Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 56.07% per annum.
- GM price at the close of March 28, 2025 was $46.68 and was lower than the bottom border of the primary price channel by $5.83 (11.11%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 41.89% per annum.
- GM price at the close of March 28, 2025 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 GM 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: August 10, 2023
End date: January 27, 2025
a = 1.8923
b = 0.0012
s = 0.0778
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 56.07%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0778) – 1
= 36.51%
August 10, 2023 calculations
Top border of price channel:
Exp(Y847)
= Exp(a + b × X847 + 2 × s)
= Exp(a + b × 1,228 + 2 × s)
= Exp(1.8923 + 0.0012 × 1,228 + 2 × 0.0778)
= Exp(3.5454)
= $34.65
Bottom border of price channel:
Exp(Y847)
= Exp(a + b × X847 – 2 × s)
= Exp(a + b × 1,228 – 2 × s)
= Exp(1.8923 + 0.0012 × 1,228 – 2 × 0.0778)
= Exp(3.2342)
= $25.39
January 27, 2025 calculations
Top border of price channel:
Exp(Y1,213)
= Exp(a + b × X1,213 + 2 × s)
= Exp(a + b × 1,764 + 2 × s)
= Exp(1.8923 + 0.0012 × 1,764 + 2 × 0.0778)
= Exp(4.1991)
= $66.63
Bottom border of price channel:
Exp(Y1,213)
= Exp(a + b × X1,213 – 2 × s)
= Exp(a + b × 1,764 – 2 × s)
= Exp(1.8923 + 0.0012 × 1,764 – 2 × 0.0778)
= Exp(3.8879)
= $48.81
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 56.07% per annum.
- GM price at the close of March 28, 2025 was $46.68 and was lower than the bottom border of the primary price channel by $5.83 (11.11%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: November 5, 2024
End date: March 14, 2025
a = 6.5338
b = -0.0015
s = 0.0317
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0015) – 1
= -41.89%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0317) – 1
= 13.51%
November 5, 2024 calculations
Top border of price channel:
Exp(Y1,159)
= Exp(a + b × X1,159 + 2 × s)
= Exp(a + b × 1,681 + 2 × s)
= Exp(6.5338 + -0.0015 × 1,681 + 2 × 0.0317)
= Exp(4.0971)
= $60.17
Bottom border of price channel:
Exp(Y1,159)
= Exp(a + b × X1,159 – 2 × s)
= Exp(a + b × 1,681 – 2 × s)
= Exp(6.5338 + -0.0015 × 1,681 – 2 × 0.0317)
= Exp(3.9705)
= $53.01
March 14, 2025 calculations
Top border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 + 2 × s)
= Exp(a + b × 1,810 + 2 × s)
= Exp(6.5338 + -0.0015 × 1,810 + 2 × 0.0317)
= Exp(3.9053)
= $49.66
Bottom border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 – 2 × s)
= Exp(a + b × 1,810 – 2 × s)
= Exp(6.5338 + -0.0015 × 1,810 – 2 × 0.0317)
= Exp(3.7786)
= $43.75
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 41.89% per annum.
- GM price at the close of March 28, 2025 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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