Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 7.56% per annum.
- OXY price at the close of May 30, 2025 was $40.78 and was lower than the bottom border of the primary price channel by $3.41 (7.72%).
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 33.09% per annum.
- OXY price at the close of May 30, 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 OXY 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: May 4, 2022
End date: April 3, 2025
a = 4.3316
b = -0.0002
s = 0.0753
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -7.56%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0753) – 1
= 35.12%
May 4, 2022 calculations
Top border of price channel:
Exp(Y486)
= Exp(a + b × X486 + 2 × s)
= Exp(a + b × 702 + 2 × s)
= Exp(4.3316 + -0.0002 × 702 + 2 × 0.0753)
= Exp(4.3310)
= $76.02
Bottom border of price channel:
Exp(Y486)
= Exp(a + b × X486 – 2 × s)
= Exp(a + b × 702 – 2 × s)
= Exp(4.3316 + -0.0002 × 702 – 2 × 0.0753)
= Exp(4.0300)
= $56.26
April 3, 2025 calculations
Top border of price channel:
Exp(Y1,217)
= Exp(a + b × X1,217 + 2 × s)
= Exp(a + b × 1,767 + 2 × s)
= Exp(4.3316 + -0.0002 × 1,767 + 2 × 0.0753)
= Exp(4.1018)
= $60.45
Bottom border of price channel:
Exp(Y1,217)
= Exp(a + b × X1,217 – 2 × s)
= Exp(a + b × 1,767 – 2 × s)
= Exp(4.3316 + -0.0002 × 1,767 – 2 × 0.0753)
= Exp(3.8008)
= $44.73
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 7.56% per annum.
- OXY price at the close of May 30, 2025 was $40.78 and was lower than the bottom border of the primary price channel by $3.41 (7.72%).
Secondary Trend
Start date: March 19, 2024
End date: May 30, 2025
a = 5.7247
b = -0.0011
s = 0.0502
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0011) – 1
= -33.09%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0502) – 1
= 22.23%
March 19, 2024 calculations
Top border of price channel:
Exp(Y956)
= Exp(a + b × X956 + 2 × s)
= Exp(a + b × 1,387 + 2 × s)
= Exp(5.7247 + -0.0011 × 1,387 + 2 × 0.0502)
= Exp(4.2980)
= $73.56
Bottom border of price channel:
Exp(Y956)
= Exp(a + b × X956 – 2 × s)
= Exp(a + b × 1,387 – 2 × s)
= Exp(5.7247 + -0.0011 × 1,387 – 2 × 0.0502)
= Exp(4.0973)
= $60.18
May 30, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(5.7247 + -0.0011 × 1,824 + 2 × 0.0502)
= Exp(3.8169)
= $45.46
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.7247 + -0.0011 × 1,824 – 2 × 0.0502)
= Exp(3.6162)
= $37.19
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 33.09% per annum.
- OXY price at the close of May 30, 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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