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I'm doing some predictions on a time series dataset and have stumbled upon what I perceive as several variables being collinear. However, does time series accept multicollinearity as a possible property or is it concerned only with autocorrelation? The first plot shows the correlation matrix for the whole dataset while the second one shows the autocorrelation for the response variable. The third is the partial autocorrelation plot:

collinearity autocorrelation partial autocorrelation Looking at the second plot, one would say the periodicity of the distribution is regular even though I'm not getting correct predictions. Should I be caring about multicollinearity in time series data?

Let me add some more details about the data I have. Specifically, this is a traffic congestion time series that originally had 14 variables plus a 15th one which is the response variable:

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')

traffic_volume is the target that I need to predict for a period from 2017 to 2018 on a daily basis. The rest of the features were engineered by me and are mostly categorical variables one hot encoded. Unfortunately I cannot plot the daily values for the response since that plot is tedious but I have decomposed it to make it more readable. trends plot

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  • $\begingroup$ Could you explain what constitutes your "time series dataset"? Currently it's unclear what your "several variables" might be or what you might even mean by "multicollinearity," because (a) that's not applicable to any univariate time series but (b) your plots strongly indicate you have a univariate time series. $\endgroup$ – whuber Oct 21 '19 at 13:29
  • $\begingroup$ For that I've described the columns above (see code snippet). Also the correlation matrix can be zoomed in and shows clear names of all the columns. $\endgroup$ – Shiv_90 Oct 21 '19 at 13:32
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No, collinearity and autocorrelation are not the same thing.

Collinearity is a relationship among different independent variables. In exact collinearity one IV is a linear combination of other IVs. In approximate collinearity, it is nearly so. Usually, collinearity isn't present to a problematic degree.

Autocorrelation is the relationship of a variable to an earlier version of itself. I am not expert on time series, but I would say that autocorrelation is the rule, rather than the exception. It's hard to think of a variable where the value at time T would not be related to the value at time T-1.

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  • 3
    $\begingroup$ This answer confusingly employs "autocorrelation" in unusual and ambiguous senses. Autocorrelation is a measure of an association between values and lagged values in a series. It always exists (at least when the marginals have finite nonzero variance). It sounds like you mean to say that empirical autocorrelation values are frequently nonzero. Note the distinction between data and model parameters: MA models for time series, for instance, characteristically have zero autocorrelation beyond a (typically small) lag. $\endgroup$ – whuber Oct 21 '19 at 16:44
  • $\begingroup$ So basically autocorrelation cannot be ruled out; it's an integral part of time series data. If that is the case, then does the time series data I described above have multicollinear variables that require treatment? Personally I think so and I'll have to test it out by removal of some of the features. $\endgroup$ – Shiv_90 Oct 22 '19 at 7:30

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