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 67.54% per annum.
- PM price at the close of April 22, 2025 was $164.11 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 184.33% per annum.
- PM price at the close of April 22, 2025 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 PM 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 19, 2024
End date: April 22, 2025
a = 2.4672
b = 0.0014
s = 0.0484
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 67.54%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0484) – 1
= 21.34%
January 19, 2024 calculations
Top border of price channel:
Exp(Y941)
= Exp(a + b × X941 + 2 × s)
= Exp(a + b × 1,366 + 2 × s)
= Exp(2.4672 + 0.0014 × 1,366 + 2 × 0.0484)
= Exp(4.4953)
= $89.60
Bottom border of price channel:
Exp(Y941)
= Exp(a + b × X941 – 2 × s)
= Exp(a + b × 1,366 – 2 × s)
= Exp(2.4672 + 0.0014 × 1,366 – 2 × 0.0484)
= Exp(4.3019)
= $73.84
April 22, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(2.4672 + 0.0014 × 1,825 + 2 × 0.0484)
= Exp(5.1443)
= $171.45
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(2.4672 + 0.0014 × 1,825 – 2 × 0.0484)
= Exp(4.9508)
= $141.29
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 67.54% per annum.
- PM price at the close of April 22, 2025 was $164.11 and was inside the primary price channel.
Secondary Trend
Start date: December 18, 2024
End date: April 22, 2025
a = -0.1044
b = 0.0029
s = 0.0462
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0029) – 1
= 184.33%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0462) – 1
= 20.32%
December 18, 2024 calculations
Top border of price channel:
Exp(Y1,172)
= Exp(a + b × X1,172 + 2 × s)
= Exp(a + b × 1,700 + 2 × s)
= Exp(-0.1044 + 0.0029 × 1,700 + 2 × 0.0462)
= Exp(4.8551)
= $128.39
Bottom border of price channel:
Exp(Y1,172)
= Exp(a + b × X1,172 – 2 × s)
= Exp(a + b × 1,700 – 2 × s)
= Exp(-0.1044 + 0.0029 × 1,700 – 2 × 0.0462)
= Exp(4.6701)
= $106.71
April 22, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(-0.1044 + 0.0029 × 1,825 + 2 × 0.0462)
= Exp(5.2129)
= $183.63
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(-0.1044 + 0.0029 × 1,825 – 2 × 0.0462)
= Exp(5.0280)
= $152.63
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 184.33% per annum.
- PM price at the close of April 22, 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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