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 30.06% per annum.
- VZ price at the close of November 1, 2024 was $41.36 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 16.72% per annum.
- VZ price at the close of November 1, 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: May 25, 2023
End date: November 1, 2024
a = 2.4682
b = 0.0007
s = 0.0496
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 30.06%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0496) – 1
= 21.92%
May 25, 2023 calculations
Top border of price channel:
Exp(Y895)
= Exp(a + b × X895 + 2 × s)
= Exp(a + b × 1,298 + 2 × s)
= Exp(2.4682 + 0.0007 × 1,298 + 2 × 0.0496)
= Exp(3.5020)
= $33.18
Bottom border of price channel:
Exp(Y895)
= Exp(a + b × X895 – 2 × s)
= Exp(a + b × 1,298 – 2 × s)
= Exp(2.4682 + 0.0007 × 1,298 – 2 × 0.0496)
= Exp(3.3038)
= $27.22
November 1, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(2.4682 + 0.0007 × 1,824 + 2 × 0.0496)
= Exp(3.8808)
= $48.46
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(2.4682 + 0.0007 × 1,824 – 2 × 0.0496)
= Exp(3.6826)
= $39.75
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 30.06% per annum.
- VZ price at the close of November 1, 2024 was $41.36 and was inside the primary price channel.
Secondary Trend
Start date: January 2, 2024
End date: November 1, 2024
a = 2.9760
b = 0.0004
s = 0.0292
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0004) – 1
= 16.72%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0292) – 1
= 12.39%
January 2, 2024 calculations
Top border of price channel:
Exp(Y1,046)
= Exp(a + b × X1,046 + 2 × s)
= Exp(a + b × 1,520 + 2 × s)
= Exp(2.9760 + 0.0004 × 1,520 + 2 × 0.0292)
= Exp(3.6782)
= $39.58
Bottom border of price channel:
Exp(Y1,046)
= Exp(a + b × X1,046 – 2 × s)
= Exp(a + b × 1,520 – 2 × s)
= Exp(2.9760 + 0.0004 × 1,520 – 2 × 0.0292)
= Exp(3.5614)
= $35.21
November 1, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(2.9760 + 0.0004 × 1,824 + 2 × 0.0292)
= Exp(3.8070)
= $45.01
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(2.9760 + 0.0004 × 1,824 – 2 × 0.0292)
= Exp(3.6902)
= $40.05
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 16.72% per annum.
- VZ price at the close of November 1, 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.
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