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 3.84% per annum.
- COP price at the close of November 19, 2024 was $113.09 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 22.83% per annum.
- COP price at the close of November 19, 2024 was higher than the top border of the secondary price channel by $0.96 (0.86%). This indicates a possible reversal in the secondary trend direction.
- 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: November 19, 2024
a = 4.5432
b = 0.0001
s = 0.0724
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 3.84%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0724) – 1
= 33.59%
August 18, 2022 calculations
Top border of price channel:
Exp(Y690)
= Exp(a + b × X690 + 2 × s)
= Exp(a + b × 1,002 + 2 × s)
= Exp(4.5432 + 0.0001 × 1,002 + 2 × 0.0724)
= Exp(4.7915)
= $120.49
Bottom border of price channel:
Exp(Y690)
= Exp(a + b × X690 – 2 × s)
= Exp(a + b × 1,002 – 2 × s)
= Exp(4.5432 + 0.0001 × 1,002 – 2 × 0.0724)
= Exp(4.5019)
= $90.19
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.5432 + 0.0001 × 1,826 + 2 × 0.0724)
= Exp(4.8767)
= $131.20
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.5432 + 0.0001 × 1,826 – 2 × 0.0724)
= Exp(4.5871)
= $98.20
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 3.84% per annum.
- COP price at the close of November 19, 2024 was $113.09 and was inside the primary price channel.
Secondary Trend
Start date: March 19, 2024
End date: November 19, 2024
a = 5.9372
b = -0.0007
s = 0.0396
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -22.83%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0396) – 1
= 17.17%
March 19, 2024 calculations
Top border of price channel:
Exp(Y1,087)
= Exp(a + b × X1,087 + 2 × s)
= Exp(a + b × 1,581 + 2 × s)
= Exp(5.9372 + -0.0007 × 1,581 + 2 × 0.0396)
= Exp(4.8936)
= $133.44
Bottom border of price channel:
Exp(Y1,087)
= Exp(a + b × X1,087 – 2 × s)
= Exp(a + b × 1,581 – 2 × s)
= Exp(5.9372 + -0.0007 × 1,581 – 2 × 0.0396)
= Exp(4.7352)
= $113.89
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.9372 + -0.0007 × 1,826 + 2 × 0.0396)
= Exp(4.7197)
= $112.13
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.9372 + -0.0007 × 1,826 – 2 × 0.0396)
= Exp(4.5612)
= $95.70
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 22.83% per annum.
- COP price at the close of November 19, 2024 was higher than the top border of the secondary price channel by $0.96 (0.86%). This indicates a possible reversal in the secondary trend direction.
- 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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