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 1.11% per annum.
- CVX price at the close of December 5, 2025 was $150.00 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 29.41% per annum.
- CVX price at the close of December 5, 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 CVX 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 2, 2022
End date: December 5, 2025
a = 4.9363
b = 0.0000
s = 0.0580
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 1.11%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0580) – 1
= 26.12%
March 2, 2022 calculations
Top border of price channel:
Exp(Y310)
= Exp(a + b × X310 + 2 × s)
= Exp(a + b × 450 + 2 × s)
= Exp(4.9363 + 0.0000 × 450 + 2 × 0.0580)
= Exp(5.0659)
= $158.53
Bottom border of price channel:
Exp(Y310)
= Exp(a + b × X310 – 2 × s)
= Exp(a + b × 450 – 2 × s)
= Exp(4.9363 + 0.0000 × 450 – 2 × 0.0580)
= Exp(4.8339)
= $125.70
December 5, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.9363 + 0.0000 × 1,824 + 2 × 0.0580)
= Exp(5.1073)
= $165.23
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.9363 + 0.0000 × 1,824 – 2 × 0.0580)
= Exp(4.8753)
= $131.01
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 1.11% per annum.
- CVX price at the close of December 5, 2025 was $150.00 and was inside the primary price channel.
Secondary Trend
Start date: April 4, 2025
End date: December 5, 2025
a = 3.7824
b = 0.0007
s = 0.0326
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 29.41%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0326) – 1
= 13.93%
April 4, 2025 calculations
Top border of price channel:
Exp(Y1,086)
= Exp(a + b × X1,086 + 2 × s)
= Exp(a + b × 1,579 + 2 × s)
= Exp(3.7824 + 0.0007 × 1,579 + 2 × 0.0326)
= Exp(4.9630)
= $143.02
Bottom border of price channel:
Exp(Y1,086)
= Exp(a + b × X1,086 – 2 × s)
= Exp(a + b × 1,579 – 2 × s)
= Exp(3.7824 + 0.0007 × 1,579 – 2 × 0.0326)
= Exp(4.8325)
= $125.52
December 5, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(3.7824 + 0.0007 × 1,824 + 2 × 0.0326)
= Exp(5.1360)
= $170.04
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(3.7824 + 0.0007 × 1,824 – 2 × 0.0326)
= Exp(5.0056)
= $149.24
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 29.41% per annum.
- CVX price at the close of December 5, 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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