36 1%: -3.43 5%: -2.86 10%: -2.57
t-stat: -2.61 p-value: 0.09 1%: -3.43 5%: -2.86 10%: -2.57
t-stat: -3.50 p-value: 0.01 1%: -3.43 5%: -2.86 10%: -2.57
d=0.45 we have a series that passes the ADF test and yet resembles the underlying to a significant extent.