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 48.71% per annum.
- TMUS price at the close of March 28, 2025 was $264.93 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 70.89% per annum.
- TMUS price at the close of March 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 TMUS 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: June 2, 2023
End date: March 28, 2025
a = 3.5392
b = 0.0011
s = 0.0516
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 48.71%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0516) – 1
= 22.91%
June 2, 2023 calculations
Top border of price channel:
Exp(Y800)
= Exp(a + b × X800 + 2 × s)
= Exp(a + b × 1,159 + 2 × s)
= Exp(3.5392 + 0.0011 × 1,159 + 2 × 0.0516)
= Exp(4.9023)
= $134.59
Bottom border of price channel:
Exp(Y800)
= Exp(a + b × X800 – 2 × s)
= Exp(a + b × 1,159 – 2 × s)
= Exp(3.5392 + 0.0011 × 1,159 – 2 × 0.0516)
= Exp(4.6960)
= $109.51
March 28, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(3.5392 + 0.0011 × 1,824 + 2 × 0.0516)
= Exp(5.6252)
= $277.33
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(3.5392 + 0.0011 × 1,824 – 2 × 0.0516)
= Exp(5.4189)
= $225.63
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 48.71% per annum.
- TMUS price at the close of March 28, 2025 was $264.93 and was inside the primary price channel.
Secondary Trend
Start date: March 18, 2024
End date: March 28, 2025
a = 2.9053
b = 0.0015
s = 0.0445
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0015) – 1
= 70.89%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0445) – 1
= 19.46%
March 18, 2024 calculations
Top border of price channel:
Exp(Y998)
= Exp(a + b × X998 + 2 × s)
= Exp(a + b × 1,449 + 2 × s)
= Exp(2.9053 + 0.0015 × 1,449 + 2 × 0.0445)
= Exp(5.1215)
= $167.58
Bottom border of price channel:
Exp(Y998)
= Exp(a + b × X998 – 2 × s)
= Exp(a + b × 1,449 – 2 × s)
= Exp(2.9053 + 0.0015 × 1,449 – 2 × 0.0445)
= Exp(4.9436)
= $140.28
March 28, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(2.9053 + 0.0015 × 1,824 + 2 × 0.0445)
= Exp(5.6720)
= $290.62
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(2.9053 + 0.0015 × 1,824 – 2 × 0.0445)
= Exp(5.4942)
= $243.27
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 70.89% per annum.
- TMUS price at the close of March 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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