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 1.75% per annum.
- LIN price at the close of April 29, 2025 was $450.58 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 24.52% per annum.
- LIN price at the close of April 29, 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 LIN 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 20, 2024
End date: April 29, 2025
a = 6.0277
b = 0.0000
s = 0.0361
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 1.75%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0361) – 1
= 15.53%
February 20, 2024 calculations
Top border of price channel:
Exp(Y957)
= Exp(a + b × X957 + 2 × s)
= Exp(a + b × 1,391 + 2 × s)
= Exp(6.0277 + 0.0000 × 1,391 + 2 × 0.0361)
= Exp(6.1660)
= $476.28
Bottom border of price channel:
Exp(Y957)
= Exp(a + b × X957 – 2 × s)
= Exp(a + b × 1,391 – 2 × s)
= Exp(6.0277 + 0.0000 × 1,391 – 2 × 0.0361)
= Exp(6.0216)
= $412.26
April 29, 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(6.0277 + 0.0000 × 1,825 + 2 × 0.0361)
= Exp(6.1867)
= $486.22
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(6.0277 + 0.0000 × 1,825 – 2 × 0.0361)
= Exp(6.0423)
= $420.85
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 1.75% per annum.
- LIN price at the close of April 29, 2025 was $450.58 and was inside the primary price channel.
Secondary Trend
Start date: December 13, 2024
End date: April 29, 2025
a = 5.0417
b = 0.0006
s = 0.0306
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0006) – 1
= 24.52%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0306) – 1
= 13.03%
December 13, 2024 calculations
Top border of price channel:
Exp(Y1,164)
= Exp(a + b × X1,164 + 2 × s)
= Exp(a + b × 1,688 + 2 × s)
= Exp(5.0417 + 0.0006 × 1,688 + 2 × 0.0306)
= Exp(6.1170)
= $453.48
Bottom border of price channel:
Exp(Y1,164)
= Exp(a + b × X1,164 – 2 × s)
= Exp(a + b × 1,688 – 2 × s)
= Exp(5.0417 + 0.0006 × 1,688 – 2 × 0.0306)
= Exp(5.9945)
= $401.21
April 29, 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(5.0417 + 0.0006 × 1,825 + 2 × 0.0306)
= Exp(6.1993)
= $492.38
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(5.0417 + 0.0006 × 1,825 – 2 × 0.0306)
= Exp(6.0768)
= $435.63
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 24.52% per annum.
- LIN price at the close of April 29, 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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