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 73.57% per annum.
- PM price at the close of February 20, 2025 was $151.57 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 1,250.03% per annum.
- PM price at the close of February 20, 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: December 10, 2024
a = 2.2411
b = 0.0015
s = 0.0347
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0015) – 1
= 73.57%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0347) – 1
= 14.88%
January 19, 2024 calculations
Top border of price channel:
Exp(Y984)
= Exp(a + b × X984 + 2 × s)
= Exp(a + b × 1,428 + 2 × s)
= Exp(2.2411 + 0.0015 × 1,428 + 2 × 0.0347)
= Exp(4.4678)
= $87.17
Bottom border of price channel:
Exp(Y984)
= Exp(a + b × X984 – 2 × s)
= Exp(a + b × 1,428 – 2 × s)
= Exp(2.2411 + 0.0015 × 1,428 – 2 × 0.0347)
= Exp(4.3291)
= $75.88
December 10, 2024 calculations
Top border of price channel:
Exp(Y1,209)
= Exp(a + b × X1,209 + 2 × s)
= Exp(a + b × 1,754 + 2 × s)
= Exp(2.2411 + 0.0015 × 1,754 + 2 × 0.0347)
= Exp(4.9603)
= $142.64
Bottom border of price channel:
Exp(Y1,209)
= Exp(a + b × X1,209 – 2 × s)
= Exp(a + b × 1,754 – 2 × s)
= Exp(2.2411 + 0.0015 × 1,754 – 2 × 0.0347)
= Exp(4.8217)
= $124.17
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 73.57% per annum.
- PM price at the close of February 20, 2025 was $151.57 and was inside the primary price channel.
Secondary Trend
Start date: January 10, 2025
End date: February 20, 2025
a = -7.9872
b = 0.0071
s = 0.0248
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0071) – 1
= 1,250.03%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0248) – 1
= 10.43%
January 10, 2025 calculations
Top border of price channel:
Exp(Y1,229)
= Exp(a + b × X1,229 + 2 × s)
= Exp(a + b × 1,785 + 2 × s)
= Exp(-7.9872 + 0.0071 × 1,785 + 2 × 0.0248)
= Exp(4.7907)
= $120.39
Bottom border of price channel:
Exp(Y1,229)
= Exp(a + b × X1,229 – 2 × s)
= Exp(a + b × 1,785 – 2 × s)
= Exp(-7.9872 + 0.0071 × 1,785 – 2 × 0.0248)
= Exp(4.6915)
= $109.02
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(-7.9872 + 0.0071 × 1,826 + 2 × 0.0248)
= Exp(5.0831)
= $161.27
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-7.9872 + 0.0071 × 1,826 – 2 × 0.0248)
= Exp(4.9839)
= $146.04
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 1,250.03% per annum.
- PM price at the close of February 20, 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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