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 3.33% per annum.
- JNJ price at the close of January 29, 2025 was $151.15 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 33.71% per annum.
- JNJ price at the close of January 29, 2025 was higher than the top border of the secondary price channel by $5.55 (3.81%). This indicates a possible reversal in the secondary trend direction.
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 24, 2024
a = 5.1509
b = -0.0001
s = 0.0376
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -3.33%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0376) – 1
= 16.21%
December 13, 2021 calculations
Top border of price channel:
Exp(Y472)
= Exp(a + b × X472 + 2 × s)
= Exp(a + b × 683 + 2 × s)
= Exp(5.1509 + -0.0001 × 683 + 2 × 0.0376)
= Exp(5.1626)
= $174.62
Bottom border of price channel:
Exp(Y472)
= Exp(a + b × X472 – 2 × s)
= Exp(a + b × 683 – 2 × s)
= Exp(5.1509 + -0.0001 × 683 – 2 × 0.0376)
= Exp(5.0124)
= $150.26
July 24, 2024 calculations
Top border of price channel:
Exp(Y1,127)
= Exp(a + b × X1,127 + 2 × s)
= Exp(a + b × 1,637 + 2 × s)
= Exp(5.1509 + -0.0001 × 1,637 + 2 × 0.0376)
= Exp(5.0740)
= $159.82
Bottom border of price channel:
Exp(Y1,127)
= Exp(a + b × X1,127 – 2 × s)
= Exp(a + b × 1,637 – 2 × s)
= Exp(5.1509 + -0.0001 × 1,637 – 2 × 0.0376)
= Exp(4.9238)
= $137.53
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 3.33% per annum.
- JNJ price at the close of January 29, 2025 was $151.15 and was inside the primary price channel.
Secondary Trend
Start date: August 28, 2024
End date: January 15, 2025
a = 7.0059
b = -0.0011
s = 0.0160
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0011) – 1
= -33.71%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0160) – 1
= 6.59%
August 28, 2024 calculations
Top border of price channel:
Exp(Y1,152)
= Exp(a + b × X1,152 + 2 × s)
= Exp(a + b × 1,672 + 2 × s)
= Exp(7.0059 + -0.0011 × 1,672 + 2 × 0.0160)
= Exp(5.1543)
= $173.18
Bottom border of price channel:
Exp(Y1,152)
= Exp(a + b × X1,152 – 2 × s)
= Exp(a + b × 1,672 – 2 × s)
= Exp(7.0059 + -0.0011 × 1,672 – 2 × 0.0160)
= Exp(5.0905)
= $162.47
January 15, 2025 calculations
Top border of price channel:
Exp(Y1,247)
= Exp(a + b × X1,247 + 2 × s)
= Exp(a + b × 1,812 + 2 × s)
= Exp(7.0059 + -0.0011 × 1,812 + 2 × 0.0160)
= Exp(4.9966)
= $147.91
Bottom border of price channel:
Exp(Y1,247)
= Exp(a + b × X1,247 – 2 × s)
= Exp(a + b × 1,812 – 2 × s)
= Exp(7.0059 + -0.0011 × 1,812 – 2 × 0.0160)
= Exp(4.9328)
= $138.76
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 33.71% per annum.
- JNJ price at the close of January 29, 2025 was higher than the top border of the secondary price channel by $5.55 (3.81%). 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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