Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 21.34% per annum.
- VZ price at the close of October 9, 2026 was $41.65 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 0.32% per annum.
- VZ price at the close of October 9, 2026 was lower than the bottom border of the secondary price channel by $0.25 (0.59%).
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: February 4, 2026
End date: July 23, 2026
a = 3.9690
b = -0.0007
s = 0.0323
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -21.34%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0323) – 1
= 13.77%
February 4, 2026 calculations
Top border of price channel:
Exp(Y101)
= Exp(a + b × X101 + 2 × s)
= Exp(a + b × 147 + 2 × s)
= Exp(3.9690 + -0.0007 × 147 + 2 × 0.0323)
= Exp(3.9369)
= $51.26
Bottom border of price channel:
Exp(Y101)
= Exp(a + b × X101 – 2 × s)
= Exp(a + b × 147 – 2 × s)
= Exp(3.9690 + -0.0007 × 147 – 2 × 0.0323)
= Exp(3.8078)
= $45.05
July 23, 2026 calculations
Top border of price channel:
Exp(Y217)
= Exp(a + b × X217 + 2 × s)
= Exp(a + b × 316 + 2 × s)
= Exp(3.9690 + -0.0007 × 316 + 2 × 0.0323)
= Exp(3.8258)
= $45.87
Bottom border of price channel:
Exp(Y217)
= Exp(a + b × X217 – 2 × s)
= Exp(a + b × 316 – 2 × s)
= Exp(3.9690 + -0.0007 × 316 – 2 × 0.0323)
= Exp(3.6967)
= $40.31
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 21.34% per annum.
- VZ price at the close of October 9, 2026 was $41.65 and was inside the primary price channel.
Secondary Trend
Start date: February 4, 2026
End date: October 8, 2026
a = 3.8318
b = 0.0000
s = 0.0466
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= -0.32%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0466) – 1
= 20.50%
February 4, 2026 calculations
Top border of price channel:
Exp(Y101)
= Exp(a + b × X101 + 2 × s)
= Exp(a + b × 147 + 2 × s)
= Exp(3.8318 + 0.0000 × 147 + 2 × 0.0466)
= Exp(3.9238)
= $50.59
Bottom border of price channel:
Exp(Y101)
= Exp(a + b × X101 – 2 × s)
= Exp(a + b × 147 – 2 × s)
= Exp(3.8318 + 0.0000 × 147 – 2 × 0.0466)
= Exp(3.7373)
= $41.99
October 8, 2026 calculations
Top border of price channel:
Exp(Y271)
= Exp(a + b × X271 + 2 × s)
= Exp(a + b × 393 + 2 × s)
= Exp(3.8318 + 0.0000 × 393 + 2 × 0.0466)
= Exp(3.9216)
= $50.48
Bottom border of price channel:
Exp(Y271)
= Exp(a + b × X271 – 2 × s)
= Exp(a + b × 393 – 2 × s)
= Exp(3.8318 + 0.0000 × 393 – 2 × 0.0466)
= Exp(3.7352)
= $41.90
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 0.32% per annum.
- VZ price at the close of October 9, 2026 was lower than the bottom border of the secondary price channel by $0.25 (0.59%).