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 109.22% per annum.
- LLY price at the close of April 25, 2024 was $724.87 and was lower than the bottom border of the primary price channel by $0.21 (0.03%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 14.14% per annum.
- LLY price at the close of April 25, 2024 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: January 19, 2023
End date: April 18, 2024
a = 3.0172
b = 0.0020
s = 0.0620
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0020) – 1
= 109.22%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0620) – 1
= 28.17%
January 19, 2023 calculations
Top border of price channel:
Exp(Y940)
= Exp(a + b × X940 + 2 × s)
= Exp(a + b × 1,364 + 2 × s)
= Exp(3.0172 + 0.0020 × 1,364 + 2 × 0.0620)
= Exp(5.9001)
= $365.06
Bottom border of price channel:
Exp(Y940)
= Exp(a + b × X940 – 2 × s)
= Exp(a + b × 1,364 – 2 × s)
= Exp(3.0172 + 0.0020 × 1,364 – 2 × 0.0620)
= Exp(5.6519)
= $284.82
April 18, 2024 calculations
Top border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 + 2 × s)
= Exp(a + b × 1,819 + 2 × s)
= Exp(3.0172 + 0.0020 × 1,819 + 2 × 0.0620)
= Exp(6.8203)
= $916.27
Bottom border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 – 2 × s)
= Exp(a + b × 1,819 – 2 × s)
= Exp(3.0172 + 0.0020 × 1,819 – 2 × 0.0620)
= Exp(6.5721)
= $714.89
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 109.22% per annum.
- LLY price at the close of April 25, 2024 was $724.87 and was lower than the bottom border of the primary price channel by $0.21 (0.03%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: February 14, 2024
End date: April 25, 2024
a = 7.3835
b = -0.0004
s = 0.0188
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0004) – 1
= -14.14%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0188) – 1
= 7.81%
February 14, 2024 calculations
Top border of price channel:
Exp(Y1,209)
= Exp(a + b × X1,209 + 2 × s)
= Exp(a + b × 1,755 + 2 × s)
= Exp(7.3835 + -0.0004 × 1,755 + 2 × 0.0188)
= Exp(6.6882)
= $802.86
Bottom border of price channel:
Exp(Y1,209)
= Exp(a + b × X1,209 – 2 × s)
= Exp(a + b × 1,755 – 2 × s)
= Exp(7.3835 + -0.0004 × 1,755 – 2 × 0.0188)
= Exp(6.6130)
= $744.71
April 25, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(7.3835 + -0.0004 × 1,826 + 2 × 0.0188)
= Exp(6.6585)
= $779.40
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(7.3835 + -0.0004 × 1,826 – 2 × 0.0188)
= Exp(6.5834)
= $722.96
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 14.14% per annum.
- LLY price at the close of April 25, 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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