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 4, 2024 was $27.76 and was higher than the top border of the primary price channel by $0.80 (2.97%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 13.53% per annum.
- PFE price at the close of November 4, 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 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 = 4.5261
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
= 32.26%
November 26, 2021 calculations
Top border of price channel:
Exp(Y519)
= Exp(a + b × X519 + 2 × s)
= Exp(a + b × 752 + 2 × s)
= Exp(4.5261 + -0.0008 × 752 + 2 × 0.0699)
= Exp(4.1011)
= $60.40
Bottom border of price channel:
Exp(Y519)
= Exp(a + b × X519 – 2 × s)
= Exp(a + b × 752 – 2 × s)
= Exp(4.5261 + -0.0008 × 752 – 2 × 0.0699)
= Exp(3.8215)
= $45.67
July 11, 2024 calculations
Top border of price channel:
Exp(Y1,176)
= Exp(a + b × X1,176 + 2 × s)
= Exp(a + b × 1,710 + 2 × s)
= Exp(4.5261 + -0.0008 × 1,710 + 2 × 0.0699)
= Exp(3.3815)
= $29.41
Bottom border of price channel:
Exp(Y1,176)
= Exp(a + b × X1,176 – 2 × s)
= Exp(a + b × 1,710 – 2 × s)
= Exp(4.5261 + -0.0008 × 1,710 – 2 × 0.0699)
= Exp(3.1019)
= $22.24
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 4, 2024 was $27.76 and was higher than the top border of the primary price channel by $0.80 (2.97%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: December 6, 2023
End date: November 1, 2024
a = 2.7440
b = 0.0003
s = 0.0370
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 13.53%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0370) – 1
= 15.97%
December 6, 2023 calculations
Top border of price channel:
Exp(Y1,028)
= Exp(a + b × X1,028 + 2 × s)
= Exp(a + b × 1,492 + 2 × s)
= Exp(2.7440 + 0.0003 × 1,492 + 2 × 0.0370)
= Exp(3.3370)
= $28.13
Bottom border of price channel:
Exp(Y1,028)
= Exp(a + b × X1,028 – 2 × s)
= Exp(a + b × 1,492 – 2 × s)
= Exp(2.7440 + 0.0003 × 1,492 – 2 × 0.0370)
= Exp(3.1888)
= $24.26
November 1, 2024 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(2.7440 + 0.0003 × 1,823 + 2 × 0.0370)
= Exp(3.4521)
= $31.57
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(2.7440 + 0.0003 × 1,823 – 2 × 0.0370)
= Exp(3.3040)
= $27.22
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 13.53% per annum.
- PFE price at the close of November 4, 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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