# Is autocorrelation the same as multicollinearity?

I have a time series dataset that has 63 features with traffic_volume as the target.

print(main_data.columns)
Index(['air_pollution_index', 'clouds_all', 'humidity', 'temperature',
'wind_direction', 'wind_speed', 'is_holiday_0', 'is_holiday_1',
'is_holiday_2', 'is_holiday_3', 'is_holiday_4', 'is_holiday_5',
'is_holiday_6', 'is_holiday_7', 'is_holiday_8', 'is_holiday_9',
'is_holiday_10', 'is_holiday_11', 'weather_descr_0', 'weather_descr_1',
'weather_descr_2', 'weather_descr_3', 'weather_descr_4',
'weather_descr_5', 'weather_descr_6', 'weather_descr_7',
'weather_descr_8', 'weather_descr_9', 'weather_descr_10',
'weather_descr_11', 'weather_descr_12', 'weather_descr_13',
'weather_descr_14', 'weather_descr_15', 'weather_descr_16',
'weather_descr_17', 'weather_descr_18', 'weather_descr_19',
'weather_descr_20', 'weather_descr_21', 'weather_descr_22',
'weather_descr_23', 'weather_type_0', 'weather_type_1',
'weather_type_2', 'weather_type_3', 'weather_type_4', 'weather_type_5',
'weather_type_6', 'weather_type_7', 'weather_type_8', 'weather_type_9',
'weather_type_10', 'dew_point_1', 'dew_point_2', 'dew_point_3',
'dew_point_4', 'dew_point_5', 'dew_point_6', 'dew_point_7',
'dew_point_8', 'dew_point_9', 'is_weekend', 'traffic_volume'],
dtype='object')


All variables are univariate including the target. However, I would like to have differences between autocorrelation and collinearity to be clarified since this has been my first major time series project and some terms are certainly different than statistics. From what I've analysed, there are collinear variables present and they seem to be hindering the accuracy of predictions but visualising the auto and partial correlation doesn't seem to be suggest that. Can someone help me out on pointing out anything wrong with this data and does it need some removal of variables to make it more robust? I've ued XGBoost algorithms with a MAE of 1635 which is not a good score. The first plot is the correlation matrix while the rest are the auto and partial correlation plots.

Please note the partial and auto correlation plots relate to response variable only.

Autocorrelation is a measure of a correlation of a signal with itself, as a function of delay.

Correlation is usually between two different variables (without respect to time). You can take it with the same variable, but that will of course equal 1.

Either way, XGB is robust to multi-colinearity (correlations between features, or explanatory variables as you'd call them in statistics), please have a look at this post for more information.

Lots of things could be wrong with the model, I would start with really understanding the data and making sure there's nothing wrong with it(missing values, unexpected distributions etc...).

• Thanks. From I've checked, there are 0 missing values and I've scaled and normalised the features so I think the data is in the best form one could transform it. – Shiv_90 Oct 22 '19 at 7:35

Answering the title of your question: autocorrelation means correlation of the response variable with lagged values of itself, whereas multicollinearity means correlation of the response variable with several other explanatory variables (i.e. to implement a multivariate regression, which afterall is the core of a time series forecast with several attributes).

From what I see in your auto-correlation and partial auto-correlation plots, I would suggest you to try out (at least as a baseline model) a simple ARIMA grid search (to find out p,d,q values) with only the response variable, and from this, try out some other models. To try this approach, here you have a nice source: https://machinelearningmastery.com/grid-search-arima-hyperparameters-with-python/

• That was helpful. – Shiv_90 Oct 22 '19 at 7:35