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 80.84% per annum.
- PM price at the close of November 19, 2024 was $129.54 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 44.79% per annum.
- PM price at the close of November 19, 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 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: February 8, 2024
End date: November 19, 2024
a = 1.9193
b = 0.0016
s = 0.0317
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0016) – 1
= 80.84%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0317) – 1
= 13.53%
February 8, 2024 calculations
Top border of price channel:
Exp(Y1,060)
= Exp(a + b × X1,060 + 2 × s)
= Exp(a + b × 1,541 + 2 × s)
= Exp(1.9193 + 0.0016 × 1,541 + 2 × 0.0317)
= Exp(4.4840)
= $88.58
Bottom border of price channel:
Exp(Y1,060)
= Exp(a + b × X1,060 – 2 × s)
= Exp(a + b × 1,541 – 2 × s)
= Exp(1.9193 + 0.0016 × 1,541 – 2 × 0.0317)
= Exp(4.3571)
= $78.03
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(1.9193 + 0.0016 × 1,826 + 2 × 0.0317)
= Exp(4.9465)
= $140.69
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.9193 + 0.0016 × 1,826 – 2 × 0.0317)
= Exp(4.8197)
= $123.92
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 80.84% per annum.
- PM price at the close of November 19, 2024 was $129.54 and was inside the primary price channel.
Secondary Trend
Start date: July 29, 2024
End date: November 19, 2024
a = 3.0084
b = 0.0010
s = 0.0282
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 44.79%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0282) – 1
= 11.95%
July 29, 2024 calculations
Top border of price channel:
Exp(Y1,177)
= Exp(a + b × X1,177 + 2 × s)
= Exp(a + b × 1,713 + 2 × s)
= Exp(3.0084 + 0.0010 × 1,713 + 2 × 0.0282)
= Exp(4.8019)
= $121.74
Bottom border of price channel:
Exp(Y1,177)
= Exp(a + b × X1,177 – 2 × s)
= Exp(a + b × 1,713 – 2 × s)
= Exp(3.0084 + 0.0010 × 1,713 – 2 × 0.0282)
= Exp(4.6891)
= $108.75
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(3.0084 + 0.0010 × 1,826 + 2 × 0.0282)
= Exp(4.9165)
= $136.52
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.0084 + 0.0010 × 1,826 – 2 × 0.0282)
= Exp(4.8037)
= $121.96
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 44.79% per annum.
- PM price at the close of November 19, 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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