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 February 20, 2025 was $47.89 and was lower than the bottom border of the primary price channel by $2.49 (4.95%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 44.14% per annum.
- GM price at the close of February 20, 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 = 1.8484
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(Y873)
= Exp(a + b × X873 + 2 × s)
= Exp(a + b × 1,266 + 2 × s)
= Exp(1.8484 + 0.0012 × 1,266 + 2 × 0.0778)
= Exp(3.5480)
= $34.74
Bottom border of price channel:
Exp(Y873)
= Exp(a + b × X873 – 2 × s)
= Exp(a + b × 1,266 – 2 × s)
= Exp(1.8484 + 0.0012 × 1,266 – 2 × 0.0778)
= Exp(3.2367)
= $25.45
January 27, 2025 calculations
Top border of price channel:
Exp(Y1,239)
= Exp(a + b × X1,239 + 2 × s)
= Exp(a + b × 1,802 + 2 × s)
= Exp(1.8484 + 0.0012 × 1,802 + 2 × 0.0778)
= Exp(4.2016)
= $66.80
Bottom border of price channel:
Exp(Y1,239)
= Exp(a + b × X1,239 – 2 × s)
= Exp(a + b × 1,802 – 2 × s)
= Exp(1.8484 + 0.0012 × 1,802 – 2 × 0.0778)
= Exp(3.8904)
= $48.93
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 56.07% per annum.
- GM price at the close of February 20, 2025 was $47.89 and was lower than the bottom border of the primary price channel by $2.49 (4.95%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: November 6, 2024
End date: February 20, 2025
a = 6.7844
b = -0.0016
s = 0.0322
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0016) – 1
= -44.14%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0322) – 1
= 13.76%
November 6, 2024 calculations
Top border of price channel:
Exp(Y1,186)
= Exp(a + b × X1,186 + 2 × s)
= Exp(a + b × 1,720 + 2 × s)
= Exp(6.7844 + -0.0016 × 1,720 + 2 × 0.0322)
= Exp(4.1051)
= $60.65
Bottom border of price channel:
Exp(Y1,186)
= Exp(a + b × X1,186 – 2 × s)
= Exp(a + b × 1,720 – 2 × s)
= Exp(6.7844 + -0.0016 × 1,720 – 2 × 0.0322)
= Exp(3.9762)
= $53.31
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(6.7844 + -0.0016 × 1,826 + 2 × 0.0322)
= Exp(3.9360)
= $51.22
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(6.7844 + -0.0016 × 1,826 – 2 × 0.0322)
= Exp(3.8071)
= $45.02
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 44.14% per annum.
- GM price at the close of February 20, 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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