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 55.73% per annum.
- AMGN price at the close of March 27, 2024 was $286.30 and was lower than the bottom border of the primary price channel by $13.84 (4.61%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 55.06% per annum.
- AMGN price at the close of March 27, 2024 was higher than the top border of the secondary price channel by $4.34 (1.54%). This indicates a possible reversal in the secondary trend direction.
- 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: May 2, 2023
End date: February 12, 2024
a = 3.5676
b = 0.0012
s = 0.0397
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 55.73%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0397) – 1
= 17.21%
May 2, 2023 calculations
Top border of price channel:
Exp(Y1,031)
= Exp(a + b × X1,031 + 2 × s)
= Exp(a + b × 1,496 + 2 × s)
= Exp(3.5676 + 0.0012 × 1,496 + 2 × 0.0397)
= Exp(5.4626)
= $235.71
Bottom border of price channel:
Exp(Y1,031)
= Exp(a + b × X1,031 – 2 × s)
= Exp(a + b × 1,496 – 2 × s)
= Exp(3.5676 + 0.0012 × 1,496 – 2 × 0.0397)
= Exp(5.3038)
= $201.09
February 12, 2024 calculations
Top border of price channel:
Exp(Y1,227)
= Exp(a + b × X1,227 + 2 × s)
= Exp(a + b × 1,782 + 2 × s)
= Exp(3.5676 + 0.0012 × 1,782 + 2 × 0.0397)
= Exp(5.8097)
= $333.51
Bottom border of price channel:
Exp(Y1,227)
= Exp(a + b × X1,227 – 2 × s)
= Exp(a + b × 1,782 – 2 × s)
= Exp(3.5676 + 0.0012 × 1,782 – 2 × 0.0397)
= Exp(5.6509)
= $284.53
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 55.73% per annum.
- AMGN price at the close of March 27, 2024 was $286.30 and was lower than the bottom border of the primary price channel by $13.84 (4.61%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: January 8, 2024
End date: March 22, 2024
a = 9.5878
b = -0.0022
s = 0.0276
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0022) – 1
= -55.06%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0276) – 1
= 11.69%
January 8, 2024 calculations
Top border of price channel:
Exp(Y1,203)
= Exp(a + b × X1,203 + 2 × s)
= Exp(a + b × 1,747 + 2 × s)
= Exp(9.5878 + -0.0022 × 1,747 + 2 × 0.0276)
= Exp(5.8149)
= $335.25
Bottom border of price channel:
Exp(Y1,203)
= Exp(a + b × X1,203 – 2 × s)
= Exp(a + b × 1,747 – 2 × s)
= Exp(9.5878 + -0.0022 × 1,747 – 2 × 0.0276)
= Exp(5.7043)
= $300.17
March 22, 2024 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,821 + 2 × s)
= Exp(9.5878 + -0.0022 × 1,821 + 2 × 0.0276)
= Exp(5.6527)
= $285.07
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,821 – 2 × s)
= Exp(9.5878 + -0.0022 × 1,821 – 2 × 0.0276)
= Exp(5.5422)
= $255.24
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 55.06% per annum.
- AMGN price at the close of March 27, 2024 was higher than the top border of the secondary price channel by $4.34 (1.54%). 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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