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 10.87% per annum.
- LLY price at the close of April 2, 2025 was $818.22 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 41.58% per annum.
- LLY price at the close of April 2, 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 LLY 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: June 3, 2024
End date: April 2, 2025
a = 7.2731
b = -0.0003
s = 0.0656
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -10.87%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0656) – 1
= 30.01%
June 3, 2024 calculations
Top border of price channel:
Exp(Y1,047)
= Exp(a + b × X1,047 + 2 × s)
= Exp(a + b × 1,522 + 2 × s)
= Exp(7.2731 + -0.0003 × 1,522 + 2 × 0.0656)
= Exp(6.9244)
= $1,016.80
Bottom border of price channel:
Exp(Y1,047)
= Exp(a + b × X1,047 – 2 × s)
= Exp(a + b × 1,522 – 2 × s)
= Exp(7.2731 + -0.0003 × 1,522 – 2 × 0.0656)
= Exp(6.6620)
= $782.10
April 2, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(7.2731 + -0.0003 × 1,825 + 2 × 0.0656)
= Exp(6.8289)
= $924.14
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(7.2731 + -0.0003 × 1,825 – 2 × 0.0656)
= Exp(6.5664)
= $710.83
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 10.87% per annum.
- LLY price at the close of April 2, 2025 was $818.22 and was inside the primary price channel.
Secondary Trend
Start date: November 14, 2024
End date: April 2, 2025
a = 5.0260
b = 0.0010
s = 0.0465
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 41.58%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0465) – 1
= 20.44%
November 14, 2024 calculations
Top border of price channel:
Exp(Y1,162)
= Exp(a + b × X1,162 + 2 × s)
= Exp(a + b × 1,686 + 2 × s)
= Exp(5.0260 + 0.0010 × 1,686 + 2 × 0.0465)
= Exp(6.7250)
= $832.98
Bottom border of price channel:
Exp(Y1,162)
= Exp(a + b × X1,162 – 2 × s)
= Exp(a + b × 1,686 – 2 × s)
= Exp(5.0260 + 0.0010 × 1,686 – 2 × 0.0465)
= Exp(6.5390)
= $691.59
April 2, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(5.0260 + 0.0010 × 1,825 + 2 × 0.0465)
= Exp(6.8574)
= $950.91
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(5.0260 + 0.0010 × 1,825 – 2 × 0.0465)
= Exp(6.6714)
= $789.50
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 41.58% per annum.
- LLY price at the close of April 2, 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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