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 28.36% per annum.
- GM price at the close of November 13, 2025 was $71.89 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 100.91% per annum.
- GM price at the close of November 13, 2025 was inside the secondary price channel.
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: March 13, 2023
End date: November 13, 2025
a = 2.8447
b = 0.0007
s = 0.1030
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 28.36%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1030) – 1
= 50.98%
March 13, 2023 calculations
Top border of price channel:
Exp(Y582)
= Exp(a + b × X582 + 2 × s)
= Exp(a + b × 847 + 2 × s)
= Exp(2.8447 + 0.0007 × 847 + 2 × 0.1030)
= Exp(3.6301)
= $37.72
Bottom border of price channel:
Exp(Y582)
= Exp(a + b × X582 – 2 × s)
= Exp(a + b × 847 – 2 × s)
= Exp(2.8447 + 0.0007 × 847 – 2 × 0.1030)
= Exp(3.2181)
= $24.98
November 13, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(2.8447 + 0.0007 × 1,823 + 2 × 0.1030)
= Exp(4.2977)
= $73.53
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(2.8447 + 0.0007 × 1,823 – 2 × 0.1030)
= Exp(3.8858)
= $48.70
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 28.36% per annum.
- GM price at the close of November 13, 2025 was $71.89 and was inside the primary price channel.
Secondary Trend
Start date: April 4, 2025
End date: November 13, 2025
a = 0.7090
b = 0.0019
s = 0.0417
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0019) – 1
= 100.91%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0417) – 1
= 18.17%
April 4, 2025 calculations
Top border of price channel:
Exp(Y1,100)
= Exp(a + b × X1,100 + 2 × s)
= Exp(a + b × 1,600 + 2 × s)
= Exp(0.7090 + 0.0019 × 1,600 + 2 × 0.0417)
= Exp(3.8509)
= $47.04
Bottom border of price channel:
Exp(Y1,100)
= Exp(a + b × X1,100 – 2 × s)
= Exp(a + b × 1,600 – 2 × s)
= Exp(0.7090 + 0.0019 × 1,600 – 2 × 0.0417)
= Exp(3.6839)
= $39.80
November 13, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(0.7090 + 0.0019 × 1,823 + 2 × 0.0417)
= Exp(4.2772)
= $72.04
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(0.7090 + 0.0019 × 1,823 – 2 × 0.0417)
= Exp(4.1102)
= $60.96
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 100.91% per annum.
- GM price at the close of November 13, 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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