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 27.47% per annum.
- VZ price at the close of February 20, 2025 was $42.49 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 9.47% per annum.
- VZ price at the close of February 20, 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: December 13, 2024
a = 2.6077
b = 0.0007
s = 0.0505
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 27.47%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0505) – 1
= 22.38%
May 15, 2023 calculations
Top border of price channel:
Exp(Y813)
= Exp(a + b × X813 + 2 × s)
= Exp(a + b × 1,179 + 2 × s)
= Exp(2.6077 + 0.0007 × 1,179 + 2 × 0.0505)
= Exp(3.4926)
= $32.87
Bottom border of price channel:
Exp(Y813)
= Exp(a + b × X813 – 2 × s)
= Exp(a + b × 1,179 – 2 × s)
= Exp(2.6077 + 0.0007 × 1,179 – 2 × 0.0505)
= Exp(3.2907)
= $26.86
December 13, 2024 calculations
Top border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 + 2 × s)
= Exp(a + b × 1,757 + 2 × s)
= Exp(2.6077 + 0.0007 × 1,757 + 2 × 0.0505)
= Exp(3.8770)
= $48.28
Bottom border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 – 2 × s)
= Exp(a + b × 1,757 – 2 × s)
= Exp(2.6077 + 0.0007 × 1,757 – 2 × 0.0505)
= Exp(3.6750)
= $39.45
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 27.47% per annum.
- VZ price at the close of February 20, 2025 was $42.49 and was inside the primary price channel.
Secondary Trend
Start date: January 3, 2024
End date: February 20, 2025
a = 3.2740
b = 0.0002
s = 0.0357
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 9.47%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0357) – 1
= 15.34%
January 3, 2024 calculations
Top border of price channel:
Exp(Y973)
= Exp(a + b × X973 + 2 × s)
= Exp(a + b × 1,412 + 2 × s)
= Exp(3.2740 + 0.0002 × 1,412 + 2 × 0.0357)
= Exp(3.6953)
= $40.26
Bottom border of price channel:
Exp(Y973)
= Exp(a + b × X973 – 2 × s)
= Exp(a + b × 1,412 – 2 × s)
= Exp(3.2740 + 0.0002 × 1,412 – 2 × 0.0357)
= Exp(3.5525)
= $34.90
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.2740 + 0.0002 × 1,826 + 2 × 0.0357)
= Exp(3.7979)
= $44.61
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.2740 + 0.0002 × 1,826 – 2 × 0.0357)
= Exp(3.6551)
= $38.67
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 9.47% per annum.
- VZ price at the close of February 20, 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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