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 22.69% per annum.
- LLY price at the close of February 20, 2025 was $873.12 and was higher than the top border of the primary price channel by $5.00 (0.58%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 875.51% per annum.
- LLY price at the close of February 20, 2025 was lower than the bottom border of the secondary price channel by $15.30 (1.72%). This indicates a possible reversal in the secondary trend direction.
- 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 7, 2024
End date: February 5, 2025
a = 7.9349
b = -0.0007
s = 0.0595
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -22.69%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0595) – 1
= 26.86%
June 7, 2024 calculations
Top border of price channel:
Exp(Y1,081)
= Exp(a + b × X1,081 + 2 × s)
= Exp(a + b × 1,568 + 2 × s)
= Exp(7.9349 + -0.0007 × 1,568 + 2 × 0.0595)
= Exp(6.9482)
= $1,041.31
Bottom border of price channel:
Exp(Y1,081)
= Exp(a + b × X1,081 – 2 × s)
= Exp(a + b × 1,568 – 2 × s)
= Exp(7.9349 + -0.0007 × 1,568 – 2 × 0.0595)
= Exp(6.7104)
= $820.87
February 5, 2025 calculations
Top border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 + 2 × s)
= Exp(a + b × 1,811 + 2 × s)
= Exp(7.9349 + -0.0007 × 1,811 + 2 × 0.0595)
= Exp(6.7769)
= $877.35
Bottom border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 – 2 × s)
= Exp(a + b × 1,811 – 2 × s)
= Exp(7.9349 + -0.0007 × 1,811 – 2 × 0.0595)
= Exp(6.5390)
= $691.61
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 22.69% per annum.
- LLY price at the close of February 20, 2025 was $873.12 and was higher than the top border of the primary price channel by $5.00 (0.58%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: January 14, 2025
End date: February 13, 2025
a = -4.5692
b = 0.0062
s = 0.0183
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0062) – 1
= 875.51%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0183) – 1
= 7.58%
January 14, 2025 calculations
Top border of price channel:
Exp(Y1,231)
= Exp(a + b × X1,231 + 2 × s)
= Exp(a + b × 1,789 + 2 × s)
= Exp(-4.5692 + 0.0062 × 1,789 + 2 × 0.0183)
= Exp(6.6316)
= $758.69
Bottom border of price channel:
Exp(Y1,231)
= Exp(a + b × X1,231 – 2 × s)
= Exp(a + b × 1,789 – 2 × s)
= Exp(-4.5692 + 0.0062 × 1,789 – 2 × 0.0183)
= Exp(6.5585)
= $705.25
February 13, 2025 calculations
Top border of price channel:
Exp(Y1,252)
= Exp(a + b × X1,252 + 2 × s)
= Exp(a + b × 1,819 + 2 × s)
= Exp(-4.5692 + 0.0062 × 1,819 + 2 × 0.0183)
= Exp(6.8188)
= $914.90
Bottom border of price channel:
Exp(Y1,252)
= Exp(a + b × X1,252 – 2 × s)
= Exp(a + b × 1,819 – 2 × s)
= Exp(-4.5692 + 0.0062 × 1,819 – 2 × 0.0183)
= Exp(6.7458)
= $850.45
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 875.51% per annum.
- LLY price at the close of February 20, 2025 was lower than the bottom border of the secondary price channel by $15.30 (1.72%). This indicates a possible reversal in the secondary trend direction.
- 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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