Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 28.04% per annum.
- LOW price at the close of March 31, 2025 was $233.23 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 59.14% per annum.
- LOW price at the close of March 31, 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: September 30, 2024
End date: March 31, 2025
a = 7.1060
b = -0.0009
s = 0.0322
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0009) – 1
= -28.04%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0322) – 1
= 13.76%
September 30, 2024 calculations
Top border of price channel:
Exp(Y1,131)
= Exp(a + b × X1,131 + 2 × s)
= Exp(a + b × 1,643 + 2 × s)
= Exp(7.1060 + -0.0009 × 1,643 + 2 × 0.0322)
= Exp(5.6894)
= $295.72
Bottom border of price channel:
Exp(Y1,131)
= Exp(a + b × X1,131 – 2 × s)
= Exp(a + b × 1,643 – 2 × s)
= Exp(7.1060 + -0.0009 × 1,643 – 2 × 0.0322)
= Exp(5.5605)
= $259.95
March 31, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(7.1060 + -0.0009 × 1,825 + 2 × 0.0322)
= Exp(5.5254)
= $250.98
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(7.1060 + -0.0009 × 1,825 – 2 × 0.0322)
= Exp(5.3964)
= $220.62
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 28.04% per annum.
- LOW price at the close of March 31, 2025 was $233.23 and was inside the primary price channel.
Secondary Trend
Start date: January 21, 2025
End date: March 31, 2025
a = 9.8885
b = -0.0025
s = 0.0207
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0025) – 1
= -59.14%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0207) – 1
= 8.65%
January 21, 2025 calculations
Top border of price channel:
Exp(Y1,207)
= Exp(a + b × X1,207 + 2 × s)
= Exp(a + b × 1,756 + 2 × s)
= Exp(9.8885 + -0.0025 × 1,756 + 2 × 0.0207)
= Exp(5.6242)
= $277.06
Bottom border of price channel:
Exp(Y1,207)
= Exp(a + b × X1,207 – 2 × s)
= Exp(a + b × 1,756 – 2 × s)
= Exp(9.8885 + -0.0025 × 1,756 – 2 × 0.0207)
= Exp(5.5413)
= $255.01
March 31, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(9.8885 + -0.0025 × 1,825 + 2 × 0.0207)
= Exp(5.4551)
= $233.94
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(9.8885 + -0.0025 × 1,825 – 2 × 0.0207)
= Exp(5.3721)
= $215.32
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 59.14% per annum.
- LOW price at the close of March 31, 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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