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 6.71% per annum.
- JNJ price at the close of April 26, 2024 was $146.14 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 47.52% per annum.
- JNJ price at the close of April 26, 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: April 26, 2024
a = 5.3758
b = -0.0002
s = 0.0368
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -6.71%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0368) – 1
= 15.87%
March 4, 2022 calculations
Top border of price channel:
Exp(Y719)
= Exp(a + b × X719 + 2 × s)
= Exp(a + b × 1,040 + 2 × s)
= Exp(5.3758 + -0.0002 × 1,040 + 2 × 0.0368)
= Exp(5.2516)
= $190.88
Bottom border of price channel:
Exp(Y719)
= Exp(a + b × X719 – 2 × s)
= Exp(a + b × 1,040 – 2 × s)
= Exp(5.3758 + -0.0002 × 1,040 – 2 × 0.0368)
= Exp(5.1043)
= $164.74
April 26, 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(5.3758 + -0.0002 × 1,824 + 2 × 0.0368)
= Exp(5.1025)
= $164.44
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.3758 + -0.0002 × 1,824 – 2 × 0.0368)
= Exp(4.9553)
= $141.92
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 6.71% per annum.
- JNJ price at the close of April 26, 2024 was $146.14 and was inside the primary price channel.
Secondary Trend
Start date: February 23, 2024
End date: April 26, 2024
a = 8.2094
b = -0.0018
s = 0.0139
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0018) – 1
= -47.52%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0139) – 1
= 5.73%
February 23, 2024 calculations
Top border of price channel:
Exp(Y1,214)
= Exp(a + b × X1,214 + 2 × s)
= Exp(a + b × 1,761 + 2 × s)
= Exp(8.2094 + -0.0018 × 1,761 + 2 × 0.0139)
= Exp(5.1270)
= $168.51
Bottom border of price channel:
Exp(Y1,214)
= Exp(a + b × X1,214 – 2 × s)
= Exp(a + b × 1,761 – 2 × s)
= Exp(8.2094 + -0.0018 × 1,761 – 2 × 0.0139)
= Exp(5.0713)
= $159.38
April 26, 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(8.2094 + -0.0018 × 1,824 + 2 × 0.0139)
= Exp(5.0157)
= $150.77
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(8.2094 + -0.0018 × 1,824 – 2 × 0.0139)
= Exp(4.9600)
= $142.60
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 47.52% per annum.
- JNJ price at the close of April 26, 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.
Check out JNJ and 1,499 other stocks on our new website