Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 21.06% per annum.
- BMY price at the close of November 20, 2024 was $57.88 and was higher than the top border of the primary price channel by $11.24 (24.09%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 123.93% per annum.
- BMY price at the close of November 20, 2024 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of BMY price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: March 30, 2022
End date: August 12, 2024
a = 4.8908
b = -0.0006
s = 0.0675
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0006) – 1
= -21.06%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0675) – 1
= 31.00%
March 30, 2022 calculations
Top border of price channel:
Exp(Y592)
= Exp(a + b × X592 + 2 × s)
= Exp(a + b × 860 + 2 × s)
= Exp(4.8908 + -0.0006 × 860 + 2 × 0.0675)
= Exp(4.4685)
= $87.22
Bottom border of price channel:
Exp(Y592)
= Exp(a + b × X592 – 2 × s)
= Exp(a + b × 860 – 2 × s)
= Exp(4.8908 + -0.0006 × 860 – 2 × 0.0675)
= Exp(4.1985)
= $66.58
August 12, 2024 calculations
Top border of price channel:
Exp(Y1,186)
= Exp(a + b × X1,186 + 2 × s)
= Exp(a + b × 1,726 + 2 × s)
= Exp(4.8908 + -0.0006 × 1,726 + 2 × 0.0675)
= Exp(3.9073)
= $49.76
Bottom border of price channel:
Exp(Y1,186)
= Exp(a + b × X1,186 – 2 × s)
= Exp(a + b × 1,726 – 2 × s)
= Exp(4.8908 + -0.0006 × 1,726 – 2 × 0.0675)
= Exp(3.6373)
= $37.99
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 21.06% per annum.
- BMY price at the close of November 20, 2024 was $57.88 and was higher than the top border of the primary price channel by $11.24 (24.09%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: May 23, 2024
End date: November 20, 2024
a = 0.0176
b = 0.0022
s = 0.0355
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0022) – 1
= 123.93%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0355) – 1
= 15.27%
May 23, 2024 calculations
Top border of price channel:
Exp(Y1,132)
= Exp(a + b × X1,132 + 2 × s)
= Exp(a + b × 1,645 + 2 × s)
= Exp(0.0176 + 0.0022 × 1,645 + 2 × 0.0355)
= Exp(3.7219)
= $41.34
Bottom border of price channel:
Exp(Y1,132)
= Exp(a + b × X1,132 – 2 × s)
= Exp(a + b × 1,645 – 2 × s)
= Exp(0.0176 + 0.0022 × 1,645 – 2 × 0.0355)
= Exp(3.5798)
= $35.87
November 20, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(0.0176 + 0.0022 × 1,826 + 2 × 0.0355)
= Exp(4.1216)
= $61.66
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(0.0176 + 0.0022 × 1,826 – 2 × 0.0355)
= Exp(3.9796)
= $53.49
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 123.93% per annum.
- BMY price at the close of November 20, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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