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 27.07% per annum.
- VZ price at the close of July 10, 2026 was $42.12 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 79.32% per annum.
- VZ price at the close of July 10, 2026 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: February 20, 2026
End date: July 10, 2026
a = 4.1189
b = -0.0009
s = 0.0285
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0009) – 1
= -27.07%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0285) – 1
= 12.07%
February 20, 2026 calculations
Top border of price channel:
Exp(Y174)
= Exp(a + b × X174 + 2 × s)
= Exp(a + b × 254 + 2 × s)
= Exp(4.1189 + -0.0009 × 254 + 2 × 0.0285)
= Exp(3.9563)
= $52.26
Bottom border of price channel:
Exp(Y174)
= Exp(a + b × X174 – 2 × s)
= Exp(a + b × 254 – 2 × s)
= Exp(4.1189 + -0.0009 × 254 – 2 × 0.0285)
= Exp(3.8423)
= $46.63
July 10, 2026 calculations
Top border of price channel:
Exp(Y270)
= Exp(a + b × X270 + 2 × s)
= Exp(a + b × 394 + 2 × s)
= Exp(4.1189 + -0.0009 × 394 + 2 × 0.0285)
= Exp(3.8352)
= $46.30
Bottom border of price channel:
Exp(Y270)
= Exp(a + b × X270 – 2 × s)
= Exp(a + b × 394 – 2 × s)
= Exp(4.1189 + -0.0009 × 394 – 2 × 0.0285)
= Exp(3.7212)
= $41.31
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 27.07% per annum.
- VZ price at the close of July 10, 2026 was $42.12 and was inside the primary price channel.
Secondary Trend
Start date: June 10, 2026
End date: July 10, 2026
a = 5.4221
b = -0.0043
s = 0.0217
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0043) – 1
= -79.32%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0217) – 1
= 9.09%
June 10, 2026 calculations
Top border of price channel:
Exp(Y250)
= Exp(a + b × X250 + 2 × s)
= Exp(a + b × 364 + 2 × s)
= Exp(5.4221 + -0.0043 × 364 + 2 × 0.0217)
= Exp(3.8937)
= $49.09
Bottom border of price channel:
Exp(Y250)
= Exp(a + b × X250 – 2 × s)
= Exp(a + b × 364 – 2 × s)
= Exp(5.4221 + -0.0043 × 364 – 2 × 0.0217)
= Exp(3.8068)
= $45.01
July 10, 2026 calculations
Top border of price channel:
Exp(Y270)
= Exp(a + b × X270 + 2 × s)
= Exp(a + b × 394 + 2 × s)
= Exp(5.4221 + -0.0043 × 394 + 2 × 0.0217)
= Exp(3.7642)
= $43.13
Bottom border of price channel:
Exp(Y270)
= Exp(a + b × X270 – 2 × s)
= Exp(a + b × 394 – 2 × s)
= Exp(5.4221 + -0.0043 × 394 – 2 × 0.0217)
= Exp(3.6772)
= $39.54
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 79.32% per annum.
- VZ price at the close of July 10, 2026 was inside the secondary price channel.