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 23.78% per annum.
- PFE price at the close of January 17, 2025 was $26.30 and was higher than the top border of the primary price channel by $1.05 (4.17%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 5.91% per annum.
- PFE price at the close of January 17, 2025 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 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 18, 2021
End date: July 11, 2024
a = 4.4434
b = -0.0007
s = 0.0708
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -23.78%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0708) – 1
= 32.75%
November 18, 2021 calculations
Top border of price channel:
Exp(Y463)
= Exp(a + b × X463 + 2 × s)
= Exp(a + b × 667 + 2 × s)
= Exp(4.4434 + -0.0007 × 667 + 2 × 0.0708)
= Exp(4.0888)
= $59.67
Bottom border of price channel:
Exp(Y463)
= Exp(a + b × X463 – 2 × s)
= Exp(a + b × 667 – 2 × s)
= Exp(4.4434 + -0.0007 × 667 – 2 × 0.0708)
= Exp(3.8054)
= $44.95
July 11, 2024 calculations
Top border of price channel:
Exp(Y1,125)
= Exp(a + b × X1,125 + 2 × s)
= Exp(a + b × 1,633 + 2 × s)
= Exp(4.4434 + -0.0007 × 1,633 + 2 × 0.0708)
= Exp(3.3700)
= $29.08
Bottom border of price channel:
Exp(Y1,125)
= Exp(a + b × X1,125 – 2 × s)
= Exp(a + b × 1,633 – 2 × s)
= Exp(4.4434 + -0.0007 × 1,633 – 2 × 0.0708)
= Exp(3.0867)
= $21.91
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 23.78% per annum.
- PFE price at the close of January 17, 2025 was $26.30 and was higher than the top border of the primary price channel by $1.05 (4.17%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: October 20, 2023
End date: November 8, 2024
a = 3.0643
b = 0.0002
s = 0.0450
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 5.91%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0450) – 1
= 19.71%
October 20, 2023 calculations
Top border of price channel:
Exp(Y945)
= Exp(a + b × X945 + 2 × s)
= Exp(a + b × 1,368 + 2 × s)
= Exp(3.0643 + 0.0002 × 1,368 + 2 × 0.0450)
= Exp(3.3693)
= $29.06
Bottom border of price channel:
Exp(Y945)
= Exp(a + b × X945 – 2 × s)
= Exp(a + b × 1,368 – 2 × s)
= Exp(3.0643 + 0.0002 × 1,368 – 2 × 0.0450)
= Exp(3.1894)
= $24.27
November 8, 2024 calculations
Top border of price channel:
Exp(Y1,210)
= Exp(a + b × X1,210 + 2 × s)
= Exp(a + b × 1,753 + 2 × s)
= Exp(3.0643 + 0.0002 × 1,753 + 2 × 0.0450)
= Exp(3.4298)
= $30.87
Bottom border of price channel:
Exp(Y1,210)
= Exp(a + b × X1,210 – 2 × s)
= Exp(a + b × 1,753 – 2 × s)
= Exp(3.0643 + 0.0002 × 1,753 – 2 × 0.0450)
= Exp(3.2499)
= $25.79
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 5.91% per annum.
- PFE price at the close of January 17, 2025 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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