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 23.98% per annum.
- PFE price at the close of November 19, 2024 was $25.10 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.61% per annum.
- PFE price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $1.74 (6.47%). 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 PFE 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: November 26, 2021
End date: July 11, 2024
a = 4.4992
b = -0.0008
s = 0.0699
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0008) – 1
= -23.98%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0699) – 1
= 32.25%
November 26, 2021 calculations
Top border of price channel:
Exp(Y508)
= Exp(a + b × X508 + 2 × s)
= Exp(a + b × 737 + 2 × s)
= Exp(4.4992 + -0.0008 × 737 + 2 × 0.0699)
= Exp(4.0854)
= $59.47
Bottom border of price channel:
Exp(Y508)
= Exp(a + b × X508 – 2 × s)
= Exp(a + b × 737 – 2 × s)
= Exp(4.4992 + -0.0008 × 737 – 2 × 0.0699)
= Exp(3.8059)
= $44.97
July 11, 2024 calculations
Top border of price channel:
Exp(Y1,165)
= Exp(a + b × X1,165 + 2 × s)
= Exp(a + b × 1,695 + 2 × s)
= Exp(4.4992 + -0.0008 × 1,695 + 2 × 0.0699)
= Exp(3.3659)
= $28.96
Bottom border of price channel:
Exp(Y1,165)
= Exp(a + b × X1,165 – 2 × s)
= Exp(a + b × 1,695 – 2 × s)
= Exp(4.4992 + -0.0008 × 1,695 – 2 × 0.0699)
= Exp(3.0863)
= $21.90
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 23.98% per annum.
- PFE price at the close of November 19, 2024 was $25.10 and was inside the primary price channel.
Secondary Trend
Start date: December 1, 2023
End date: November 5, 2024
a = 2.7709
b = 0.0003
s = 0.0376
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 12.61%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0376) – 1
= 16.24%
December 1, 2023 calculations
Top border of price channel:
Exp(Y1,014)
= Exp(a + b × X1,014 + 2 × s)
= Exp(a + b × 1,472 + 2 × s)
= Exp(2.7709 + 0.0003 × 1,472 + 2 × 0.0376)
= Exp(3.3251)
= $27.80
Bottom border of price channel:
Exp(Y1,014)
= Exp(a + b × X1,014 – 2 × s)
= Exp(a + b × 1,472 – 2 × s)
= Exp(2.7709 + 0.0003 × 1,472 – 2 × 0.0376)
= Exp(3.1746)
= $23.92
November 5, 2024 calculations
Top border of price channel:
Exp(Y1,247)
= Exp(a + b × X1,247 + 2 × s)
= Exp(a + b × 1,812 + 2 × s)
= Exp(2.7709 + 0.0003 × 1,812 + 2 × 0.0376)
= Exp(3.4357)
= $31.05
Bottom border of price channel:
Exp(Y1,247)
= Exp(a + b × X1,247 – 2 × s)
= Exp(a + b × 1,812 – 2 × s)
= Exp(2.7709 + 0.0003 × 1,812 – 2 × 0.0376)
= Exp(3.2852)
= $26.72
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.61% per annum.
- PFE price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $1.74 (6.47%). 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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