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 2.21% per annum.
- COP price at the close of January 17, 2025 was $105.85 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 21.83% per annum.
- COP price at the close of January 17, 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: January 17, 2025
a = 4.6028
b = 0.0001
s = 0.0748
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 2.21%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0748) – 1
= 34.86%
August 18, 2022 calculations
Top border of price channel:
Exp(Y650)
= Exp(a + b × X650 + 2 × s)
= Exp(a + b × 940 + 2 × s)
= Exp(4.6028 + 0.0001 × 940 + 2 × 0.0748)
= Exp(4.8086)
= $122.56
Bottom border of price channel:
Exp(Y650)
= Exp(a + b × X650 – 2 × s)
= Exp(a + b × 940 – 2 × s)
= Exp(4.6028 + 0.0001 × 940 – 2 × 0.0748)
= Exp(4.5096)
= $90.88
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(4.6028 + 0.0001 × 1,823 + 2 × 0.0748)
= Exp(4.8615)
= $129.22
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.6028 + 0.0001 × 1,823 – 2 × 0.0748)
= Exp(4.5624)
= $95.82
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 2.21% per annum.
- COP price at the close of January 17, 2025 was $105.85 and was inside the primary price channel.
Secondary Trend
Start date: March 15, 2024
End date: January 17, 2025
a = 5.8353
b = -0.0007
s = 0.0400
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -21.83%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0400) – 1
= 17.35%
March 15, 2024 calculations
Top border of price channel:
Exp(Y1,045)
= Exp(a + b × X1,045 + 2 × s)
= Exp(a + b × 1,515 + 2 × s)
= Exp(5.8353 + -0.0007 × 1,515 + 2 × 0.0400)
= Exp(4.8932)
= $133.38
Bottom border of price channel:
Exp(Y1,045)
= Exp(a + b × X1,045 – 2 × s)
= Exp(a + b × 1,515 – 2 × s)
= Exp(5.8353 + -0.0007 × 1,515 – 2 × 0.0400)
= Exp(4.7332)
= $113.66
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(5.8353 + -0.0007 × 1,823 + 2 × 0.0400)
= Exp(4.6854)
= $108.35
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(5.8353 + -0.0007 × 1,823 – 2 × 0.0400)
= Exp(4.5254)
= $92.33
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 21.83% per annum.
- COP price at the close of January 17, 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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