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 61.21% per annum.
- GM price at the close of November 19, 2024 was $55.11 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 555.34% per annum.
- GM price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $0.25 (0.45%). This indicates a possible reversal in the secondary trend direction.
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 16, 2023
End date: November 19, 2024
a = 1.5986
b = 0.0013
s = 0.0783
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 61.21%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0783) – 1
= 36.76%
August 16, 2023 calculations
Top border of price channel:
Exp(Y939)
= Exp(a + b × X939 + 2 × s)
= Exp(a + b × 1,365 + 2 × s)
= Exp(1.5986 + 0.0013 × 1,365 + 2 × 0.0783)
= Exp(3.5409)
= $34.50
Bottom border of price channel:
Exp(Y939)
= Exp(a + b × X939 – 2 × s)
= Exp(a + b × 1,365 – 2 × s)
= Exp(1.5986 + 0.0013 × 1,365 – 2 × 0.0783)
= Exp(3.2279)
= $25.23
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(1.5986 + 0.0013 × 1,826 + 2 × 0.0783)
= Exp(4.1440)
= $63.06
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.5986 + 0.0013 × 1,826 – 2 × 0.0783)
= Exp(3.8310)
= $46.11
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 61.21% per annum.
- GM price at the close of November 19, 2024 was $55.11 and was inside the primary price channel.
Secondary Trend
Start date: September 30, 2024
End date: November 19, 2024
a = -5.3414
b = 0.0052
s = 0.0249
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0052) – 1
= 555.34%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0249) – 1
= 10.46%
September 30, 2024 calculations
Top border of price channel:
Exp(Y1,221)
= Exp(a + b × X1,221 + 2 × s)
= Exp(a + b × 1,776 + 2 × s)
= Exp(-5.3414 + 0.0052 × 1,776 + 2 × 0.0249)
= Exp(3.8559)
= $47.27
Bottom border of price channel:
Exp(Y1,221)
= Exp(a + b × X1,221 – 2 × s)
= Exp(a + b × 1,776 – 2 × s)
= Exp(-5.3414 + 0.0052 × 1,776 – 2 × 0.0249)
= Exp(3.7563)
= $42.79
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(-5.3414 + 0.0052 × 1,826 + 2 × 0.0249)
= Exp(4.1134)
= $61.15
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-5.3414 + 0.0052 × 1,826 – 2 × 0.0249)
= Exp(4.0139)
= $55.36
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 555.34% per annum.
- GM price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $0.25 (0.45%). 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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