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 20.35% per annum.
- VZ price at the close of June 29, 2026 was $44.10 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 4.57% per annum.
- VZ price at the close of June 29, 2026 was lower than the bottom border of the secondary price channel by $0.48 (1.08%).
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 20, 2026
End date: June 29, 2026
a = 4.1209
b = -0.0006
s = 0.0229
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0006) – 1
= -20.35%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0229) – 1
= 9.61%
February 20, 2026 calculations
Top border of price channel:
Exp(Y238)
= Exp(a + b × X238 + 2 × s)
= Exp(a + b × 346 + 2 × s)
= Exp(4.1209 + -0.0006 × 346 + 2 × 0.0229)
= Exp(3.9511)
= $51.99
Bottom border of price channel:
Exp(Y238)
= Exp(a + b × X238 – 2 × s)
= Exp(a + b × 346 – 2 × s)
= Exp(4.1209 + -0.0006 × 346 – 2 × 0.0229)
= Exp(3.8593)
= $47.43
June 29, 2026 calculations
Top border of price channel:
Exp(Y326)
= Exp(a + b × X326 + 2 × s)
= Exp(a + b × 475 + 2 × s)
= Exp(4.1209 + -0.0006 × 475 + 2 × 0.0229)
= Exp(3.8707)
= $47.97
Bottom border of price channel:
Exp(Y326)
= Exp(a + b × X326 – 2 × s)
= Exp(a + b × 475 – 2 × s)
= Exp(4.1209 + -0.0006 × 475 – 2 × 0.0229)
= Exp(3.7789)
= $43.77
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 20.35% per annum.
- VZ price at the close of June 29, 2026 was $44.10 and was inside the primary price channel.
Secondary Trend
Start date: April 8, 2026
End date: June 29, 2026
a = 3.9014
b = -0.0001
s = 0.0216
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -4.57%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0216) – 1
= 9.02%
April 8, 2026 calculations
Top border of price channel:
Exp(Y270)
= Exp(a + b × X270 + 2 × s)
= Exp(a + b × 393 + 2 × s)
= Exp(3.9014 + -0.0001 × 393 + 2 × 0.0216)
= Exp(3.8942)
= $49.12
Bottom border of price channel:
Exp(Y270)
= Exp(a + b × X270 – 2 × s)
= Exp(a + b × 393 – 2 × s)
= Exp(3.9014 + -0.0001 × 393 – 2 × 0.0216)
= Exp(3.8078)
= $45.05
June 29, 2026 calculations
Top border of price channel:
Exp(Y326)
= Exp(a + b × X326 + 2 × s)
= Exp(a + b × 475 + 2 × s)
= Exp(3.9014 + -0.0001 × 475 + 2 × 0.0216)
= Exp(3.8837)
= $48.60
Bottom border of price channel:
Exp(Y326)
= Exp(a + b × X326 – 2 × s)
= Exp(a + b × 475 – 2 × s)
= Exp(3.9014 + -0.0001 × 475 – 2 × 0.0216)
= Exp(3.7973)
= $44.58
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 4.57% per annum.
- VZ price at the close of June 29, 2026 was lower than the bottom border of the secondary price channel by $0.48 (1.08%).