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 5.02% per annum.
- LOW price at the close of February 28, 2025 was $248.64 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 15.04% per annum.
- LOW price at the close of February 28, 2025 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 LOW 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: March 22, 2021
End date: August 14, 2024
a = 5.1737
b = 0.0001
s = 0.0832
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 5.02%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0832) – 1
= 39.50%
March 22, 2021 calculations
Top border of price channel:
Exp(Y266)
= Exp(a + b × X266 + 2 × s)
= Exp(a + b × 385 + 2 × s)
= Exp(5.1737 + 0.0001 × 385 + 2 × 0.0832)
= Exp(5.3918)
= $219.60
Bottom border of price channel:
Exp(Y266)
= Exp(a + b × X266 – 2 × s)
= Exp(a + b × 385 – 2 × s)
= Exp(5.1737 + 0.0001 × 385 – 2 × 0.0832)
= Exp(5.0589)
= $157.41
August 14, 2024 calculations
Top border of price channel:
Exp(Y1,121)
= Exp(a + b × X1,121 + 2 × s)
= Exp(a + b × 1,626 + 2 × s)
= Exp(5.1737 + 0.0001 × 1,626 + 2 × 0.0832)
= Exp(5.5583)
= $259.39
Bottom border of price channel:
Exp(Y1,121)
= Exp(a + b × X1,121 – 2 × s)
= Exp(a + b × 1,626 – 2 × s)
= Exp(5.1737 + 0.0001 × 1,626 – 2 × 0.0832)
= Exp(5.2254)
= $185.93
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 5.02% per annum.
- LOW price at the close of February 28, 2025 was $248.64 and was inside the primary price channel.
Secondary Trend
Start date: May 5, 2022
End date: February 20, 2025
a = 4.8584
b = 0.0004
s = 0.0579
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0004) – 1
= 15.04%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0579) – 1
= 26.07%
May 5, 2022 calculations
Top border of price channel:
Exp(Y550)
= Exp(a + b × X550 + 2 × s)
= Exp(a + b × 794 + 2 × s)
= Exp(4.8584 + 0.0004 × 794 + 2 × 0.0579)
= Exp(5.2791)
= $196.19
Bottom border of price channel:
Exp(Y550)
= Exp(a + b × X550 – 2 × s)
= Exp(a + b × 794 – 2 × s)
= Exp(4.8584 + 0.0004 × 794 – 2 × 0.0579)
= Exp(5.0474)
= $155.62
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 + 2 × s)
= Exp(a + b × 1,816 + 2 × s)
= Exp(4.8584 + 0.0004 × 1,816 + 2 × 0.0579)
= Exp(5.6715)
= $290.47
Bottom border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 – 2 × s)
= Exp(a + b × 1,816 – 2 × s)
= Exp(4.8584 + 0.0004 × 1,816 – 2 × 0.0579)
= Exp(5.4398)
= $230.40
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 15.04% per annum.
- LOW price at the close of February 28, 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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