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 7.24% per annum.
- COP price at the close of April 26, 2024 was $130.24 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 126.40% per annum.
- COP price at the close of April 26, 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: February 28, 2022
End date: April 1, 2024
a = 4.4250
b = 0.0002
s = 0.0852
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 7.24%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0852) – 1
= 40.60%
February 28, 2022 calculations
Top border of price channel:
Exp(Y715)
= Exp(a + b × X715 + 2 × s)
= Exp(a + b × 1,036 + 2 × s)
= Exp(4.4250 + 0.0002 × 1,036 + 2 × 0.0852)
= Exp(4.7937)
= $120.75
Bottom border of price channel:
Exp(Y715)
= Exp(a + b × X715 – 2 × s)
= Exp(a + b × 1,036 – 2 × s)
= Exp(4.4250 + 0.0002 × 1,036 – 2 × 0.0852)
= Exp(4.4530)
= $85.88
April 1, 2024 calculations
Top border of price channel:
Exp(Y1,239)
= Exp(a + b × X1,239 + 2 × s)
= Exp(a + b × 1,799 + 2 × s)
= Exp(4.4250 + 0.0002 × 1,799 + 2 × 0.0852)
= Exp(4.9398)
= $139.75
Bottom border of price channel:
Exp(Y1,239)
= Exp(a + b × X1,239 – 2 × s)
= Exp(a + b × 1,799 – 2 × s)
= Exp(4.4250 + 0.0002 × 1,799 – 2 × 0.0852)
= Exp(4.5991)
= $99.39
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 7.24% per annum.
- COP price at the close of April 26, 2024 was $130.24 and was inside the primary price channel.
Secondary Trend
Start date: January 16, 2024
End date: April 26, 2024
a = 0.8024
b = 0.0022
s = 0.0286
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0022) – 1
= 126.40%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0286) – 1
= 12.14%
January 16, 2024 calculations
Top border of price channel:
Exp(Y1,187)
= Exp(a + b × X1,187 + 2 × s)
= Exp(a + b × 1,723 + 2 × s)
= Exp(0.8024 + 0.0022 × 1,723 + 2 × 0.0286)
= Exp(4.7169)
= $111.82
Bottom border of price channel:
Exp(Y1,187)
= Exp(a + b × X1,187 – 2 × s)
= Exp(a + b × 1,723 – 2 × s)
= Exp(0.8024 + 0.0022 × 1,723 – 2 × 0.0286)
= Exp(4.6024)
= $99.72
April 26, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(0.8024 + 0.0022 × 1,824 + 2 × 0.0286)
= Exp(4.9430)
= $140.19
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(0.8024 + 0.0022 × 1,824 – 2 × 0.0286)
= Exp(4.8285)
= $125.02
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 126.40% per annum.
- COP price at the close of April 26, 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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