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 144.61% per annum.
- GM price at the close of May 20, 2024 was $45.11 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 28.51% per annum.
- GM price at the close of May 20, 2024 was inside the secondary price channel.
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: October 13, 2023
End date: May 20, 2024
a = -0.6000
b = 0.0025
s = 0.0482
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0025) – 1
= 144.61%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0482) – 1
= 21.25%
October 13, 2023 calculations
Top border of price channel:
Exp(Y1,108)
= Exp(a + b × X1,108 + 2 × s)
= Exp(a + b × 1,606 + 2 × s)
= Exp(-0.6000 + 0.0025 × 1,606 + 2 × 0.0482)
= Exp(3.4321)
= $30.94
Bottom border of price channel:
Exp(Y1,108)
= Exp(a + b × X1,108 – 2 × s)
= Exp(a + b × 1,606 – 2 × s)
= Exp(-0.6000 + 0.0025 × 1,606 – 2 × 0.0482)
= Exp(3.2394)
= $25.52
May 20, 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(-0.6000 + 0.0025 × 1,826 + 2 × 0.0482)
= Exp(3.9712)
= $53.05
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-0.6000 + 0.0025 × 1,826 – 2 × 0.0482)
= Exp(3.7785)
= $43.75
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 144.61% per annum.
- GM price at the close of May 20, 2024 was $45.11 and was inside the primary price channel.
Secondary Trend
Start date: March 20, 2024
End date: May 20, 2024
a = 2.5596
b = 0.0007
s = 0.0212
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 28.51%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0212) – 1
= 8.84%
March 20, 2024 calculations
Top border of price channel:
Exp(Y1,216)
= Exp(a + b × X1,216 + 2 × s)
= Exp(a + b × 1,765 + 2 × s)
= Exp(2.5596 + 0.0007 × 1,765 + 2 × 0.0212)
= Exp(3.8150)
= $45.38
Bottom border of price channel:
Exp(Y1,216)
= Exp(a + b × X1,216 – 2 × s)
= Exp(a + b × 1,765 – 2 × s)
= Exp(2.5596 + 0.0007 × 1,765 – 2 × 0.0212)
= Exp(3.7303)
= $41.69
May 20, 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(2.5596 + 0.0007 × 1,826 + 2 × 0.0212)
= Exp(3.8569)
= $47.32
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.5596 + 0.0007 × 1,826 – 2 × 0.0212)
= Exp(3.7722)
= $43.48
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 28.51% per annum.
- GM price at the close of May 20, 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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