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 27.47% per annum.
- VZ price at the close of March 28, 2025 was $44.93 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 10.19% per annum.
- VZ 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 VZ 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: May 15, 2023
End date: December 13, 2024
a = 2.6330
b = 0.0007
s = 0.0505
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 27.47%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0505) – 1
= 22.38%
May 15, 2023 calculations
Top border of price channel:
Exp(Y787)
= Exp(a + b × X787 + 2 × s)
= Exp(a + b × 1,141 + 2 × s)
= Exp(2.6330 + 0.0007 × 1,141 + 2 × 0.0505)
= Exp(3.4926)
= $32.87
Bottom border of price channel:
Exp(Y787)
= Exp(a + b × X787 – 2 × s)
= Exp(a + b × 1,141 – 2 × s)
= Exp(2.6330 + 0.0007 × 1,141 – 2 × 0.0505)
= Exp(3.2907)
= $26.86
December 13, 2024 calculations
Top border of price channel:
Exp(Y1,186)
= Exp(a + b × X1,186 + 2 × s)
= Exp(a + b × 1,719 + 2 × s)
= Exp(2.6330 + 0.0007 × 1,719 + 2 × 0.0505)
= Exp(3.8770)
= $48.28
Bottom border of price channel:
Exp(Y1,186)
= Exp(a + b × X1,186 – 2 × s)
= Exp(a + b × 1,719 – 2 × s)
= Exp(2.6330 + 0.0007 × 1,719 – 2 × 0.0505)
= Exp(3.6750)
= $39.45
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 27.47% per annum.
- VZ price at the close of March 28, 2025 was $44.93 and was inside the primary price channel.
Secondary Trend
Start date: January 2, 2024
End date: March 5, 2025
a = 3.2557
b = 0.0003
s = 0.0357
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 10.19%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0357) – 1
= 15.37%
January 2, 2024 calculations
Top border of price channel:
Exp(Y946)
= Exp(a + b × X946 + 2 × s)
= Exp(a + b × 1,373 + 2 × s)
= Exp(3.2557 + 0.0003 × 1,373 + 2 × 0.0357)
= Exp(3.6923)
= $40.14
Bottom border of price channel:
Exp(Y946)
= Exp(a + b × X946 – 2 × s)
= Exp(a + b × 1,373 – 2 × s)
= Exp(3.2557 + 0.0003 × 1,373 – 2 × 0.0357)
= Exp(3.5493)
= $34.79
March 5, 2025 calculations
Top border of price channel:
Exp(Y1,239)
= Exp(a + b × X1,239 + 2 × s)
= Exp(a + b × 1,801 + 2 × s)
= Exp(3.2557 + 0.0003 × 1,801 + 2 × 0.0357)
= Exp(3.8061)
= $44.97
Bottom border of price channel:
Exp(Y1,239)
= Exp(a + b × X1,239 – 2 × s)
= Exp(a + b × 1,801 – 2 × s)
= Exp(3.2557 + 0.0003 × 1,801 – 2 × 0.0357)
= Exp(3.6631)
= $38.98
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 10.19% per annum.
- VZ 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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