Cross Validated Asked by Grantx on November 2, 2021
In the screenshot, you will see the daily prices of Nasdaq. Each candle has a High, Low, Open and Close price.
I have drawn a regression line with a 2 standard deviation channel on either side.
How would I go about determining the following odds:
Price reversing back to the mean from the top of the channel
Price reversing back to the mean from the bottom of the channel
Here is the relevant data in CSV format:
Date,open,high,low,close 2020-04-22,8638.04,8791.67,8584.55,8606.75 2020-04-23,8606.75,8786.69,8503.14,8773.93 2020-04-26,8773.93,8904.59,8736.59,8824.04 2020-04-27,8824.04,8953.96,8662.47,8707.38 2020-04-28,8707.38,9128.59,8707.38,9128.17 2020-04-29,9128.17,9154.75,8866.86,8879.61 2020-04-30,8879.61,8888.91,8682.93,8727.01 2020-05-03,8727.01,8838.2,8568.02,8820.48 2020-05-04,8820.48,9030.75,8810.19,8945.63 2020-05-05,8945.63,9068.2,8890.4,8957.83 2020-05-06,8957.83,9137.67,8942.08,9129.77 2020-05-07,9129.77,9246.73,9115.09,9225.91 2020-05-10,9225.91,9346.54,9127.77,9289.57 2020-05-11,9289.57,9354.5,9048.46,9050.96 2020-05-12,9050.96,9212.14,8886.47,9022.94 2020-05-13,9022.94,9113.27,8856.21,9097.25 2020-05-14,9097.25,9156.71,8933.83,9103.21 2020-05-17,9103.21,9369.66,9103.21,9324.09 2020-05-18,9324.09,9424.65,9291.39,9305.1 2020-05-19,9305.1,9502.52,9280.79,9499.07 2020-05-20,9499.07,9515.22,9355.88,9363.9 2020-05-21,9363.9,9422.59,9246.58,9410.25 2020-05-24,9410.25,9541.35,9395.05,9534.01 2020-05-25,9534.01,9608.78,9376.65,9416.38 2020-05-26,9416.38,9512.9,9177.67,9446.79 2020-05-27,9446.79,9569.72,9324.69,9462.54 2020-05-28,9462.54,9586.35,9376.22,9580.78 2020-05-31,9580.78,9609.06,9454.77,9596.79 2020-06-01,9596.79,9673.83,9509.08,9661.21 2020-06-02,9661.21,9730.72,9638.96,9692.7 2020-06-03,9692.7,9744.5,9574.55,9645.42 2020-06-04,9645.42,9847.5,9603.96,9810.66 2020-06-07,9810.66,9902.49,9748.95,9884.84 2020-06-08,9884.84,10006.7,9813.53,9963.26 2020-06-09,9963.26,10157.12,9960.27,10088.48 2020-06-10,10088.48,10108.41,9585.13,9621.5 2020-06-11,9621.5,9849.63,9495.38,9646 2020-06-14,9646,9816,9381.75,9811.77 2020-06-15,9811.77,10014,9797.8,9969.67 2020-06-16,9969.67,10059.42,9926.92,9998.25 2020-06-17,9998.25,10041.38,9879.25,10003.09 2020-06-18,10003.09,10125.67,9929.69,9932.92 2020-06-21,9932.92,10147.67,9856.86,10134.79 2020-06-22,10134.79,10309.42,9985.74,10190.49 2020-06-23,10190.49,10255.2,9941.56,10029.03 2020-06-24,10029.03,10120.51,9899.8,10109.29 2020-06-25,10109.29,10134.14,9837.73,9880.49 2020-06-28,9880.49,10010.65,9743.03,9999.65 2020-06-29,9999.65,10184.18,9953.2,10151.46 2020-06-30,10151.46,10321.62,10088.89,10268.39 2020-07-01,10268.39,10433.51,10259.41,10360.82 2020-07-02,10360.82,10400.9,10320.4,10338.29 2020-07-05,10338.29,10626.21,10338.29,10610.1 2020-07-06,10610.1,10706.55,10517.89,10538.77 2020-07-07,10538.77,10685.05,10517.73,10683.92 2020-07-08,10683.92,10786.46,10572.29,10735.73 2020-07-09,10735.73,10854.72,10637.74,10850.22 2020-07-12,10850.22,11070.48,10574.11,10610.96 2020-07-13,10610.96,10705.54,10371.63,10656 2020-07-14,10656,10778.78,10563.94,10701.21 2020-07-15,10701.21,10710.39,10488.15,10546.97 2020-07-16,10546.97,10681.67,10535.74,10636.56 2020-07-19,10636.56,10972.65,10558.93,10959.53
Many thanks.
Linear regression is a model that can predict values in unrestricted domain, from $-infty$ to $infty$. If you want a regression model to predict probabilities, then the to-go model is logistic regression that restricts the outputs to $[0, 1]$ range.
For more details see other questions tagged as logistic-regression, for example the What is the difference between linear regression and logistic regression? thread.
Answered by Tim on November 2, 2021
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