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 58.47% per annum.
- GM price at the close of January 17, 2025 was $50.97 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 44.19% per annum.
- GM price at the close of January 17, 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 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: August 15, 2023
End date: January 8, 2025
a = 1.7471
b = 0.0013
s = 0.0769
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 58.47%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0769) – 1
= 36.02%
August 15, 2023 calculations
Top border of price channel:
Exp(Y898)
= Exp(a + b × X898 + 2 × s)
= Exp(a + b × 1,302 + 2 × s)
= Exp(1.7471 + 0.0013 × 1,302 + 2 × 0.0769)
= Exp(3.5431)
= $34.57
Bottom border of price channel:
Exp(Y898)
= Exp(a + b × X898 – 2 × s)
= Exp(a + b × 1,302 – 2 × s)
= Exp(1.7471 + 0.0013 × 1,302 – 2 × 0.0769)
= Exp(3.2354)
= $25.42
January 8, 2025 calculations
Top border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 + 2 × s)
= Exp(a + b × 1,814 + 2 × s)
= Exp(1.7471 + 0.0013 × 1,814 + 2 × 0.0769)
= Exp(4.1889)
= $65.95
Bottom border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 – 2 × s)
= Exp(a + b × 1,814 – 2 × s)
= Exp(1.7471 + 0.0013 × 1,814 – 2 × 0.0769)
= Exp(3.8812)
= $48.48
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 58.47% per annum.
- GM price at the close of January 17, 2025 was $50.97 and was inside the primary price channel.
Secondary Trend
Start date: November 6, 2024
End date: January 17, 2025
a = 6.8366
b = -0.0016
s = 0.0277
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0016) – 1
= -44.19%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0277) – 1
= 11.71%
November 6, 2024 calculations
Top border of price channel:
Exp(Y1,208)
= Exp(a + b × X1,208 + 2 × s)
= Exp(a + b × 1,751 + 2 × s)
= Exp(6.8366 + -0.0016 × 1,751 + 2 × 0.0277)
= Exp(4.0941)
= $59.99
Bottom border of price channel:
Exp(Y1,208)
= Exp(a + b × X1,208 – 2 × s)
= Exp(a + b × 1,751 – 2 × s)
= Exp(6.8366 + -0.0016 × 1,751 – 2 × 0.0277)
= Exp(3.9834)
= $53.70
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(6.8366 + -0.0016 × 1,823 + 2 × 0.0277)
= Exp(3.9791)
= $53.47
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(6.8366 + -0.0016 × 1,823 – 2 × 0.0277)
= Exp(3.8683)
= $47.86
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 44.19% per annum.
- GM price at the close of January 17, 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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