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 111.03% per annum.
- LLY price at the close of May 20, 2024 was $783.18 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 4.64% per annum.
- LLY price at the close of May 20, 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 18, 2023
End date: April 17, 2024
a = 3.0253
b = 0.0020
s = 0.0622
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0020) – 1
= 111.03%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0622) – 1
= 28.24%
January 18, 2023 calculations
Top border of price channel:
Exp(Y922)
= Exp(a + b × X922 + 2 × s)
= Exp(a + b × 1,338 + 2 × s)
= Exp(3.0253 + 0.0020 × 1,338 + 2 × 0.0622)
= Exp(5.8873)
= $360.44
Bottom border of price channel:
Exp(Y922)
= Exp(a + b × X922 – 2 × s)
= Exp(a + b × 1,338 – 2 × s)
= Exp(3.0253 + 0.0020 × 1,338 – 2 × 0.0622)
= Exp(5.6386)
= $281.07
April 17, 2024 calculations
Top border of price channel:
Exp(Y1,235)
= Exp(a + b × X1,235 + 2 × s)
= Exp(a + b × 1,793 + 2 × s)
= Exp(3.0253 + 0.0020 × 1,793 + 2 × 0.0622)
= Exp(6.8183)
= $914.44
Bottom border of price channel:
Exp(Y1,235)
= Exp(a + b × X1,235 – 2 × s)
= Exp(a + b × 1,793 – 2 × s)
= Exp(3.0253 + 0.0020 × 1,793 – 2 × 0.0622)
= Exp(6.5696)
= $713.09
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 111.03% per annum.
- LLY price at the close of May 20, 2024 was $783.18 and was inside the primary price channel.
Secondary Trend
Start date: February 14, 2024
End date: May 17, 2024
a = 6.8661
b = -0.0001
s = 0.0206
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -4.64%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0206) – 1
= 8.61%
February 14, 2024 calculations
Top border of price channel:
Exp(Y1,192)
= Exp(a + b × X1,192 + 2 × s)
= Exp(a + b × 1,730 + 2 × s)
= Exp(6.8661 + -0.0001 × 1,730 + 2 × 0.0206)
= Exp(6.6820)
= $797.93
Bottom border of price channel:
Exp(Y1,192)
= Exp(a + b × X1,192 – 2 × s)
= Exp(a + b × 1,730 – 2 × s)
= Exp(6.8661 + -0.0001 × 1,730 – 2 × 0.0206)
= Exp(6.5994)
= $734.69
May 17, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(6.8661 + -0.0001 × 1,823 + 2 × 0.0206)
= Exp(6.6699)
= $788.33
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(6.8661 + -0.0001 × 1,823 – 2 × 0.0206)
= Exp(6.5873)
= $725.84
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 4.64% per annum.
- LLY price at the close of May 20, 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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