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 37.78% per annum.
- AMGN price at the close of February 20, 2025 was $297.93 and was higher than the top border of the primary price channel by $20.69 (7.46%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 221.13% per annum.
- AMGN price at the close of February 20, 2025 was inside the secondary price channel.
- 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: July 11, 2024
End date: January 24, 2025
a = 7.9164
b = -0.0013
s = 0.0411
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0013) – 1
= -37.78%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0411) – 1
= 17.87%
July 11, 2024 calculations
Top border of price channel:
Exp(Y1,103)
= Exp(a + b × X1,103 + 2 × s)
= Exp(a + b × 1,602 + 2 × s)
= Exp(7.9164 + -0.0013 × 1,602 + 2 × 0.0411)
= Exp(5.9161)
= $370.95
Bottom border of price channel:
Exp(Y1,103)
= Exp(a + b × X1,103 – 2 × s)
= Exp(a + b × 1,602 – 2 × s)
= Exp(7.9164 + -0.0013 × 1,602 – 2 × 0.0411)
= Exp(5.7517)
= $314.72
January 24, 2025 calculations
Top border of price channel:
Exp(Y1,238)
= Exp(a + b × X1,238 + 2 × s)
= Exp(a + b × 1,799 + 2 × s)
= Exp(7.9164 + -0.0013 × 1,799 + 2 × 0.0411)
= Exp(5.6600)
= $287.14
Bottom border of price channel:
Exp(Y1,238)
= Exp(a + b × X1,238 – 2 × s)
= Exp(a + b × 1,799 – 2 × s)
= Exp(7.9164 + -0.0013 × 1,799 – 2 × 0.0411)
= Exp(5.4956)
= $243.61
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 37.78% per annum.
- AMGN price at the close of February 20, 2025 was $297.93 and was higher than the top border of the primary price channel by $20.69 (7.46%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: December 30, 2024
End date: February 4, 2025
a = -0.1315
b = 0.0032
s = 0.0075
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0032) – 1
= 221.13%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0075) – 1
= 3.04%
December 30, 2024 calculations
Top border of price channel:
Exp(Y1,222)
= Exp(a + b × X1,222 + 2 × s)
= Exp(a + b × 1,774 + 2 × s)
= Exp(-0.1315 + 0.0032 × 1,774 + 2 × 0.0075)
= Exp(5.5538)
= $258.22
Bottom border of price channel:
Exp(Y1,222)
= Exp(a + b × X1,222 – 2 × s)
= Exp(a + b × 1,774 – 2 × s)
= Exp(-0.1315 + 0.0032 × 1,774 – 2 × 0.0075)
= Exp(5.5239)
= $250.61
February 4, 2025 calculations
Top border of price channel:
Exp(Y1,245)
= Exp(a + b × X1,245 + 2 × s)
= Exp(a + b × 1,810 + 2 × s)
= Exp(-0.1315 + 0.0032 × 1,810 + 2 × 0.0075)
= Exp(5.6689)
= $289.71
Bottom border of price channel:
Exp(Y1,245)
= Exp(a + b × X1,245 – 2 × s)
= Exp(a + b × 1,810 – 2 × s)
= Exp(-0.1315 + 0.0032 × 1,810 – 2 × 0.0075)
= Exp(5.6390)
= $281.17
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 221.13% per annum.
- AMGN price at the close of February 20, 2025 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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