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 3.34% per annum.
- JNJ price at the close of June 13, 2025 was $157.10 and was higher than the top border of the primary price channel by $4.59 (3.01%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 1.37% per annum.
- JNJ price at the close of June 13, 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 JNJ 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: December 13, 2021
End date: July 23, 2024
a = 5.1221
b = -0.0001
s = 0.0376
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -3.34%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0376) – 1
= 16.21%
December 13, 2021 calculations
Top border of price channel:
Exp(Y378)
= Exp(a + b × X378 + 2 × s)
= Exp(a + b × 546 + 2 × s)
= Exp(5.1221 + -0.0001 × 546 + 2 × 0.0376)
= Exp(5.1463)
= $171.80
Bottom border of price channel:
Exp(Y378)
= Exp(a + b × X378 – 2 × s)
= Exp(a + b × 546 – 2 × s)
= Exp(5.1221 + -0.0001 × 546 – 2 × 0.0376)
= Exp(4.9961)
= $147.83
July 23, 2024 calculations
Top border of price channel:
Exp(Y1,032)
= Exp(a + b × X1,032 + 2 × s)
= Exp(a + b × 1,499 + 2 × s)
= Exp(5.1221 + -0.0001 × 1,499 + 2 × 0.0376)
= Exp(5.0575)
= $157.20
Bottom border of price channel:
Exp(Y1,032)
= Exp(a + b × X1,032 – 2 × s)
= Exp(a + b × 1,499 – 2 × s)
= Exp(5.1221 + -0.0001 × 1,499 – 2 × 0.0376)
= Exp(4.9073)
= $135.27
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 3.34% per annum.
- JNJ price at the close of June 13, 2025 was $157.10 and was higher than the top border of the primary price channel by $4.59 (3.01%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: January 30, 2023
End date: June 13, 2025
a = 4.9634
b = 0.0000
s = 0.0408
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 1.37%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0408) – 1
= 17.74%
January 30, 2023 calculations
Top border of price channel:
Exp(Y661)
= Exp(a + b × X661 + 2 × s)
= Exp(a + b × 959 + 2 × s)
= Exp(4.9634 + 0.0000 × 959 + 2 × 0.0408)
= Exp(5.0809)
= $160.91
Bottom border of price channel:
Exp(Y661)
= Exp(a + b × X661 – 2 × s)
= Exp(a + b × 959 – 2 × s)
= Exp(4.9634 + 0.0000 × 959 – 2 × 0.0408)
= Exp(4.9176)
= $136.67
June 13, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.9634 + 0.0000 × 1,824 + 2 × 0.0408)
= Exp(5.1132)
= $166.20
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.9634 + 0.0000 × 1,824 – 2 × 0.0408)
= Exp(4.9499)
= $141.16
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 1.37% per annum.
- JNJ price at the close of June 13, 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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