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 1.10% per annum.
- LIN price at the close of February 20, 2025 was $461.90 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 146.80% per annum.
- LIN 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 LIN 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 20, 2024
End date: February 20, 2025
a = 6.0553
b = 0.0000
s = 0.0376
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 1.10%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0376) – 1
= 16.24%
February 20, 2024 calculations
Top border of price channel:
Exp(Y1,005)
= Exp(a + b × X1,005 + 2 × s)
= Exp(a + b × 1,460 + 2 × s)
= Exp(6.0553 + 0.0000 × 1,460 + 2 × 0.0376)
= Exp(6.1744)
= $480.30
Bottom border of price channel:
Exp(Y1,005)
= Exp(a + b × X1,005 – 2 × s)
= Exp(a + b × 1,460 – 2 × s)
= Exp(6.0553 + 0.0000 × 1,460 – 2 × 0.0376)
= Exp(6.0240)
= $413.21
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(6.0553 + 0.0000 × 1,826 + 2 × 0.0376)
= Exp(6.1854)
= $485.62
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(6.0553 + 0.0000 × 1,826 – 2 × 0.0376)
= Exp(6.0350)
= $417.78
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 1.10% per annum.
- LIN price at the close of February 20, 2025 was $461.90 and was inside the primary price channel.
Secondary Trend
Start date: December 30, 2024
End date: February 20, 2025
a = 1.6303
b = 0.0025
s = 0.0107
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0025) – 1
= 146.80%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0107) – 1
= 4.36%
December 30, 2024 calculations
Top border of price channel:
Exp(Y1,222)
= Exp(a + b × X1,222 + 2 × s)
= Exp(a + b × 1,774 + 2 × s)
= Exp(1.6303 + 0.0025 × 1,774 + 2 × 0.0107)
= Exp(6.0425)
= $420.94
Bottom border of price channel:
Exp(Y1,222)
= Exp(a + b × X1,222 – 2 × s)
= Exp(a + b × 1,774 – 2 × s)
= Exp(1.6303 + 0.0025 × 1,774 – 2 × 0.0107)
= Exp(5.9998)
= $403.35
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(1.6303 + 0.0025 × 1,826 + 2 × 0.0107)
= Exp(6.1712)
= $478.76
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.6303 + 0.0025 × 1,826 – 2 × 0.0107)
= Exp(6.1285)
= $458.75
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 146.80% per annum.
- LIN 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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