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 21.70% per annum.
- GM price at the close of April 25, 2024 was $45.62 and was higher than the top border of the primary price channel by $11.34 (33.07%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 158.23% per annum.
- GM price at the close of April 25, 2024 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 GM 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: January 14, 2021
End date: December 13, 2023
a = 4.5281
b = -0.0007
s = 0.1150
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -21.70%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1150) – 1
= 58.42%
January 14, 2021 calculations
Top border of price channel:
Exp(Y434)
= Exp(a + b × X434 + 2 × s)
= Exp(a + b × 629 + 2 × s)
= Exp(4.5281 + -0.0007 × 629 + 2 × 0.1150)
= Exp(4.3367)
= $76.45
Bottom border of price channel:
Exp(Y434)
= Exp(a + b × X434 – 2 × s)
= Exp(a + b × 629 – 2 × s)
= Exp(4.5281 + -0.0007 × 629 – 2 × 0.1150)
= Exp(3.8766)
= $48.26
December 13, 2023 calculations
Top border of price channel:
Exp(Y1,167)
= Exp(a + b × X1,167 + 2 × s)
= Exp(a + b × 1,692 + 2 × s)
= Exp(4.5281 + -0.0007 × 1,692 + 2 × 0.1150)
= Exp(3.6244)
= $37.50
Bottom border of price channel:
Exp(Y1,167)
= Exp(a + b × X1,167 – 2 × s)
= Exp(a + b × 1,692 – 2 × s)
= Exp(4.5281 + -0.0007 × 1,692 – 2 × 0.1150)
= Exp(3.1643)
= $23.67
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 21.70% per annum.
- GM price at the close of April 25, 2024 was $45.62 and was higher than the top border of the primary price channel by $11.34 (33.07%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: October 13, 2023
End date: April 25, 2024
a = -0.9137
b = 0.0026
s = 0.0484
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0026) – 1
= 158.23%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0484) – 1
= 21.34%
October 13, 2023 calculations
Top border of price channel:
Exp(Y1,125)
= Exp(a + b × X1,125 + 2 × s)
= Exp(a + b × 1,631 + 2 × s)
= Exp(-0.9137 + 0.0026 × 1,631 + 2 × 0.0484)
= Exp(3.4222)
= $30.64
Bottom border of price channel:
Exp(Y1,125)
= Exp(a + b × X1,125 – 2 × s)
= Exp(a + b × 1,631 – 2 × s)
= Exp(-0.9137 + 0.0026 × 1,631 – 2 × 0.0484)
= Exp(3.2287)
= $25.25
April 25, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(-0.9137 + 0.0026 × 1,826 + 2 × 0.0484)
= Exp(3.9290)
= $50.86
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-0.9137 + 0.0026 × 1,826 – 2 × 0.0484)
= Exp(3.7356)
= $41.91
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 158.23% per annum.
- GM price at the close of April 25, 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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