# Detrending inputs still produces uncorrelated residuals but Durbin Watson is still low

I have two time series, and I am using one to forecast the other. Both are trend-nonstationary, so I de-trended them. The resulting model produces non-autocorrelatated residuals, but the Durbin-Watson is still low.

First, my independent variable is plotted, and I see that it is trend-nonstationary.

I can test and see that it is indeed trend-nonstationary, and that a removal of a trend would yield a stationary series.

from statsmodels.tsa.statstools import adfuller

df_temp['past_flow'].plot()
plt.show()
plt.hist(df_temp['past_flow'])
plt.show()
print('p-value: %f' % result[1])

p-value: 0.003948


So I detrend the series

df_temp['past_flow'] = signal.detrend(df_temp['past_flow'] )


I do the same with my dependent series, and I yield the following model:

This model has a rather low Durbin-Watson, but plotting the residuals, I see no autocorrelation:

• You have 11 observations. All stats are just snake oil at this point. Get more data, or don't take the numbers too seriously. For instance, take a look at lag 1 correlation, it's 0.4! And you say there's no autocorrelation – Aksakal Oct 1 '19 at 17:48