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 0.50% per annum.
- CVX price at the close of February 20, 2025 was $158.79 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 241.71% per annum.
- CVX price at the close of February 20, 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: February 20, 2025
a = 4.9817
b = 0.0000
s = 0.0575
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 0.50%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0575) – 1
= 25.87%
March 2, 2022 calculations
Top border of price channel:
Exp(Y511)
= Exp(a + b × X511 + 2 × s)
= Exp(a + b × 740 + 2 × s)
= Exp(4.9817 + 0.0000 × 740 + 2 × 0.0575)
= Exp(5.1068)
= $165.15
Bottom border of price channel:
Exp(Y511)
= Exp(a + b × X511 – 2 × s)
= Exp(a + b × 740 – 2 × s)
= Exp(4.9817 + 0.0000 × 740 – 2 × 0.0575)
= Exp(4.8767)
= $131.20
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(4.9817 + 0.0000 × 1,826 + 2 × 0.0575)
= Exp(5.1216)
= $167.60
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.9817 + 0.0000 × 1,826 – 2 × 0.0575)
= Exp(4.8915)
= $133.15
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 0.50% per annum.
- CVX price at the close of February 20, 2025 was $158.79 and was inside the primary price channel.
Secondary Trend
Start date: January 31, 2025
End date: February 20, 2025
a = -1.0830
b = 0.0034
s = 0.0075
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0034) – 1
= 241.71%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0075) – 1
= 3.05%
January 31, 2025 calculations
Top border of price channel:
Exp(Y1,243)
= Exp(a + b × X1,243 + 2 × s)
= Exp(a + b × 1,806 + 2 × s)
= Exp(-1.0830 + 0.0034 × 1,806 + 2 × 0.0075)
= Exp(5.0120)
= $150.21
Bottom border of price channel:
Exp(Y1,243)
= Exp(a + b × X1,243 – 2 × s)
= Exp(a + b × 1,806 – 2 × s)
= Exp(-1.0830 + 0.0034 × 1,806 – 2 × 0.0075)
= Exp(4.9820)
= $145.77
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(-1.0830 + 0.0034 × 1,826 + 2 × 0.0075)
= Exp(5.0794)
= $160.67
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-1.0830 + 0.0034 × 1,826 – 2 × 0.0075)
= Exp(5.0494)
= $155.92
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 241.71% per annum.
- CVX 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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