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 6.81% per annum.
- JNJ price at the close of May 17, 2024 was $154.64 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 21.88% per annum.
- JNJ price at the close of May 17, 2024 was inside the secondary price channel.
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: March 4, 2022
End date: May 17, 2024
a = 5.3755
b = -0.0002
s = 0.0365
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -6.81%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0365) – 1
= 15.73%
March 4, 2022 calculations
Top border of price channel:
Exp(Y704)
= Exp(a + b × X704 + 2 × s)
= Exp(a + b × 1,019 + 2 × s)
= Exp(5.3755 + -0.0002 × 1,019 + 2 × 0.0365)
= Exp(5.2518)
= $190.91
Bottom border of price channel:
Exp(Y704)
= Exp(a + b × X704 – 2 × s)
= Exp(a + b × 1,019 – 2 × s)
= Exp(5.3755 + -0.0002 × 1,019 – 2 × 0.0365)
= Exp(5.1057)
= $164.96
May 17, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(5.3755 + -0.0002 × 1,824 + 2 × 0.0365)
= Exp(5.0963)
= $163.42
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.3755 + -0.0002 × 1,824 – 2 × 0.0365)
= Exp(4.9503)
= $141.22
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 6.81% per annum.
- JNJ price at the close of May 17, 2024 was $154.64 and was inside the primary price channel.
Secondary Trend
Start date: January 3, 2024
End date: May 17, 2024
a = 6.2364
b = -0.0007
s = 0.0203
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -21.88%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0203) – 1
= 8.44%
January 3, 2024 calculations
Top border of price channel:
Exp(Y1,164)
= Exp(a + b × X1,164 + 2 × s)
= Exp(a + b × 1,689 + 2 × s)
= Exp(6.2364 + -0.0007 × 1,689 + 2 × 0.0203)
= Exp(5.1346)
= $169.79
Bottom border of price channel:
Exp(Y1,164)
= Exp(a + b × X1,164 – 2 × s)
= Exp(a + b × 1,689 – 2 × s)
= Exp(6.2364 + -0.0007 × 1,689 – 2 × 0.0203)
= Exp(5.0536)
= $156.58
May 17, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(6.2364 + -0.0007 × 1,824 + 2 × 0.0203)
= Exp(5.0433)
= $154.98
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(6.2364 + -0.0007 × 1,824 – 2 × 0.0203)
= Exp(4.9623)
= $142.92
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 21.88% per annum.
- JNJ price at the close of May 17, 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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