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 1.36% per annum.
- COP price at the close of February 20, 2025 was $102.00 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 20.99% per annum.
- COP 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 COP 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 18, 2022
End date: February 20, 2025
a = 4.6243
b = 0.0000
s = 0.0757
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 1.36%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0757) – 1
= 35.36%
August 18, 2022 calculations
Top border of price channel:
Exp(Y628)
= Exp(a + b × X628 + 2 × s)
= Exp(a + b × 909 + 2 × s)
= Exp(4.6243 + 0.0000 × 909 + 2 × 0.0757)
= Exp(4.8093)
= $122.65
Bottom border of price channel:
Exp(Y628)
= Exp(a + b × X628 – 2 × s)
= Exp(a + b × 909 – 2 × s)
= Exp(4.6243 + 0.0000 × 909 – 2 × 0.0757)
= Exp(4.5065)
= $90.61
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(4.6243 + 0.0000 × 1,826 + 2 × 0.0757)
= Exp(4.8432)
= $126.88
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.6243 + 0.0000 × 1,826 – 2 × 0.0757)
= Exp(4.5404)
= $93.73
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 1.36% per annum.
- COP price at the close of February 20, 2025 was $102.00 and was inside the primary price channel.
Secondary Trend
Start date: March 14, 2024
End date: February 20, 2025
a = 5.7592
b = -0.0006
s = 0.0387
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0006) – 1
= -20.99%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0387) – 1
= 16.76%
March 14, 2024 calculations
Top border of price channel:
Exp(Y1,022)
= Exp(a + b × X1,022 + 2 × s)
= Exp(a + b × 1,483 + 2 × s)
= Exp(5.7592 + -0.0006 × 1,483 + 2 × 0.0387)
= Exp(4.8797)
= $131.59
Bottom border of price channel:
Exp(Y1,022)
= Exp(a + b × X1,022 – 2 × s)
= Exp(a + b × 1,483 – 2 × s)
= Exp(5.7592 + -0.0006 × 1,483 – 2 × 0.0387)
= Exp(4.7247)
= $112.70
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(5.7592 + -0.0006 × 1,826 + 2 × 0.0387)
= Exp(4.6583)
= $105.46
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.7592 + -0.0006 × 1,826 – 2 × 0.0387)
= Exp(4.5033)
= $90.32
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 20.99% per annum.
- COP 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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