异常测试 - 线性回归与 t 或不与 t？ 理解设置的问题

Question

If you want to check an anomaly in stock data many studies use a linear regression. Let's say you want to check if there is a Monday effect, meaning that monday is significantly worse than other days. I understood that we can use a regression like: return = a + b DummyMon + ea is the constant, b the regression coefficient, we have the Dummy for Monday and the error term e. That's what I used in python: First you add a constant to the anomaly:

anomaly = sm.add_constant(anomaly)

Then you build the model:

model = sm.OLS(return, anomaly)

The you fit the model:

results = model.fit()

1. I wonder if this is the correct model setup.
2. In this case a plot of the linear regression would just show two vertical areas above 0 (for no Monday) and 1 (for Monday) with all the returns. It looks pretty strange. Is this correct?
3. Should I somehow try to use the time (t) in the regression? If so, how can I do it with python? I thought about giving each date an increasing number, but then I wondered how to treat weekends.
4. I would assume that with many data points both approaches are similar, if the time series is stationary, right? In the end I do a cross section anaylsis and don't care about the aspect of the time series in this case, correct? ( I heard about GARCH models etc, where this is a different)

Well, I am just learning and hope someone could give me some ideas about the topic. Thank you very much in advance.

Answer 1

For time series analysis tasks (such as forecasting or anomaly detection), you may need a more advanced model, such as Recurrent Neural Networks (RNN) in deep learning. You can assign any time step to an RNN Cell, in your case, every RNN Cell can represent a day or maybe an hour or half a day etc.

The main purpose of the RNNs is to make the model understand the time dependencies in the data. For example, if monday has a bad affect, then corresponding RNN Cells will have reasonable parameters. I would recommend you to do some further research about it. Here there are some documentations that may help:

https://colah.github.io/posts/2015-08-Understanding-LSTMs/ (Also includes different types of RNN)

https://towardsdatascience.com/understanding-rnn-and-lstm-f7cdf6dfc14e

And you can use tensorflow, keras or PyTorch libraries.