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 39.74% per annum.
- VZ price at the close of July 25, 2024 was $39.95 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 5.05% per annum.
- VZ price at the close of July 25, 2024 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: July 12, 2023
End date: July 19, 2024
a = 2.0877
b = 0.0009
s = 0.0477
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0009) – 1
= 39.74%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0477) – 1
= 21.00%
July 12, 2023 calculations
Top border of price channel:
Exp(Y996)
= Exp(a + b × X996 + 2 × s)
= Exp(a + b × 1,447 + 2 × s)
= Exp(2.0877 + 0.0009 × 1,447 + 2 × 0.0477)
= Exp(3.5095)
= $33.43
Bottom border of price channel:
Exp(Y996)
= Exp(a + b × X996 – 2 × s)
= Exp(a + b × 1,447 – 2 × s)
= Exp(2.0877 + 0.0009 × 1,447 – 2 × 0.0477)
= Exp(3.3188)
= $27.63
July 19, 2024 calculations
Top border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 + 2 × s)
= Exp(a + b × 1,820 + 2 × s)
= Exp(2.0877 + 0.0009 × 1,820 + 2 × 0.0477)
= Exp(3.8514)
= $47.06
Bottom border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 – 2 × s)
= Exp(a + b × 1,820 – 2 × s)
= Exp(2.0877 + 0.0009 × 1,820 – 2 × 0.0477)
= Exp(3.6608)
= $38.89
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 39.74% per annum.
- VZ price at the close of July 25, 2024 was $39.95 and was inside the primary price channel.
Secondary Trend
Start date: January 19, 2024
End date: July 25, 2024
a = 3.4463
b = 0.0001
s = 0.0230
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 5.05%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0230) – 1
= 9.62%
January 19, 2024 calculations
Top border of price channel:
Exp(Y1,128)
= Exp(a + b × X1,128 + 2 × s)
= Exp(a + b × 1,638 + 2 × s)
= Exp(3.4463 + 0.0001 × 1,638 + 2 × 0.0230)
= Exp(3.7134)
= $40.99
Bottom border of price channel:
Exp(Y1,128)
= Exp(a + b × X1,128 – 2 × s)
= Exp(a + b × 1,638 – 2 × s)
= Exp(3.4463 + 0.0001 × 1,638 – 2 × 0.0230)
= Exp(3.6215)
= $37.39
July 25, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.4463 + 0.0001 × 1,826 + 2 × 0.0230)
= Exp(3.7387)
= $42.04
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.4463 + 0.0001 × 1,826 – 2 × 0.0230)
= Exp(3.6469)
= $38.35
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 5.05% per annum.
- VZ price at the close of July 25, 2024 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.
Check out VZ and 1,499 other stocks on our new website