Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 29.79% per annum.
- AMGN price at the close of December 2, 2024 was $278.10 and was lower than the bottom border of the primary price channel by $27.89 (9.12%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 9.90% per annum.
- AMGN price at the close of December 2, 2024 was lower than the bottom border of the secondary price channel by $26.70 (8.76%).
- 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 AMGN 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: February 8, 2023
End date: November 11, 2024
a = 4.5256
b = 0.0007
s = 0.0533
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 29.79%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0533) – 1
= 23.77%
February 8, 2023 calculations
Top border of price channel:
Exp(Y801)
= Exp(a + b × X801 + 2 × s)
= Exp(a + b × 1,163 + 2 × s)
= Exp(4.5256 + 0.0007 × 1,163 + 2 × 0.0533)
= Exp(5.4631)
= $235.84
Bottom border of price channel:
Exp(Y801)
= Exp(a + b × X801 – 2 × s)
= Exp(a + b × 1,163 – 2 × s)
= Exp(4.5256 + 0.0007 × 1,163 – 2 × 0.0533)
= Exp(5.2499)
= $190.54
November 11, 2024 calculations
Top border of price channel:
Exp(Y1,243)
= Exp(a + b × X1,243 + 2 × s)
= Exp(a + b × 1,805 + 2 × s)
= Exp(4.5256 + 0.0007 × 1,805 + 2 × 0.0533)
= Exp(5.9218)
= $373.10
Bottom border of price channel:
Exp(Y1,243)
= Exp(a + b × X1,243 – 2 × s)
= Exp(a + b × 1,805 – 2 × s)
= Exp(4.5256 + 0.0007 × 1,805 – 2 × 0.0533)
= Exp(5.7086)
= $301.43
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 29.79% per annum.
- AMGN price at the close of December 2, 2024 was $278.10 and was lower than the bottom border of the primary price channel by $27.89 (9.12%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: July 12, 2024
End date: November 11, 2024
a = 6.2742
b = -0.0003
s = 0.0164
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -9.90%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0164) – 1
= 6.79%
July 12, 2024 calculations
Top border of price channel:
Exp(Y1,158)
= Exp(a + b × X1,158 + 2 × s)
= Exp(a + b × 1,683 + 2 × s)
= Exp(6.2742 + -0.0003 × 1,683 + 2 × 0.0164)
= Exp(5.8262)
= $339.08
Bottom border of price channel:
Exp(Y1,158)
= Exp(a + b × X1,158 – 2 × s)
= Exp(a + b × 1,683 – 2 × s)
= Exp(6.2742 + -0.0003 × 1,683 – 2 × 0.0164)
= Exp(5.7605)
= $317.51
November 11, 2024 calculations
Top border of price channel:
Exp(Y1,243)
= Exp(a + b × X1,243 + 2 × s)
= Exp(a + b × 1,805 + 2 × s)
= Exp(6.2742 + -0.0003 × 1,805 + 2 × 0.0164)
= Exp(5.7914)
= $327.47
Bottom border of price channel:
Exp(Y1,243)
= Exp(a + b × X1,243 – 2 × s)
= Exp(a + b × 1,805 – 2 × s)
= Exp(6.2742 + -0.0003 × 1,805 – 2 × 0.0164)
= Exp(5.7257)
= $306.64
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 9.90% per annum.
- AMGN price at the close of December 2, 2024 was lower than the bottom border of the secondary price channel by $26.70 (8.76%).
- 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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