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 4.70% per annum.
- COP price at the close of May 20, 2024 was $120.89 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 21.78% per annum.
- COP price at the close of May 20, 2024 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 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: March 22, 2024
a = 4.5024
b = 0.0001
s = 0.0731
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 4.70%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0731) – 1
= 33.97%
August 18, 2022 calculations
Top border of price channel:
Exp(Y818)
= Exp(a + b × X818 + 2 × s)
= Exp(a + b × 1,185 + 2 × s)
= Exp(4.5024 + 0.0001 × 1,185 + 2 × 0.0731)
= Exp(4.7979)
= $121.25
Bottom border of price channel:
Exp(Y818)
= Exp(a + b × X818 – 2 × s)
= Exp(a + b × 1,185 – 2 × s)
= Exp(4.5024 + 0.0001 × 1,185 – 2 × 0.0731)
= Exp(4.5054)
= $90.51
March 22, 2024 calculations
Top border of price channel:
Exp(Y1,218)
= Exp(a + b × X1,218 + 2 × s)
= Exp(a + b × 1,767 + 2 × s)
= Exp(4.5024 + 0.0001 × 1,767 + 2 × 0.0731)
= Exp(4.8712)
= $130.47
Bottom border of price channel:
Exp(Y1,218)
= Exp(a + b × X1,218 – 2 × s)
= Exp(a + b × 1,767 – 2 × s)
= Exp(4.5024 + 0.0001 × 1,767 – 2 × 0.0731)
= Exp(4.5787)
= $97.39
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 4.70% per annum.
- COP price at the close of May 20, 2024 was $120.89 and was inside the primary price channel.
Secondary Trend
Start date: February 17, 2023
End date: May 20, 2024
a = 3.8400
b = 0.0005
s = 0.0540
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 21.78%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0540) – 1
= 24.13%
February 17, 2023 calculations
Top border of price channel:
Exp(Y944)
= Exp(a + b × X944 + 2 × s)
= Exp(a + b × 1,368 + 2 × s)
= Exp(3.8400 + 0.0005 × 1,368 + 2 × 0.0540)
= Exp(4.6866)
= $108.48
Bottom border of price channel:
Exp(Y944)
= Exp(a + b × X944 – 2 × s)
= Exp(a + b × 1,368 – 2 × s)
= Exp(3.8400 + 0.0005 × 1,368 – 2 × 0.0540)
= Exp(4.4704)
= $87.39
May 20, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.8400 + 0.0005 × 1,826 + 2 × 0.0540)
= Exp(4.9338)
= $138.91
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.8400 + 0.0005 × 1,826 – 2 × 0.0540)
= Exp(4.7176)
= $111.90
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 21.78% per annum.
- COP price at the close of May 20, 2024 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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