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 20.89% per annum.
- VZ price at the close of July 15, 2025 was $41.26 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.31% per annum.
- VZ price at the close of July 15, 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: July 14, 2025
a = 2.8544
b = 0.0005
s = 0.0546
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 20.89%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0546) – 1
= 24.39%
May 15, 2023 calculations
Top border of price channel:
Exp(Y712)
= Exp(a + b × X712 + 2 × s)
= Exp(a + b × 1,033 + 2 × s)
= Exp(2.8544 + 0.0005 × 1,033 + 2 × 0.0546)
= Exp(3.5005)
= $33.13
Bottom border of price channel:
Exp(Y712)
= Exp(a + b × X712 – 2 × s)
= Exp(a + b × 1,033 – 2 × s)
= Exp(2.8544 + 0.0005 × 1,033 – 2 × 0.0546)
= Exp(3.2823)
= $26.64
July 14, 2025 calculations
Top border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(2.8544 + 0.0005 × 1,824 + 2 × 0.0546)
= Exp(3.9116)
= $49.98
Bottom border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(2.8544 + 0.0005 × 1,824 – 2 × 0.0546)
= Exp(3.6934)
= $40.18
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 20.89% per annum.
- VZ price at the close of July 15, 2025 was $41.26 and was inside the primary price channel.
Secondary Trend
Start date: January 3, 2024
End date: July 15, 2025
a = 3.1796
b = 0.0003
s = 0.0348
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 12.31%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0348) – 1
= 14.92%
January 3, 2024 calculations
Top border of price channel:
Exp(Y872)
= Exp(a + b × X872 + 2 × s)
= Exp(a + b × 1,266 + 2 × s)
= Exp(3.1796 + 0.0003 × 1,266 + 2 × 0.0348)
= Exp(3.6517)
= $38.54
Bottom border of price channel:
Exp(Y872)
= Exp(a + b × X872 – 2 × s)
= Exp(a + b × 1,266 – 2 × s)
= Exp(3.1796 + 0.0003 × 1,266 – 2 × 0.0348)
= Exp(3.5126)
= $33.54
July 15, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(3.1796 + 0.0003 × 1,825 + 2 × 0.0348)
= Exp(3.8295)
= $46.04
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(3.1796 + 0.0003 × 1,825 – 2 × 0.0348)
= Exp(3.6904)
= $40.06
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.31% per annum.
- VZ price at the close of July 15, 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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