As said in the title, are stationarity and low autocorrelation the prerequisite of general / linear regression model ? That is, if a time series is non-stationary or has large autocorrelation, would it be easier or harder to be predicted using regression model such as linear model and deep learning ?
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2 Answers
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For (linear) regression models, the following assumptions have to hold:
- Linear Relationship
- Multivariate normality including your error term with zero mean + some infinite variance following a normal distribution
- No-autocorrelation
- No (strong) multicollinearity
- No homoscedasticity
Non-stationarity (caused by changing mean or/and variance over time) is prevailing in most level data (e.g. stock prices) - as it has a unit root or is trend stationary.
To cure your data from non-stationarity in most of the times, it is sufficient to use the relative change (percentage change - or log changes). Taking logarithmic changes, can also cure of homoscedasticity a bit.
To test for stationarity, you can use the Augmented-Dickey-Fuller-Test where the Null hypothesis states that a unit-root is present in your data set, thus you have a non-stationary variable.
Coming to your second question about time-series and deep learning. Unfortunately, I haven't found a good paper/article yet that discusses the assumptions on the main data properties that have to be satisfied to get correct statistical results. See my own post - not answered yet
However, as deep learning models make use of the same underlying statistical assumptions - e.g. probability distributions etc. or even the underlying models (see e.g. linear activation function) - I guess, in a time-series framework, the same assumptions have to hold, otherwise, there is the chance of spurious regression.
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You can use regression models, but for the correlation, if you are using any categorical columns one hot encoded data, you need to ensure that you are handling the dummy variable trap properly as it highly affects your model accuracy. Refer here to know more about this:
