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 27.58% per annum.
- VZ price at the close of January 17, 2025 was $38.78 and was lower than the bottom border of the primary price channel by $1.63 (4.04%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 26.22% per annum.
- VZ price at the close of January 17, 2025 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 16, 2023
End date: December 13, 2024
a = 2.5833
b = 0.0007
s = 0.0503
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 27.58%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0503) – 1
= 22.31%
May 16, 2023 calculations
Top border of price channel:
Exp(Y836)
= Exp(a + b × X836 + 2 × s)
= Exp(a + b × 1,211 + 2 × s)
= Exp(2.5833 + 0.0007 × 1,211 + 2 × 0.0503)
= Exp(3.4921)
= $32.85
Bottom border of price channel:
Exp(Y836)
= Exp(a + b × X836 – 2 × s)
= Exp(a + b × 1,211 – 2 × s)
= Exp(2.5833 + 0.0007 × 1,211 – 2 × 0.0503)
= Exp(3.2907)
= $26.86
December 13, 2024 calculations
Top border of price channel:
Exp(Y1,234)
= Exp(a + b × X1,234 + 2 × s)
= Exp(a + b × 1,788 + 2 × s)
= Exp(2.5833 + 0.0007 × 1,788 + 2 × 0.0503)
= Exp(3.8771)
= $48.28
Bottom border of price channel:
Exp(Y1,234)
= Exp(a + b × X1,234 – 2 × s)
= Exp(a + b × 1,788 – 2 × s)
= Exp(2.5833 + 0.0007 × 1,788 – 2 × 0.0503)
= Exp(3.6758)
= $39.48
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 27.58% per annum.
- VZ price at the close of January 17, 2025 was $38.78 and was lower than the bottom border of the primary price channel by $1.63 (4.04%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: September 10, 2024
End date: January 17, 2025
a = 5.1832
b = -0.0008
s = 0.0265
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0008) – 1
= -26.22%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0265) – 1
= 11.19%
September 10, 2024 calculations
Top border of price channel:
Exp(Y1,167)
= Exp(a + b × X1,167 + 2 × s)
= Exp(a + b × 1,694 + 2 × s)
= Exp(5.1832 + -0.0008 × 1,694 + 2 × 0.0265)
= Exp(3.8248)
= $45.82
Bottom border of price channel:
Exp(Y1,167)
= Exp(a + b × X1,167 – 2 × s)
= Exp(a + b × 1,694 – 2 × s)
= Exp(5.1832 + -0.0008 × 1,694 – 2 × 0.0265)
= Exp(3.7188)
= $41.21
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(5.1832 + -0.0008 × 1,823 + 2 × 0.0265)
= Exp(3.7173)
= $41.15
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(5.1832 + -0.0008 × 1,823 – 2 × 0.0265)
= Exp(3.6113)
= $37.01
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 26.22% per annum.
- VZ price at the close of January 17, 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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