I am working with time series and want test different forecasting methods but first I need to test if my time series (sales) data is stationary or not. So I have been learning about KPSS and Dickey-fuller tests.
My data is monetary value in Million USD
I am VERY new, so I am still learning, reading and watching tutorials on how to do it.
I developed a dickey-fuller:
- No drift:
t-stat=-1.6899
- With drift:
t-stat=9.9672
- drift + trend:
t-stat=-9.9099
- Augmented (2 lags):
t-stat=-4.6365
My dickey-fuller critical values are:
| Values | no trend | trend |
|---|---|---|
| 1% | -3.43 | -3.96 |
| 5% | -2.86 | -3.41 |
What I see (please correct me if I am wrong) is that all but the “No drift” t-stat showed that my time series data is stationary.
First question: Can I assume that because 3 out of 4 t-stats passed the stationarity test my series data is stationarity? I am not clear what should I conclude if the no drift t-stat shows to be no stationary.
Second question: my cumulative residuals don’t add to zero, so this mean I did something wrong?
Because I was confused with Dickey-fuller, I also attended to do a KPSS test. Below are my results:
| Values | Constant | Constant + trend |
|---|---|---|
| KPSS | 0.02090016 | 0.020655886 |
| C. Value 95% | 0.463 | 0.146 |
| C. Value 99% | 0.739 | 0.216 |
So because my critical value is higher than my KPSS statistics I accept the null hypothesis and my data series is stationary.
After doing all the test, it looks like my data is indeed stationary, but I am not sure if the fact that my residuals don’t add to zero means I did something wrong and if that t-stat in the no drift, showing the existence of unit root is that relevant for me to proceed with forecasting methods that required stationary data.
Please let me know if you can support me.
Thank you in advance.
As mentioned before I did:
Created a graph of the data
Dickey-fuller test
- No drift:
- With drift
- drift + trend
- Augmented (2 lags)
KPSS
you can seethe results above.