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 23.63% per annum.
- HD price at the close of January 17, 2025 was $409.38 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 43.71% per annum.
- HD price at the close of January 17, 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 HD 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 21, 2023
End date: January 17, 2025
a = 4.9479
b = 0.0006
s = 0.0552
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0006) – 1
= 23.63%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0552) – 1
= 24.71%
February 21, 2023 calculations
Top border of price channel:
Exp(Y777)
= Exp(a + b × X777 + 2 × s)
= Exp(a + b × 1,127 + 2 × s)
= Exp(4.9479 + 0.0006 × 1,127 + 2 × 0.0552)
= Exp(5.7132)
= $302.84
Bottom border of price channel:
Exp(Y777)
= Exp(a + b × X777 – 2 × s)
= Exp(a + b × 1,127 – 2 × s)
= Exp(4.9479 + 0.0006 × 1,127 – 2 × 0.0552)
= Exp(5.4924)
= $242.84
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(4.9479 + 0.0006 × 1,823 + 2 × 0.0552)
= Exp(6.1177)
= $453.81
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.9479 + 0.0006 × 1,823 – 2 × 0.0552)
= Exp(5.8969)
= $363.90
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 23.63% per annum.
- HD price at the close of January 17, 2025 was $409.38 and was inside the primary price channel.
Secondary Trend
Start date: April 15, 2024
End date: January 17, 2025
a = 4.2392
b = 0.0010
s = 0.0384
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 43.71%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0384) – 1
= 16.62%
April 15, 2024 calculations
Top border of price channel:
Exp(Y1,065)
= Exp(a + b × X1,065 + 2 × s)
= Exp(a + b × 1,546 + 2 × s)
= Exp(4.2392 + 0.0010 × 1,546 + 2 × 0.0384)
= Exp(5.8519)
= $347.89
Bottom border of price channel:
Exp(Y1,065)
= Exp(a + b × X1,065 – 2 × s)
= Exp(a + b × 1,546 – 2 × s)
= Exp(4.2392 + 0.0010 × 1,546 – 2 × 0.0384)
= Exp(5.6982)
= $298.32
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(4.2392 + 0.0010 × 1,823 + 2 × 0.0384)
= Exp(6.1271)
= $458.09
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.2392 + 0.0010 × 1,823 – 2 × 0.0384)
= Exp(5.9733)
= $392.81
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 43.71% per annum.
- HD price at the close of January 17, 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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