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 45.06% per annum.
- LLY price at the close of January 17, 2025 was $725.72 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 1.23% per annum.
- LLY price at the close of January 17, 2025 was lower than the bottom border of the secondary price channel by $0.38 (0.05%).
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: August 14, 2024
End date: January 17, 2025
a = 9.6050
b = -0.0016
s = 0.0388
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0016) – 1
= -45.06%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0388) – 1
= 16.80%
August 14, 2024 calculations
Top border of price channel:
Exp(Y1,149)
= Exp(a + b × X1,149 + 2 × s)
= Exp(a + b × 1,667 + 2 × s)
= Exp(9.6050 + -0.0016 × 1,667 + 2 × 0.0388)
= Exp(6.9472)
= $1,040.23
Bottom border of price channel:
Exp(Y1,149)
= Exp(a + b × X1,149 – 2 × s)
= Exp(a + b × 1,667 – 2 × s)
= Exp(9.6050 + -0.0016 × 1,667 – 2 × 0.0388)
= Exp(6.7919)
= $890.59
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(9.6050 + -0.0016 × 1,823 + 2 × 0.0388)
= Exp(6.6912)
= $805.30
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(9.6050 + -0.0016 × 1,823 – 2 × 0.0388)
= Exp(6.5359)
= $689.46
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 45.06% per annum.
- LLY price at the close of January 17, 2025 was $725.72 and was inside the primary price channel.
Secondary Trend
Start date: November 14, 2024
End date: January 17, 2025
a = 6.7170
b = 0.0000
s = 0.0337
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= -1.23%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0337) – 1
= 14.43%
November 14, 2024 calculations
Top border of price channel:
Exp(Y1,214)
= Exp(a + b × X1,214 + 2 × s)
= Exp(a + b × 1,759 + 2 × s)
= Exp(6.7170 + 0.0000 × 1,759 + 2 × 0.0337)
= Exp(6.7247)
= $832.70
Bottom border of price channel:
Exp(Y1,214)
= Exp(a + b × X1,214 – 2 × s)
= Exp(a + b × 1,759 – 2 × s)
= Exp(6.7170 + 0.0000 × 1,759 – 2 × 0.0337)
= Exp(6.5899)
= $727.68
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(6.7170 + 0.0000 × 1,823 + 2 × 0.0337)
= Exp(6.7225)
= $830.89
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(6.7170 + 0.0000 × 1,823 – 2 × 0.0337)
= Exp(6.5877)
= $726.10
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 1.23% per annum.
- LLY price at the close of January 17, 2025 was lower than the bottom border of the secondary price channel by $0.38 (0.05%).
- 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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