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 22.41% per annum.
- VZ price at the close of April 25, 2025 was $41.91 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.28% per annum.
- VZ price at the close of April 25, 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: April 25, 2025
a = 2.7822
b = 0.0006
s = 0.0553
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0006) – 1
= 22.41%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0553) – 1
= 24.77%
May 15, 2023 calculations
Top border of price channel:
Exp(Y768)
= Exp(a + b × X768 + 2 × s)
= Exp(a + b × 1,113 + 2 × s)
= Exp(2.7822 + 0.0006 × 1,113 + 2 × 0.0553)
= Exp(3.5094)
= $33.43
Bottom border of price channel:
Exp(Y768)
= Exp(a + b × X768 – 2 × s)
= Exp(a + b × 1,113 – 2 × s)
= Exp(2.7822 + 0.0006 × 1,113 – 2 × 0.0553)
= Exp(3.2881)
= $26.79
April 25, 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(2.7822 + 0.0006 × 1,824 + 2 × 0.0553)
= Exp(3.9033)
= $49.56
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(2.7822 + 0.0006 × 1,824 – 2 × 0.0553)
= Exp(3.6820)
= $39.73
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 22.41% per annum.
- VZ price at the close of April 25, 2025 was $41.91 and was inside the primary price channel.
Secondary Trend
Start date: January 3, 2024
End date: April 25, 2025
a = 3.1708
b = 0.0003
s = 0.0365
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 12.28%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0365) – 1
= 15.73%
January 3, 2024 calculations
Top border of price channel:
Exp(Y928)
= Exp(a + b × X928 + 2 × s)
= Exp(a + b × 1,346 + 2 × s)
= Exp(3.1708 + 0.0003 × 1,346 + 2 × 0.0365)
= Exp(3.6711)
= $39.30
Bottom border of price channel:
Exp(Y928)
= Exp(a + b × X928 – 2 × s)
= Exp(a + b × 1,346 – 2 × s)
= Exp(3.1708 + 0.0003 × 1,346 – 2 × 0.0365)
= Exp(3.5250)
= $33.95
April 25, 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(3.1708 + 0.0003 × 1,824 + 2 × 0.0365)
= Exp(3.8229)
= $45.73
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(3.1708 + 0.0003 × 1,824 – 2 × 0.0365)
= Exp(3.6768)
= $39.52
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.28% per annum.
- VZ price at the close of April 25, 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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