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1) Explanations on My Model
As my model is a stock trading model, I will explain to you how I trade stocks. Please bear with me for explaining how I trade stocks. It is not a long explanation.

  • I am using Bollinger bands to trade stocks. (All the stock data in this example is daily).
  • In short, I calculate simple moving average (SMA) and standard deviation of N days long stock prices. (Yes, I assume that the stock prices follow the Gaussian distribution.) The upper band is SMA + k*stdev, while the lower band is SMA - k*stdev.
  • I buy the stock when the stock price is above the upper band ('Too_High_Buy') or below the lower band ('Too_Low_Buy'). For the 'Too_High_Buy' case, I sell the stock when the stock price goes below the SMA. For the 'Too_Low_Buy' case, I sell the stock when the stock price goes above the SMA.

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  • The parameters of my model is SMA and Stdev, while the hyper-parameters are N and k.
    • N: It decides how smooth SMA (the yellow line) will be.
    • k: It decides how far the upper and lower bands will be located from the SMA.

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  • As different values of N and K show different characteristics, we should search which values of N and K are good for stock price data.

2) How to decide the hyper-parameters(N & k)

  • I use 'sliding steps' to decide the appropriate number for two hyper-parameters, N and K.
  • Sliding steps use the fixed amount of training data to decide the hyper parameter and check the performance of these hyper-parameters on the validation dataset, which immediately follows the training dataset.

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  • I thought sliding steps is a good cross-validation tool to apply on stock data, because statistical properties of stocks can change while time goes by. For example, 30 years ago, McDonald and Coca-cola shows the similar price movements because they were sold together. However, nowadays, Coca-cola focuses on healthy drinks while McDonald stays as unhealthy food brands, they can show different price movements.

  • The hyper-parameter here can be several things, but for the sake of simplicity, let's say the hyper-parameters that we should decide is the duration of training dataset (N). The duration of dropped and forecasting is set to 1 day.

  • Using grid-search of different values of N and K, I calculate which values of N and K shows the best performance during the validation period in the training dataset.

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3) My question

  • Can I use different k for different training sets? In other words, can I dynamically change which value of K to use based on the performance of sub-training dataset?

  • While performing the grid-search in the sliding step window method, we use the same value of K in all the training datasets to trade a stock during the validation period.

  • However, we can use different values of K based on the performance of sub-training data.

  • For example, let's say N is fixed to be 30 days. Then from the 1st Jan to 30th Jan, k=0.6 shows the best performance and we use this k=0.6 for the 31st Jan. Then from the 2nd Jan to 31st Jan, k=1.5 shows the best performance, then we use this K value for the 1st Feb, and so on.

  • Why should we use the shared hyper-parameter K all across the model? For parameters, it makes sense because it allows reduction of the parameters that the model has to learn. (source: Recurrent NNs: what's the point of parameter sharing? Doesn't padding do the trick anyway?)

  • But for using shared hyper-parameters, the amount of hyper-parameters is the same whether I use the shared hyper-parameters or not. It is only 1 hyper-parameter, which is K. The amount of computations needed is the same as well.

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  • $\begingroup$ Hi: I would consider K a parameter just like any other parameter. Why do you call it a hyper-parameter ? Also, all of this training stuff you're doing is interesting but the strategy's effectiveness is still going to be dependent on the chosen parameters holding up in the future. So, the issue is really parameter robustness. I'm not sure or clear on how any training or sub-training methodology can help with the issue of robustness ? $\endgroup$
    – mark leeds
    Feb 12 '21 at 6:27
  • $\begingroup$ If you consider 'k' to be a parameter rather than a hyperparameter, do you also consider 'n' to be a parameter as well? And can you also back up your reasons for it? The reason that I consider 'n' and 'k' to be hyperparameters is that I am using a Gaussian distribution to describe stock prices. And robusteness is an important topic, but I naïvely assume robustess holds up, based on several academic papers claiming that statistical properties of stock price movements keeps almost the same for a limited amount of time. Definitely needs to get improved. $\endgroup$
    – Eiffelbear
    Feb 12 '21 at 6:48
  • $\begingroup$ Hi EiffelBear: yes, I would view $n $ and $k$ as parameters also. I'm not sure how to explain why except to say that they are model inputs that effect the output of the model. A distribution has parameters of course but I would claim that anything that effects the output is also a parameter. Maybe it doesn't matter whether you call them parameters or hyperparameters ? I just mentioned that because I didn't understand what the difference was ? Do you treat hyperparameters differently than parameters ? $\endgroup$
    – mark leeds
    Feb 12 '21 at 22:51
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Quoting George Box, "All models are wrong, but some are useful." The model with static parameters would be at least somewhat explanatory, but not necessarily predictive. By parameterizing too much one might stumble upon a perfect fit, which will fail miserably on future data.

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